www.elsevier.com/locate/procbio

Process Biochemistry 41 (2006) 2218–2235

A novel systems biology/engineering approach solves fundamental

molecular mechanistic problems in bioenergetics and motility

Sunil Nath *

Department of Biochemical Engineering and Biotechnology, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi 110016, India

Received 13 March 2006; received in revised form 30 June 2006; accepted 4 July 2006

Dedicated to Prof. Dr. Wolf-Dieter Deckwer on the occasion of his 65th birthday

Abstract

A large number of new insights and further intricate details of the molecular mechanisms of ATP synthesis and muscle contraction have been

offered from the perspective of the torsional mechanism of energy transduction and ATP synthesis and the rotation-uncoiling-tilt (RUT) energy

storage mechanism of muscle contraction. In this paper, a new systems thermodynamics analysis of oxidative- and photo-phosphorylation has been

performed. New experimental data has been reported on the inhibition of ATP synthesis by known specific anion channel blockers: the triorganotin

compound, tributyltin chloride (TBTCl), and the stilbene compound 4,40-diisothiocyanostilbene-2,20-disulfonate (DIDS), and interpreted as

supporting the new framework. A bioinformatic analysis of the interacting a–c regions in FO has been carried out to locate the anion binding pocket

in the anion–proton symsequenceporter and insights into the coordination chemistry of the bound chloride in its internal cavity at the lipid–water

interface have been obtained. The need to look at ATP synthesis in FO as a multisubstrate reaction has been emphasized and a detailed microscopic

explanation of the mechanism of inhibition by these blockers and its relationship to the conformational cycle within FO has been postulated. Such

detailed explanations of the role of membrane elements in a lipophilic region have been shown to lead to deeper understanding and to offer a more

realistic and complete picture of biological energy transduction than considering the bilayer as ‘‘mere insulation’’, as in chemiosmotic dogma.

Details of the elementary force production events by myosin II have been provided within the novel molecular systems framework of the RUT

mechanism in which the S-1, the S-1–S-2 hinge, and the S-2 coiled coil all have essential roles in the in vivo contractile process. The new paradigm

is shown to be consistent with the great body of experiments usually considered to support the swinging crossbridge/lever arm models of muscle

contraction, because these events also occur during the cycle but as events preliminary to the occurrence of the power stroke. The crucial role of

energy storage in mechanically strained nonequilibrium conformational states of myosin, specifically as a high-energy state of S-2 with uncoiled

first few N-terminal heptads is highlighted. The propensity of these heptads to recoil and regain the resting state of the coiled coil is postulated to be

a primary driving force of the power stroke. The new paradigms of ATP synthesis/muscle contraction have been shown to remove the

inconsistencies present in previous theories and to have the sound backing of the first and second laws of thermodynamics, the principle of

electrical neutrality, the laws of Newtonian mechanics, and the great conservation laws of mechanics. A systems integration of muscle contraction

has been successfully made and a systems electrical analog constructed. The unifying laws and principles in the new theories have been further

applied to understand the functioning of other protein molecular machines such as kinesin, ncd and unconventional myosins. Finally, the major

physical, chemical, biological and technological implications arising as a result of this research have been discussed. Taken together, the new

paradigms have been shown to solve fundamental molecular mechanistic problems in bioenergetics and motility and to offer a most detailed,

unified and appealing picture of energy generation, transduction, storage and utilization processes in systems of biological molecular machines.

# 2006 Elsevier Ltd. All rights reserved.

Keywords: ATP synthase; ATP synthesis; Muscle contraction; Myosin; Molecular mechanism; Torsional mechanism; Rotation-uncoiling-tilt energy storage

mechanism; Chemiosmotic theory; Binding change mechanism; Energy transduction; Nanotechnology; Systems biology; First law of thermodynamics; Second law

of thermodynamics

* Tel.: +91 11 26857457; fax: +91 11 26582282.

E-mail address: sunath@dbeb.iitd.ernet.in.

1359-5113/$ – see front matter # 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.procbio.2006.07.003

1. Introduction

The molecular mechanism of the synthesis of the universal

biological energy carrier adenosine-50-triphosphate (ATP) and

the detailed molecular mechanism of muscle contraction using

the energy of ATP hydrolysis has literally inspired an immense

S. Nath / Process Biochemistr

amount of research. Yet the detailed molecular mechanism of

these most fundamental processes in biology has proved very

difficult to solve. Here, based on a novel molecular systems

biology/engineering approach, the elusive details of the

mechanism of these processes have been offered from the

perspective of the torsional mechanism of energy transduction

and ATP synthesis and the rotation-uncoiling-tilt energy

storage mechanism of muscle contraction [1–17]. It is not

the aim here to provide an exhaustive list of references, an

impossible task on which brave attempts have been made

earlier [1–3]. However, key experimental results that are

absolutely crucial for elucidation of the detailed mechanism, in

this researcher’s opinion, but have not received the attention

they warrant, have been emphasized. New experimental data

from our laboratory that further supports the new paradigm of

ATP synthesis has been presented, and the major scientific

implications arising have been discussed.

2. Materials and methods

Spinach chloroplast thylakoid membranes were isolated and acid-base

phosphorylation carried out as described earlier in detail [1]. Briefly, the

isolated membranes were adjusted to a chlorophyll concentration of 0.5 mg/

ml. 0.5 ml of the membranes were injected into the acid stage buffer containing

0.5 mM HCl/1.0 mM succinate, pH 4.0 for 15 s. The mixture was then injected

into base stage buffer containing anion channel inhibitor DIDS (4,40-diisothio-

cyanostilbene-2,20-disulfonate) or TBTCl (tributyltin chloride) at the final

concentrations (10 or 100 nM). The phosphorylation was studied for 15, 30,

45, 60, and 75 s. For the control, tricine-NaOH buffer pH 7.4 was added to the

thylakoid membranes in place of inhibitor and phosphorylation was performed

as above. Rates of ATP synthesis were calculated and plotted against time.

3. Relationship between linear nonequilibrium

thermodynamic analysis of ATP synthesis at

macroscopic systems and single molecule levels

A linear nonequilibrium thermodynamic analysis of

oxidative and photophosphorylation has already been carried

out in detail [2,12,16,17]. Such an analysis at a macroscopic

systems level has been shown to be in harmony with the

molecular mechanism of ATP synthesis [3,5]. It would be

interesting to know why such a good correspondence between

the single molecule level, single organelle systems level (e.g. a

single mitochondrion or chloroplast thylakoid) and even the

macroscopic systems level (e.g. an ensemble of organelles/

tissue) is obtained. The derived equations for the coupled

processes of oxidative or photophosphorylation at steady state

with the original notation, and with LOP = 0, LOH = �nOLOO,

LPH = nPLPP, and LHH ¼ CH þ n2OLOO þ n2

PLPP read as [12]:

JO ¼�

LOO �n2

OL2OO

LHH

�AO þ

�nOnPLOOLPP

LHH

�AP (1)

JP ¼�

nOnPLOOLPP

LHH

�AO þ

�LPP �

n2PL2

PP

LHH

�AP (2)

or

JO ¼ L11AO þ L01AP (3)

JP ¼ L01AO þ L00AP (4)

Eqs. (1)–(4) are valid for each individual molecule pair (e.g.

redox/photosystem + ATPase). If n is the total number of

working enzyme molecules:

JwholeO ¼ nJO (5)

JwholeP ¼ nJP (6)

Substituting for JO and JP, we have for the whole organelle/

macroscopic system with n number of working redox/photo-

system + ATPase molecules:

JwholeO ¼ n½L11AO þ L01AP� ¼ Lwhole

11 AO þ Lwhole01 AP (7)

JwholeP ¼ n½L01AO þ L00AP� ¼ Lwhole

01 AO þ Lwhole00 AP (8)

because the local AO, AP = global or bulk AO, AP, respective-

ly.Therefore

Lwhole11 ¼ nL11; Lwhole

00 ¼ nL00; Lwhole01 ¼ nL01 (9)

and

Lwhole11

Lwhole00

¼ L11

L00

; etc: (10)

With X = AP/AO:

JP

JO

¼ Zqþ ZX

1þ qZX(11)

h ¼ � JP

JO

X (12)

It is readily seen that Zwhole = Z, qwhole = q, JwholeP =Jwhole

O ¼JP=JO and hwhole = h. Hence the results expressed as ratios (JP/

JO and h) are valid at both individual molecular coupling level

as well as whole organelle or macromolecular systems level

with a large number of working molecules and therefore the

correspondence between different levels holds [2,3,12]. In ATP

synthase, each FOF1 machine produces its own output (ATP)

independently of the other FOF1 molecules. Forces and torques

produced by a single FOF1 molecule are not summed up with

that produced by other FOF1 molecules. Only the ATP pro-

duced adds to the common pool. In summary, the final output is

the chemical species ATP, which is summed up. Thus, a

macroscopic consequence and novel prediction of Nath’s tor-

sional mechanism of energy transduction and ATP synthesis is

that torque produced by single ATP synthase molecules

(�40 pN nm) is independent of ATP concentration (in hydro-

lysis mode) and ADP or H+/A� concentrations or delocalized

Dc (in synthesis mode) over the entire range of concentrations

(pM–mM), even though rates of ATP synthesis/hydrolysis are a

function of these parameters of state [15]. It would be inter-

esting to find out how these relationships scale for energy

utilization by muscle, where the output is not a chemical

species but is a mechanical entity (force). We now turn to

certain molecular aspects of ATP synthesis.

y 41 (2006) 2218–2235 2219

S. Nath / Process Biochemistry 41 (2006) 2218–22352220

4. New experimental results and their interpretation by

Nath’s torsional mechanism

Recently, we have shown that several lines of biochemical

evidence from our laboratory negate the old theories and offer

further support to Nath’s torsional mechanism [1]. These include:

(i) the acid concentration dependence of the rate of ATP

synthesis, (ii) the isolation and characterization of several

uncoupler-resistant mutants of oxidative phosphorylation, (iii)

the increase in oxidative phosphorylation uncoupling efficacies

with increase in lipid solubility of the uncoupler, other things

remaining the same. Here we report new experimental data on the

inhibition of ATP synthesis by known specific anion channel

blockers: the triorganotin compound, tributyltin chloride

(TBTCl) and the stilbene compound 4,40-diisothiocyanostil-

bene-2,20-disulfonate (DIDS). Fig. 1 compares the kinetics for

incubation of spinach thylakoids in the acid stage (pH 4.0) for

15 s at an initial HCl concentration of 0.5 mM and the base stage

rates of ATP synthesis (pH 8.3) as a function of time in the

absence of TBTCl, and in the presence of 10 and 100 nM TBTCl.

A two- to four-fold inhibition of the rate of ATP synthesis was

found at the 10 nM concentration (Fig. 1). Similar trends were

found at lower TBTCl concentrations and further, similar results

were obtained with DIDS in the inhibitory range of 1–10 nM

DIDS concentrations with HCl as the acid (Agarwal and Nath, in

preparation). It is impossible to explain why specific anion

channel blockers inhibit the rate of ATP synthesis using theories

such as chemiosmosis [18] that energetically link ATP synthesis

to the translocation of a single substrate only, i.e. protons.

However, if �half the energy to synthesize ATP comes from

anion translocation (chloride being the physiological ion under

our experimental conditions in this plant system), and the other

�half is donated by proton movement through specific half-

access channels in the FO portion of ATP synthase, and both Cl�

and H+ move in a strongly coupled way (with 1:1 stoichiometry

being the most interesting case) through access pathways that

form a rigid intramembrane link, a structural union, as it were, in

the membrane for the addition and collaborative utilization of

energy and for regulation of transport and metabolism, as

predicted by the torsional mechanism [1–3,14], then such an

inhibition in the concentration range of inhibitor that does not

Fig. 1. Rates of ATP synthesis as a function of base stage (pH 8.3) phosphoryla-

tion time in spinach thylakoids incubated in 0.5 mM HCl (pH 4.0) in the acid stage

for 15 s in the absence (~) and presence of 10 nM (�) and 100 nM TBTCl (&).

saturate the membrane binding sites is in fact the expected

outcome. Thus, ATP synthesis becomes a multisubstrate reaction

involving anions and protons, and the FO portion of ATP

synthase is then a Cl�–H+ symsequencecotransporter. In fact, the

major difference then, as per the torsional mechanism of ATP

synthesis, between the molecular mechanisms in mitochondria,

chloroplasts, and bacteria is the nature of the anion (chloride,

organic anion) and cation (proton, sodium ion) to which the

energy-transducing membrane is permeable. At higher concen-

trations of TBTCl, a rate enhancement (up to eight-fold) was

consistently found (Fig. 1). Similar results were obtained with the

DIDS-HCl system in the higher 100 nM to 2 mM concentration

range, except that the rate enhancement was much lower than that

found with TBTCl, and measured less than two-fold. This is not

to suggest that the mechanisms by which DIDS and TBTCl

inhibit/enhance ATP synthesis is the same. In fact, since TBTCl

is a potent chloride channel blocker but also an anionophore, and

at higher concentrations (>10 nM) is known to mediate a Cl�–

OH� exchange [though of course it can readily inhibit the

synthase (phenomenologically similar to DIDS though mechan-

istically different from it) at doses lower than those required to

catalyze rapid rates of Cl�–OH� exchange], it may be more

insightful to focus on the class of reversible inhibitors such as

DIDS. Fig. 2 shows the rates of phosphorylation as a function of

base stage times with 1 mM succinate and 10 and 100 nM DIDS,

other conditions being the same as in Fig. 1. If the inhibitor had

blocked the chloride channel, and anion was required merely to

maintain electroneutrality, then the presence of 1 mM succinate

should have rescued the phosphorylation rates to close to control

values by permeation through alternative sites other than the

anion access channels in the FO portion of the ATP synthase. This

was not observed; rather, inhibition was obtained at both

concentrations (Fig. 2). Thus, though both chloride and

dicarboxylic acid monoanions such as succinate support ATP

synthesis in our experimental system [1], chloride gave the

maximum rates among all anions tested, and further, as Fig. 2

shows, succinate does not have the required affinity for the

binding sites to cause a rate enhancement in the presence of

DIDS, at least under the conditions studied, again pointing to the

small lipophilic Cl� as the physiological anion in this system, and

indicating an energy provision role of the anion in ATP synthesis

Fig. 2. Rates of ATP synthesis as a function of base stage (pH 8.3) phosphor-

ylation time in spinach thylakoids incubated in 1.0 mM succinate (pH 4.0) in the

acid stage for 15 s in the absence (&) and presence of 10 nM (~) and 100 nM

DIDS (�).

S. Nath / Process Biochemistry 41 (2006) 2218–2235 2221

by translocation through the membrane-bound FO portion and

binding to the protein-in-the-membrane (i.e. trapping of chloride

in its binding pocket in a lipophilic region of the membrane), and

not just a passive role to maintain electrical neutrality of bulk

aqueous phases. The properties of these lipophilic regions have

been considered and detailed molecular mechanisms developed

within FO [1–4,7,11]; such detailed explanations of the role of

membrane elements lead to deeper understanding and offer a

more realistic and complete picture of biological energy

transduction than considering the bilayer as ‘‘mere insulation’’,

as in Mitchell’s chemiosmotic theory [18].

Given the above results, any theory of ATP synthesis must be

able to explain both the inhibition of ATP synthesis at low

reversible anion inhibitor (DIDS) concentrations as well as the

enhancement in synthesis rates at higher inhibitor concentra-

tions based on a general enzymological inhibition scheme at the

macroscopic level, as well as at the microscopic level by the

DpH–Dc two mutually non-colinear half-access channel model

[3,4,7,11] within the torsional mechanism. Since DIDS has no

way of entering the membrane and affecting the inlet half-

access anion channel (linked to the inlet half-access proton

channel), it can only act on the exit half-access anion channel

(which is coupled to the exit half-access proton channel). In any

case, this is also true under the experimental conditions because

the inhibitor was added at the base stage, i.e. at the time of

phosphorylation, and the enzyme already had bound Cl� and

H+ during the acid stage. All our experimental results on ATP

synthesis can be explained by considering the inhibition to be of

mixed type, composed of competitive and uncompetitive

inhibitions, for example by the scheme E + S$ ES! P;

ES + I$ ESI with inhibition constant K 0I; E + I$ EI with

inhibition constant KI. Such a scheme is commonly encoun-

tered in multisubstrate enzyme reactions where the inhibitor is

competitive with respect to one substrate and uncompetitive

with respect to another. Inhibitor can bind to either E or ES

depending on the values of KI or K 0I. When [I]� KI, EI is

formed. Formation of ESI complex leads to decreased rates.

Since the inhibitor used is an anion channel blocker, the

inhibition can be considered uncompetitive with respect to H+

and competitive with respect to Cl�. Thus in the scheme given

above, S = H+. Let the characteristic time for unbinding of

chloride from its site be t1, the time for conformational change

and subsequent unbinding of proton from its site be t2, and the

time taken for binding of inhibitor (DIDS) to its site (which can

be different from the chloride binding site) be t3. At low

(<10 nM) inhibitor concentration, the order of the events in the

exit half-access channel is Cl� unbinding, followed by binding

of inhibitor to its site which prevents H+ unbinding. This could

happen for many reasons; for example, the chloride exit half-

access channel does not close due to the presence of bound

inhibitor in the channel, and unless the anion exit half-access

channel closes, the proton exit access half-channel does not

open and the proton does not unbind. In any case, this has to be

so from the uncompetitive nature of the inhibition with respect

to the H+: the proton cannot leave as long as the inhibitor stays

bound. Hence we obtain inhibition. In other words, for

inhibition, at the microscopic level, t3 < t2 (after Cl�

unbinding). In macroscopic terms, ESI complex is formed

and leads to decreased rates of ATP synthesis. On the other

hand, at high inhibitor concentrations (�10 nM), [I] exceeds KI

and EI is formed, i.e. the proton unbinds from its site before the

inhibitor binds to its respective site. Or, in terms of

characteristic times in the microscopic framework, t2 < t3.

Also the value of t1 itself may be smaller than the corresponding

unbinding time of chloride at low inhibitor concentrations, i.e.

the affinity of the site for chloride is lowered by the interaction

of inhibitor and Cl� unbinding is faster at high [I]. In addition to

this greater driving force for unbinding of chloride at high

inhibitor concentrations, the affinity of inhibitor for its own site

is also reduced and tight binding of DIDS is hindered due to the

changes in the microenvironment of the site at these sought-for

(and optimized) experimental conditions (leading for instance

to lowered pKa that favor unbinding of the inhibitor from the

exit aqueous pathway). In any case, H+ unbinds first, and the c-

rotor rotates by �158, and now the Cl� at the inlet access half-

channel binds rapidly to its site due to its presence at high

concentration and its high affinity for its binding site in the

microenvironment of the inlet half-access channel, following

which the H+ binds to its own site, another rotation of �158occurs and the cycle continues [1,3–5,7]. Thus, more number of

cycles occur per unit time, and a rate enhancement is obtained

under these conditions, as observed experimentally.

The use of ‘‘low’’ and ‘‘high’’ for [I] above can be

quantified. In our spinach thylakoid samples, we have 1.3 nmol

ATP synthase per milligram chlorophyll. In 0.5 ml of 0.5 mg/

ml chlorophyll concentration in the acid stage, we therefore

have, for a 0.25 mg chlorophyll basis, 1.3 � 10�9 � 6 �1023 � 0.25 or �1014 ATP synthase enzyme molecules. At

10 nM inhibitor concentration in 2 ml of base stage we have

10 � 10�9 � 2 � 10�3 � 6 � 1023 or �1013 inhibitor mole-

cules. Since [I] < [E] at this concentration and below, we

expect inhibition below 10 nM and hence 10 nM can be

considered a ‘‘low’’ concentration in this context. Thus, the

calculated value of the inhibitory dose agrees with what is

obtained experimentally (Figs. 1 and 2), and serves as a

valuable aid in the design of the ATP rate inhibition/

enhancement experiments.

5. Bioinformatic analysis to identify the anion access

channel in the FO portion of ATP synthase

Since the inception of the torsional mechanism, it was

considered that the a-Arg-210–c-Asp-61 interacting regions

form the proton access channels [7,9–11]; it is now seen that the

helix 4-a–helix 2-c interacting faces at the a–c interface of the

membrane-bound FO portion also constitute the anion access

channels. Since the A� and H+ channels should be in close

proximity to enable the direct and local energy transduction

envisaged by the torsional mechanism [1–3,14], this is logical.

Also, since the triorganotin compounds preferentially target

and block the a-subunit, and since these tin compounds are

potent inhibitors of anion channels, it logically follows that the

a-subunit entry and exit aqueous half-channels known to be

present by research work of great significance by Fillingame

S. Nath / Process Biochemistry 41 (2006) 2218–22352222

and co-worker [19] are meant for anions with the binding site/

pocket located at the a–c interface. We have already made the

novel prediction [1,14] that the conserved Arg-210 (Escher-

ichia coli numbering) residue in the polar helical segment of

helix 4 of the a-subunit at the a–c interface of the ATP synthase

forms part of the anion binding (transport) site/pocket in the

immediate vicinity of the cAsp-61 proton binding site, and that

the subunit-a access channel is an anion (e.g. Cl�) channel and

not a proton channel, as currently believed. It is possible that the

subunit-a anion access channel at the a–c interface belongs to

the family of cystic fibrosis conductance regulator (CFTR)

family of anion channels, since these channels are known to be

permeable to both Cl� and large organic anions [20], and these

properties are found in our experiments (Figs. 1 and 2). For the

occurrence of anion binding in such a scenario, it can be

predicted that a cationic group (e.g. Arg/dipole) will attract

anions into water structured around hydrophobic groups (e.g.

Leu). That is, the amide nitrogen of the peptide backbone can

form a lyotropic anion attracting group only if it lies in close

proximity to one or more hydrophobic amino acid side chains.

A bioinformatic approach to test the above prediction is

shown in Fig. 3; the sequences of the interacting a–c helical

segments were aligned with the interacting helical faces (helix

C–helix G) of the known chloride channel/pump halorhodopsin

(pHR and sHR). The key roles of the conserved Arg and the

hydrophobic Leu around this arginine residue, and the essential

nature of the Ser and Thr residues for chloride binding is clearly

revealed (Fig. 3) from the sequence alignment. The single residue

differences with the proton pump bacteriorhodopsin are also

highlighted [D versus T/R and the lack of the equivalent of a-Leu-

207 in BR (Fig. 3)]. Moreover, inspection of the sequences of the

two interacting helical arms as a whole reveals that BR contains

the negatively charged D residues in each arm (proton binding);

in HR, instead of the negatively charged D, one of the arms

contain polar T residues (anion binding), while in the

amphiphatic helical arms of a–c, the T is replaced by the

positively charged R in one arm which is ‘‘balanced’’ by the

negatively charged D in the interacting helical arm (binding

anion and proton) (Fig. 3). This progressive increase in

amphoteric character from BR to HR to the interacting groups

in the a–c subunits of FO clearly show that these FO sequences

are tailored to bind both A� and H+ at some stage of the

conformational cycle in FO. The conserved a-Arg-210 can

electrostatically (directly through its guanidinium group), but

more likely indirectly through coordination via a water cluster

interact with the bound chloride. These interactions will stabilize

the Cl� in its internal cavity/binding pocket and keep the ion

Fig. 3. Segments of interacting helix C-helix G (BR, sHR, pHR) or a-helix 4–c-

helix 2 (FO portion of Escherichia coli ATP synthase) from aligned protein

sequences for bacteriorhodopsin from Halobacterium salinarum (BR) and

halorhodopsin from H. salinarum (sHR) and halorhodopsin from Natronobac-

terium pharaonis (pHR).

solvated and also maintain the structure of the bound water. The

specificity of the anion access channel is then determined by the

steric and electrostatic properties of the Arg-210 transport site;

the inlet and outlet access pathways (the anion conducting

pathways) are relatively non-specific. The walls of these

pathways are lined with hydrophobic residues like Leu, Ile,

Val and the movement of anion through these access pathways is

akin to diffusion and is relatively non-specific. These could

reflect general properties of anion channels. Thus a-Leu-207, a-

Arg-210 and c-Asp-61 must pack together at some stage of the

conformational cycle in FO during function: this will bring the

Cl� and the H+ very close to each other. Yet they do not combine

to form a covalent bond to make HCl in the lipophilic region of

the biological membrane in mitochondria/chloroplast/bacteria,

though this bonding of the ions may occur in artificial

membranes. This combination of proton and anion also occurs

in biological membranes between an uncoupler anion U� and H+,

due to the lipid solubility of the uncoupler, as described in a new

rationale of uncoupling action [1]. This emphasizes the critical

need for the specificity of the lipophilic anion (e.g. Cl�) and the

cation (e.g. H+) for coupled symsequenceport [1–3] translocation

as separate charges without recombination in the membrane, and

for energy addition, joint energy utilization and ATP synthesis.

Thus, both the universally conserved residues of ATP synthesis –

c-Glu/Asp-61 and a-Arg-210 – possess a unique functional role,

the former as the binding site of the proton, and the latter as

constituting the binding pocket of the anion.

A role for helix 5 on a-subunit is also indicated in the ATP

synthesis process in FO. Thus, a-Arg-210 on helix 4 and a-Gln-

252 on helix 5 (not shown in Fig. 3) are packed in close

proximity because the two positions can be switched around as

in the Q-210–R-252 mutant with partial retention of function

revealed by the thoughtful experiments of Cox, Hatch and

coworkers [21]. The guanidinium group of Arg-210 can form a

hydrogen bond with the side chain of Gln-252 and further

stabilize the anion. Thus ion-ion (e.g. Arg-210–Asp-61), ion

dipole (e.g. Arg-210–Gln-252), the apolar hydrogens around

the anion (e.g. aliphatic hydrogens of Leu-207) all greatly

stabilize it in its internal cavity along with the stabilization

achieved by coordination of Arg-210 indirectly through an

intervening water cluster.

While the role of specific amino acids (Fig. 3) is of interest in

understanding anion transport through the anion access half-

channels of the A�–H+ symsequenceporter in the FO portion of

ATP synthase, the structure, specific three-dimensional

arrangement and coordination chemistry aspects are key to

anion binding. In this new view, a pentacoordinated trigonal

bipyramid structure for the chloride is predicted with

stabilization from ion–ion, ion–dipole contributions (through

direct interaction of the anion with the guanidinium group of

Arg-210 and indirectly through bound water molecules at the a–

c interface that will ensure that the anion remains solvated in

this internal site at the lipid–water a–c interface and help

maintain the correct structure of bound water, along with the

aliphatic hydrogens of the conserved non-polar Leu-207 in the

otherwise polar arm of helix 4 of a-subunit) in the very

immediate vicinity of the proton access half-channel binding

S. Nath / Process Biochemistry 41 (2006) 2218–2235 2223

site Glu/Asp-61 on helix 2 of the c-subunit of FO. The

inhibiting/ionophoric triorganotin compounds must target a-

subunit such that the structure of the polyhedron around tin

mimics the pentacoordinated trigonal bipyramid structure in

three dimensions found in the physiological case with anion

(e.g. chloride) coordination to its ligands—the amino acids Ser,

Thr and Lys, and indirectly through water the amino acids Arg,

Gln, Asp or the other Ser residues (Fig. 3). Such a novel

structural pattern as the eventual outcome is clearly visualiz-

able in three dimensions in the biochemical setting depicted in

Fig. 3. While we can catch a glimpse of the structure and

dynamics of nature’s splendid symsequenceport machinery of

anion–proton coupled translocation in the membrane-bound

portion of ATP synthase, the exact details of structure and

course of anion through the membrane must await an X-ray

structure of the a–c interface in FO, a major challenge for

structural and membrane biologists.

6. Details of Nath’s rotation-uncoiling-tilt (RUT) energy

storage mechanism of muscle contraction

Five years ago, I proposed [6] and subsequently further

developed and analyzed [1,2] and defended [22–24] a novel

mechanism of muscle contraction in which energy transduction

occurs at the elementary step of hydrolytic cleavage of bound

MgATP. A detailed mechanical analysis of this process has been

made [2]; a general thermodynamic analysis for the performance

of useful external work by open, steady state, ATP-hydrolyzing

systems has also been carried out [1]. The only major uncertainty

that remained was with the unknown sense of the torque

produced upon cleavage of the Pb–Pg bond during ATP

hydrolysis, and previously it was assumed that the sense of

the torque was so as to cause a higher energy state of myosin

associated with supercoiling of the myosin S-2 coiled coil. This

intuitively worked with a purely mechanical picture of the

coupling. While such a process may actually occur in vitro in

various motility assay protocols, a careful scrutiny of the sub-

molecular aspects of the problem and amino acid sequences of

the myosin amino terminal region suggests that, in vivo, the free

energy of ATP hydrolysis is used to uncoil the first few amino

terminus heptads of myosin S-2 coiled coil. We are then forced to

consider the state of myosin with uncoiled N-terminal S-2

heptads as a state of higher free energy with respect to the resting

state of myosin. We then progress to an electromechanical model

of the coiled coil with its solvent/ionic environment outside (e.g.

coiled coil with charges/hydrophobic residues on it at specified

spatial locations in an electrolyte medium), the packing and

interaction of hydrophobic/ionic residues within the coiled coil,

and their hydration effects, and need to consider free energy

changes. The propensity of the S-2 coiled coil to recoil is the

thermodynamic driving force of the muscle power stroke. This

recoiling of the S-2 N-terminal heptads leads to untilting and

constrained rotation of the myosin heads bound to actin filaments

which causes the power stroke exactly as detailed before [1,2,6].

The magnitude of the force generated by the elementary power

stroke obtained from thermodynamic analysis [1] is in perfect

accord with both single molecule data [25] as well as estimations

of force generated by stage 2 insect flight muscle crossbridges

using 3D electron tomographic visualization [26]. The mechan-

ism also explains the valuable anti-S-2 antibody data of Sugi and

Harrington [27]. Above all, Nath’s rotation-uncoiling-tilt (RUT)

energy storage mechanism of muscle contraction elucidates why

myosin II possesses a double-headed [1,22–24] and double-

tailed [22–24] structure, which had puzzled scientists for several

decades [28]. The thermodynamic propensity of the myosin

hydrophobic residues to repel water and regain the more stable

resting state of S-2 coiled coil is then a primary driving force for

the coiling back of myosin S-2. If S-2 were not a coiled coil but a

single helix, then no shielding of the amino acid residues in the S-

2 rod from solvent/electrolyte would have been possible: hence

we need a double tailed (coiled coil) structure for myosin II. The

double-headed structure of myosin II enables the two myosin

heads to bind to actin subunits on two different actin filaments

and permits the two heads of myosin to execute their power

strokes simultaneously upon recoiling of the S-2 coiled coil that

is common to both heads of the myosin molecule and thereby

�double the efficiency of the muscle contraction process, as

discussed earlier [1]. This raison d’etre for two heads (though not

for the coiled coil) appears to have been first suggested in a

prescient and visionary paper by Offer (termed ‘‘two-filament

interaction’’ by him) [29]. Several further details can now be

incorporated into the RUT Energy Storage Mechanism of muscle

contraction for the first time. These details further reveal the

requirement of a double-headed structure for myosin II to

perform its mechanical functions.

As discussed above, a novel prediction of the RUT

mechanism of muscle contraction is that myosin head

experiences a counterclockwise torque/rotation about its axis

(looking from the side of the myosin S-1 heads) due to the ATP

hydrolysis elementary event in one of the myosin heads [1],

which causes uncoiling of the first few N-terminal heptads of

the myosin S-2 coiled coil. This uncoiling is associated

simultaneously with tilting of myosin heads about the S-1–S-2

hinge [1,2,6,22–24] such that the heads can reach out and bind

to their binding sites on the actin filaments. The reasons why

uncoiling is favored are:

1. T

he coiled coil structure near the S-1–S-2 junction is very

weak and the weakness decreases progressively as we move

away from S-1–S-2 junction towards the carboxy-terminus.

The structure of myosin suggests that this weakness is

deliberately introduced to lower the energy barrier between

coiled and uncoiled states to make the actomyosin cycle

feasible. In other words, unlike normal canonical coiled

coils, in myosin, the free energy difference between the

coiled and uncoiled states is close to the free energy released

by ATP hydrolysis. The weakness itself is due to:

(i) P

olar residues that are buried inside the core making the

core hydrophilic (and some hydrophobic residues on the

myosin coiled coil surface), hence making the coiled

structure less stable. For example, the first three nominal

‘d’ positions of the sequence are occupied by a proline and

two glutamine residues. Moreover, the two ‘d’-position

glutamine residues pack in the core in an asymmetric

S. Nath / Process Biochemistry 41 (2006) 2218–22352224

fashion, with only one of the side chains forming a knob-

into-hole contact with the opposite helix as clearly inferred

from the recent X-ray structure of scallop striated muscle

myosin rod fragment [30]; the other side chain is oriented

towards the solvent. The residues that are exposed because

of the lack of ‘g–e’ links include the three consecutive ‘d’-

position leucines as well as other apolar core side chains

[30].

(ii) L

ack of inter-helical bridges between the two coiled

helices of myosin making the coiled structure weak.

(iii) I

nstead of following the ‘‘knobs in the holes’’ model

followed throughout myosin chain, the first few N-terminal

heptads do not follow the model and hence the strength of

the coiled coil is further reduced.

2. I

f there were no uncoiling then it would not have been

possible for the myosin heads to increase the angle they

make with myosin S-2 axis. And without increasing this

angle, it is not possible for myosin heads to tilt enough to

bind with actin.

3. T

here is no tendency in the residues forming the S-1–S-2

hinge to form a coil so supercoiling is impossible.

4. I

f there were supercoiling, the heads would approach closer

to each other which is sterically not favorable.

5. S

Fig. 4. Representation of conformational changes in myosin upon ATP hydro-

lysis from the initial resting state (left) to the final high-energy state (right). The

first few N-terminal heptads of S-2 have uncoiled in the final state and there is

conformational strain at the S-1–S-2 hinge (right). The diagram is not to scale,

but angle g > a, angle b > a and angle g 6¼ angle b.

ince in spite of all the above factors, the uncoiled state

remains less stable than the coiled conformation, the myosin

coil starts coiling back progressively as it goes through

power stroke to rigor state and then to fully coiled structure.

This perfectly justifies the progressively decreasing strength

of the myosin coiled coil as we move towards the amino

terminus. The role of the C-terminal heptads of S-2 is to

provide rigidity to the coiled coil and thus allow the torque

upon ATP hydrolysis to cause uncoiling instead of rotation of

the entire molecule about its axis without any uncoiling.

In view of the above and earlier considerations [1,2,6], the

conformational changes in myosin head upon ATP hydrolysis

should enable the heads to rotate and tilt and allow the catalytic

domains of the heads to bind loosely (at first) to their respective

binding sites on the same or different actin filaments. If the two

heads of a myosin molecule were to bind to neighbouring

subunits on the same actin filaments, then the two myosin heads

would be bent in opposite directions (if the heads are required to

loosely bind to actin with the same conformation); such a strain

would necessarily decrease the binding strength. On this basis,

and for a number of other geometrical and steric reasons it was

suggested that the two heads bind to actin binding sites on

different actin filaments [1,29]. This was also in line with the way

the RUT mechanism was conceived originally [6] especially

keeping the novel torque element of RUT in mind and the need

for conservation of linear and angular momentum after release of

the stored energy upon coiling back of the S-2. However, it

should be noted that the mechanistic elements of RUT would

hold even if the myosin heads were to bind to the same actin

filament, as might happen for instance under invitro conditions in

the absence of the myosin–actin super-lattice structure and

supramolecular biology arrangement. Subsequently, upon Pi

release due to actomyosin interactions, the myosin head binding

to actin is known to become tight from its initial loose binding

[31]. It is also necessary that the high energy uncoiled state of

myosin be trapped in a long-living intermediate state (e.g.

M**.ADP.Pi) and the stored energy not be released until the

myosin heads have bound tightly and stereospecifically to actin.

In other words, we want to block the myosin coiled coil from

recoiling and coming back to its resting state, i.e. we wish to let it

remain in its high energy uncoiled state. To use this stored energy,

actin must first interact with the myosin head in the M**.ADP.Pi

state, and activate the next step in the series of steps in the

enzymatic pathway that will eventually unblock this high energy

‘‘latch’’ state of the crossbridge and allow it to proceed through

the lower free energy states. It is proposed here that this kinetic

block or latch is created during the ATP hydrolysis step by a kink

or bend/distortion at the S-1–S-2 hinge. This kink serves to

separate the S-2 coiled coil from the myosin S-1 such that they

act mechanically as two separate bodies and the stored energy

remains trapped in the S-2 and its milieu. We also propose for the

first time that only upon ADP release (which is subsequent to Pi

release) is this localized strain at the S-1–S-2 hinge removed to

enable the recoiling of the S-2 coiled coil, utilization of the stored

energy, and generation of the elementary power stroke.

The above analysis shows that distortion/kink or localized

conformational strain at the S-1–S-2 junction takes place during

the ATP hydrolysis elementary step due to the Pb–Pg bond

cleavage event in one of the myosin heads, i.e. it occurs due to

chemical reaction-linked conformational changes. Due to

hydrolysis-linked conformational changes, there exist rotation

of the myosin head about its axis, tilt of the head about the S-1–

S-2 hinge, and uncoiling of the first few N-terminal heptads of

the S-2 coiled coil, as per the tenets of the RUT mechanism

[1,2,6]. This is diagrammatically depicted in Fig. 4. The

rotation of the myosin head (in which the ATP hydrolysis

S. Nath / Process Biochemistry 41 (2006) 2218–2235 2225

elementary event occurs) about it axis can be communicated to

the second head of the myosin molecule (the head that was

enzymatically silent) so that the second head can also exhibit

the same rotational motion about its own axis. This is only

possible because the rotational motion of the head about its own

axis is small [2,6,31]; hence it is possible to communicate this

motion to the other head due to the common S-1–S-2 hinge and

the common S-2 coiled coil as can be readily visualized

physically upon analysis of the motion. The heads, which were

initially symmetric about the central axis of the double-headed

myosin molecule before the ATP hydrolysis reaction occurred,

become disposed dissymmetrically about the central axis/head–

rod junction (Fig. 4). Because of the absence of any mechanical

constraint from the common-hinged, coiled coil structure for

such a tilting of one head off the central axis, this tilt motion of

one myosin head will be independent of the other head and will

not be communicated to the second head. This dissymmetry is

analogous to producing a kink or bend/distortion in the myosin

neck which acts as a kinetic block or latch preventing the

uncoiled heptads of S-2 from recoiling, and hence making the

S-2 remain in a high-energy state (Fig. 4). It should be noted

that the occurrence of ATP hydrolysis in both the heads will

eliminate any possibility of dissymmetry of arrangement of

myosin heads; thus, this offers independent mechanical reasons

(separate from thermodynamic arguments in Ref. [1]) that the

two heads of myosin are functionally different [1]. This is also

in accordance with the pioneering biochemical work of

Tonomura and colleagues [32] indicating two different heads

on the myosin molecule which offered important clues to the

real molecular mechanism of muscle contraction.

The loose binding of myosin head to actin discussed above

opens a trapdoor to release Pi [33] through the 50 K cleft. Let Pi

be ejected out with velocity v (Fig. 5). If Pi were not prevented

from release during ATP hydrolysis on myosin, i.e., if it could

release without requiring loose actin binding, then the required

conformational changes described below that are necessary for

the proper functioning of the mechanism would not occur. The

50 K cleft/pocket through which Pi is ejected out is proximal to

the actomyosin interface. The conformational changes in the

myosin head should enable the catalytic domains of both heads

Fig. 5. Coordinate system for analysis of conformational changes in myosin

upon release of nucleotide from its site with velocity v at an angle u to the axial

direction (x-axis). The x-axis is along actin and the y-axis lies in a plane

perpendicular to the axial direction.

to bind tightly to their respective binding sites on actin. The

v sin u component (Fig. 5) will cause the myosin head from

which Pi was released to rotate about its own axis which helps

the catalytic domain of that head to bind to actin binding site

tightly. This motion can be communicated to the second silent

non-Pi burst head so that the second head can make a similar

rotational motion about its own axis and bind tightly to its actin-

binding site. Once again this is possible because the rotational

motion about the head’s own axis is small (only a few degrees),

and because of the presence of the common S-1–S-2 hinge and

S-2 coiled coil. Thus there also exists a small rotational motion

about the central axis (S-2 coiled coil). The v cos u (tilt)

component of the Pi release (Fig. 5) is perpendicular to the

plane of the head, hence it will cause a small rotation about the

contact between myosin and actin, as shown in Fig. 6. The axis

of this rotation is perpendicular to the central axis as well as the

head’s own axis (Fig. 6) about which the two rotations

discussed above took place. This tilt motion due to Pi release

may or may not be present—it depends on the angle of ejection

of plain inorganic phosphate, which is not available from any

experiments. We can say however that for 08 < u < 908, as u

increases, the tilt component will decrease in magnitude and it

will be in the same sense as the tilt caused by ATP hydrolysis

(define as positive tilt). For 908 < u < 1808, the tilt component

will increase in magnitude as u increases, but it will be in the

opposite sense to the tilt caused by ATP hydrolysis (define as

negative tilt). The tilt part of the motion due to Pi release can be

represented as follows for the myosin head (catalytic + regu-

latory domain)(Fig. 7). The angle between the catalytic and

regulatory domains remains the same before and after the tilt, as

diagrammed in Fig. 7. All the above rotations about their

Fig. 6. The point of rotation (P) for any v cos u (tilt) component of the motion

upon phosphate release. The axis of rotation is perpendicular to both the central

axis and the body axis and passes through P. Actin is represented by barred

vertical lines. In this and subsequent figures (i.e., Figs. 6–8), the Z-line is below

and the M-line is above.

S. Nath / Process Biochemistry 41 (2006) 2218–22352226

Fig. 7. Representation of the tilt part of the motion in myosin head due to Pi

release. The catalytic domain of myosin head is represented by a thicker line than

the regulatory domain. Bold line is before and dashed line after the conformational

change. The angle between catalytic and regulatory domains remains the same

before and after. a could be equal to b and g could be equal to d.

Fig. 8. Representation of the tilt motion of the distal portion of the crossbridge

(i.e. lever arm movement) in myosin head due to ADP release. The catalytic

domain orientation with respect to actin remains the same before and after. Bold

line represents the initial state of myosin and the dashed line represents the final

state of myosin after ADP release. The re-gaining of a symmetrical disposition

of myosin heads about the central axis is represented by the equality of the

angles D in the final state.

defined axes are the result of angular momentum conservation

upon Pi release. The physical analysis carried out here is very

general and is applicable whatever be the biochemical details of

the reactions because although there exist external forces

between actin–myosin at the actomyosin contacts, there exists

no external torque about those contacts after the ATP hydrolysis

elementary event is complete. It should also be noted that the

light chains can coordinate and stabilize the conformational

changes upon ATP hydrolysis and phosphate release discussed

here, and moreover, can help the two heads to communicate

with each other.

The tight binding of myosin heads to actin leads to release of

bound ADP from its active site through closure of the myosin

50 K cleft [6]. It is very important that ADP release not alter the

orientation of the tightly and stereoscopically bound myosin

catalytic domain on actin. To achieve this, ADP release occurs

from a different pocket/active site (‘‘front door’’) as opposed to

Pi release. This is located in the distal portion of the actin-bound

myosin head. Experiments show that upon ADP release, the

regulatory domain in smooth muscle myosin II swings �258 as

a rigid structural unit, resulting in a�3.5 nm movement about a

pivot in the vicinity of the junction of the catalytic and

regulatory domains inside the myosin motor domain [34]. The

tilt motion of the distal portion of the crossbridge (lever arm

movement) on ADP release is represented in Fig. 8. The

catalytic domain orientation with respect to actin stays the same

before and after in this representation (Fig. 8).

Thus, on ADP release, a symmetrical placement of the myosin

heads about the tail has been regained, as seen clearly from Fig. 8

(angles D are equal in the final state). Now the entire (S-1 + S-2)

behaves as a single elastic body because the kink/distortion at the

S-1–S-2 hinge has been removed. Hence recoiling of the

N-terminal heptads of S-2 takes place and the power stroke

occurs with its fulcrum at the S-1–S-2 hinge, exactly as described

in consummate detail in the RUT mechanism [1,2,6,22–24]. The

rotary motion in S-2 can be converted to the linear (translation)

motion of tightly bound myosin heads on actin due to the

presence of mechanical constraints on actin filaments which

enables only axial movement, as already explained in the

engineering analysis of this system [2].

For the case of ADP release, it is essential to have a negative

tilt (defined above) so as to restore the double-headed myosin

system to a symmetrical disposition about the head–rod

junction and thus unblock the kink/latch and allow the stored

energy to be utilized for performance of useful external work

because there is no other subsequent chemical step left that can

achieve this effect. The rotational component of ADP release

ðvADP sin uADPÞ is irrelevant to the process and may or may not

be present: moreover, experiments indicate that this is primarily

a tilt motion of the lever arm [34]. Special cases of the above

general analysis are possible. An interesting case is one where

Pi release only contributes to tight binding via a rotation of the

myosin head about its actomyosin contact and ADP release

only provides tilt of the head–rod junction in the negative sense

and removes the localized conformational strain (the marked

change in angle (tilt)) at the S-1–S-2 hinge.

The power strokes occur and the rigor state is formed with

the two heads bound to actin and with �one N-terminal S-2

heptad of the myosin molecule still in its uncoiled state, and the

binding of MgATP breaks the actomyosin complex of one of

the myosin heads with actin as described earlier [2,6]. MgATP

binding also reverses the lever arm movement in that myosin

head that had occurred upon MgADP/MgADP and Pi release.

However now, a difference in the two myosin heads arises

S. Nath / Process Biochemistry 41 (2006) 2218–2235 2227

Fig. 9. Representation of the swinging crossbridge model (left) as a transition

from the resting state to the high-energy stretched state in myosin along with

performance of useful external work (lifting of the load). The diagram on the

right shows the observed behavior in all natural systems [transition from a high-

energy state (compressed state in this diagram) to the resting state along with

performance of useful work].

because the burst head (head 1), when it disassociates from

actin due to MgATP binding, has a closed catalytic binding site

but an open 50 K cleft. This subsequently promotes the

hydrolysis of MgATP to MgADP + Pi in this myosin head

(head 1) when it is detached from actin. The remaining rotational

strain in the hinge region of the myosin molecule detaches the

second enzymatically silent non-burst head (head 2) from actin;

this silent head 2 has an open catalytic binding site but a closed

50 K cleft, unlike head 1. MgATP can bind to this non-burst head

2 when it is detached from actin, but due to the absence of actin,

the myosin catalytic site conformation upon MgATP binding is

not identical to that in the presence of interactions with actin. In

other words, we predict that MgATP is positioned differently in

the two myosin heads and the two heads are functionally

different. Thus the non-burst head (head 2) has an intrinsic

inhibition to cleavage of MgATP that can only be relieved in the

subsequent steps of the enzymatic cycle by its interaction with

actin. Thus, unless MgATP binds to the S-1 catalytic site while

the myosin head is bound to actin, it will not be in the correct

conformation to hydrolyze MgATP subsequently when myosin

head is free from actin. Thus, only one head can hydrolyze

MgATP at a time during the enzymatic cycle per two myosin

heads of a myosin molecule (i.e. per dimer).

The above novel analysis shows that only one of the myosin

heads (head 1) is able to cleave bound MgATP while it is free

from actin; the second head (head 2) cannot cleave bound

MgATP at its catalytic site when free of actin [i.e. head 2 is held

in the M.ATP (or similar) state]. The major difference between

the two myosin heads according to the RUT mechanism is in

the positioning of MgATP in the active site when actin is absent.

This intrinsic inhibition to cleavage of MgATP by head 2 can

only be overcome in steps subsequent to combination of actin

with myosin, i.e. it requires activation by actin. Other

microscopic details can also be predicted and incorporated

into the RUT’s framework. For instance, the bound heads of a

myosin molecule will be released from actin in two stages.

During the power stroke at the tightly bound actomyosin state,

the myosin heads will try to unrotate, but due to the constraint

of tight binding of myosin heads to actin complete unrotation

cannot occur, though there will be strain in the actomyosin

interactions due to this constrained unrotation [2,6]. After the

power strokes, and after MgATP binding to one of the myosin

heads’ (head 1) binding site has broken the strained actomyosin

interactions of that head with actin [2,6] and detached that head

from actin, the remaining unrotation of that myosin head (head

1) will take place as the last S-2 N-terminal heptad reforms its

initial coiled coil structure. This unrotation of head 1 is opposite

in sense to the rotation incurred during ATP hydrolysis and is in

the right sense to relieve the remaining rotational strain at the S-

1–S-2 hinge that had occurred during the hydrolysis and

subsequent processes. Thus the recoiling of S-2 to its initial

conformation and unrotation of head 1 causes the second

myosin head (head 2) to unrotate and break the strained

actomyosin interactions between the second silent non-burst

head (head 2) and actin and detaches that head from actin. In

summary, there exists a kind of cooperation between the

myosin heads through the medium of actin and the common

myosin S-1–S-2 hinge and S-2 coiled coil. Finally, both heads

of a myosin molecule have achieved their original orientation in

terms of rotation and also in terms of tilt (due to their untilting

during the power strokes [2,6]), and recoiling of the S-2 coiled

coil is also complete and a new enzymatic cycle can begin [2,6].

7. Generic differences with existing models of muscle

contraction

Detailed differences of the RUT Mechanism with other

current models of muscle contraction applicable at the

molecular level have been discussed earlier [2]. Here, more

generic and absolutely fundamental differences not treated

earlier are taken up. In the well-known swinging crossbridge

model of Huxley [28,35], increasing attraction between myosin

head and actin is the seat of the force generation by muscle.

Thus, the primary rotation of myosin head about its actomyosin

contact is the cause of the power stroke (lifting of the load) as

well as stretching of a spring/elastic element (Fig. 9). Both

these processes (stretching of the elastic element and lifting of

the load) require energy. However, in the RUT energy storage

mechanism, and in all mechanical systems that we see in nature,

it is the other way around, i.e., one of the processes releases

energy to do useful work: for example, a spring/elastic element

being restored to its resting state from a high-energy state (e.g.

compressed/stretched), thereby lifting the load (Fig. 9). This is

not to say that the swinging crossbridge is impossible: it is

possible if we supply enough energy, but the energy relations in

muscle are not as postulated in the swinging crossbridge model

(e.g. equilibrium between stepper at actomyosin and S-2

spring), and nature does not behave in the way the model

postulates. Further, in this and other such models, including the

lever arm model, distal interactions between myosin and actin

are the primary drive that passively alter the lever arm angle at a

distant S-1–S-2 hinge region of myosin. In the RUT

mechanism, there exists a bi-directional communication bet-

ween S-1 and S-2 along the helical structure of myosin, and

S. Nath / Process Biochemistry 41 (2006) 2218–22352228

angle changes about the S-1–S-2 hinge region of myosin

constitute a primary process induced by the MgATP hydrolysis

reaction and the reaction-linked conformational changes. These

movements of myosin head about the S-1–S-2 hinge due to

active MgATP bond cleavage reactions lead subsequently to

myosin head-actin interactions distal to the hinge and to loose

actomyosin binding, which is converted to strong actomyosin

binding and bond formation by conformational changes upon

chemical (e.g. inorganic phosphate) release events in the

myosin head. The power stroke takes place about the S-1–S-2

hinge in the RUT theory, unlike in all current conceptions of the

muscle contraction mechanism. Thus, primary and secondary

drives are interchanged in the new theory versus old

conceptions of the power stroke. Further, in the new paradigm,

energy changes associated with myosin–actin binding or

release, or nucleotide binding or release are not directly

coupled to the performance of useful external work. In fact,

nucleotide (e.g. MgADP) release processes only relieve the

distortion/block at the S-1–S-2 hinge and enable the power

stroke to take place, i.e. they trigger the power stroke, but are

not the true driving force of the elementary force production by

muscle. Rather, free energy released upon cleavage of the Pb–

Pg bond during the MgATP hydrolysis step in myosin S-1 is

directly transduced to conformational strain and stored as a

high energy uncoiled state in the S-2 coiled coil that is

subsequently released to execute the powerstroke and perform

useful mechanical work.

Thus, current conceptions of the molecular mechanism of

muscle contraction do not feel the need to include the aspect of

energy storage in myosin (while in the RUT Mechanism the

energy storage aspect is a central one) since in these models,

force generation and movement is directly coupled to the

release of bound ligands/nucleotides. It should also be noted

that this standpoint adopted ubiquitously by the motility field is

diametrically opposite and contradictory to the view widely

accepted within the bioenergetics community, where release of

bound nucleotides requires energy of the ion gradients/light/

redox energy, far from it being used to perform useful work, as

has been reviewed in detail [1–3]. However, neither community

has given the chemical step (synthesis/hydrolysis reaction) the

central importance that it deserves, dismissing it as energe-

tically inconsequential [35–37] (with the torsional mechanism

stating from its inception that all the elementary steps require

energy, including chemical synthesis [3,8–11]), but both

communities emphasize different physical steps (useful

external work performed by nucleotide (e.g. MgATP) binding

versus bound nucleotide (e.g. MgADP) release in bioenergetics

and motility respectively). It is only when ATP synthesis and

ATP utilization are studied together as exemplified by this

scientist-engineer’s research program of the past 15 years [1–

17] that unified and coherent theories of both processes, without

inconsistencies, emerge. Otherwise, how can we be absolutely

certain that we are not violating the universal laws of science?

Thus the torsional mechanism and the rotation-uncoiling-tilt

mechanisms have been conceived in a unified way and they are

not beset with the inconsistencies of all other previous theories,

and the several things that appear different, and the seemingly

disparate observations, are now seen and grasped as various

aspects of one underlying phenomenon.

Current conceptions of the force generation mechanism in

muscle do not attribute any role for the S-2 region unlike the

RUT Mechanism (however, see Ref. [27]). This is due in large

part to the success of in vitro motility assays. However, if the

energy is stored physically, as we propose, and not chemically,

then the linkers that couple the myosin S-1 to the substrate (e.g.

a-actinin and streptavidin) could store energy physically, for

example by acting as a torsional spring in the in vitro assays and

could thereby support motility, albeit at reduced velocities than

in vivo muscle myosin, as found. Thus, only those connectors

that in some way mimic the energy storage function of S-2

coiled coil would support motility in these assays, and the

speeds are lower than the in vivo velocities because of the

inefficiencies of the coupling in the in vitro motility system.

Yet, because of the absence of the S-2 coiled coil in these in

vitro assays one could easily be led to the false conclusion that

S-2 is not essential for motility. Moreover, the observation of

motility in these assays does not mean that the motility can only

occur by a lever arm mechanism, as tacitly assumed. Other

mechanisms are also possible. Finally, as the new paradigm

shows, the in vitro assays do not exactly match the in vivo

system of force production taking place in living muscle in each

and every way.

The fulcrum of the power stroke is different in the new

paradigm compared to current models. Thus according to the

new paradigm, the hinge at the LMM–HMM junction of

myosin II is for muscle activation, the actomyosin contact for

rotation to convert loose actomyosin to tight binding upon

phosphate release, the pivot within the myosin head at the

junction of the catalytic and regulatory domains for tilting of

the lever arm upon MgADP release to help relieve the kink/

latch state of the crossbridge, and the S-1–S-2 hinge is the

fulcrum about which the power stroke occurs. Thus a

mechanical function is ascribed to each flexible junction/hinge

known to be present in myosin II. It should be noted that the

new theory retains the pioneering and other verified aspects of

the old; for instance, it agrees completely with lever arm

theories that the postulated rotations upon phosphate release

[38] and the envisaged tilts and swings upon ADP release do

occur [34]; however in the new paradigm these are not the true

cause of the power stroke as postulated by the lever arm model,

but are merely preliminary to the power stroke. They are

precursor events that unblock the kink at the S-1–S-2 hinge and

trigger the coiling back of the N-terminal heptads of S-2 which

initiates the powerstroke. Thus, if the aim of current research

programs of muscle contraction is to understand the effect of

nucleotide binding and release steps and the conformational

changes they produce in myosin head (e.g. swings of the lever

arm and other events preceding in time to the power stroke that

serve as initiation steps to make the power stroke happen), then

the current program can be considered highly successful. But if

the aim is to understand in a unified way the cause of the

elementary force production processes during muscle contrac-

tion, and the way the powerstroke is generated on actin, then a

reorientation is necessary, and the new theory provides a way

S. Nath / Process Biochemistry 41 (2006) 2218–2235 2229

for future progress and will certainly prove a most valuable

guide for further experimentation in the field if we are willing to

listen to it with an open mind.

In the swinging crossbridge and lever arm models of muscle

contraction, ATP has a single role only, that of detaching the

crossbridge from actin and collapsing the spring/elastic element

and thereby dissipating that energy. This is not the most

efficient way of utilization of energy! This difficulty does not

arise in the RUT Mechanism because in that theory, ATP plays a

dual role. In the lever arm model, translating the head–rod

junction�5–10 nm axially need not lift the load, because there

exists a hinge inside the myosin head and the lever arm can tilt

relative to the catalytic domain, and the angle between the

catalytic domain and the lever arm can alter (Fig. 10). This

raises the crucial question: if the whole myosin head does not

tilt as one rigid entity (as envisaged by the early Huxley

swinging crossbridge models [35,36]), but rather tilting of only

part of the myosin head is involved, as conceived in later

modifications of the swinging crossbridge models by lever arm

models [38], and the angle/orientation of the catalytic domain

with respect to actin remains fixed (Fig. 10), why will the lever

arm swing move actin? In other words, the presence of the

hinge in the myosin head in the vicinity of the junction of the

catalytic and regulatory domains will not permit transmission

of the lever arm swing or axial movement of the head–rod

junction to actin filament. If the myosin head moves/tilts on

actin, the orientation of the catalytic domain relative to actin

must change, and if this orientation does not change, as

proposed by the lever arm model, then actin will not be pulled

with myosin head given the structure, architecture and

connectivity in the actin–myosin system. In fact, a pure lever

arm tilt will not generate a sufficiently large torque to cause

filament sliding and that too under external load conditions.

This conclusion is consistent with the principles of Newtonian

mechanics. We would do well not to violate it. Thus, the older

models are translation models and do not include the key role of

torque as addressed by the new mechanism where a rotary

motion (recoiling in S-2) is converted to a translation/linear

motion in S-1–actin, a mechanism that is proven in man-made

engines, and can definitely occur as per the laws of mechanics,

Fig. 10. Schematic diagram for a lever arm model representing the absorption

of energy by the internal hinge of myosin/change in angle (tilt) at the junction of

the catalytic and regulatory domains of myosin upon �axial translation of the

myosin head–rod junction during the power stroke without lifting of any load or

movement along actin.

given the architecture of the myosin–actin and the mechanical

constraints present on the system [2]. For torque to exercise its

effects, the myosin heads must be free from actin (i.e. the

myosin heads must be free to rotate about their axes in an

unconstrained way). However, the myosin heads are bound to

actin during ATP binding, and during bound phosphate/ADP

release from myosin head. Hence ATP binding or Pi/ADP

release steps cannot cause the rotation of myosin heads and

uncoiling of the N-terminal S-2 heptads. Only the ATP

hydrolysis step occurs when myosin heads are free of actin;

hence the bond scission event during the ATP hydrolysis

elementary step can readily cause the rotation-uncoiling-tilt

envisaged in the RUT mechanism, i.e. the required conforma-

tional changes, in the myosin molecules.

Finally, there is the correspondence with experiment,

especially the powerful single molecule imaging studies on

myosin II to be dealt with. The classical kinetic studies of

Tonomura and co-workers [32] on the heterogeneous nature of

the myosin dimer have already been alluded to; yet, no

consideration (let alone even a rudimentary attempt at

explanation) of the large body of his experimental work has

been given even after the passage of over three decades. More

recently, in an experiment of great technical virtuosity and

exceptional complexity, a simultaneous measurement of ATPase

and mechanical events in single myosin molecules during force

generation and interaction with actin has been pioneered by

Yanagida and co-workers [39]. The experiment shows unam-

biguously that myosin II can produce force several hundred

milliseconds after ATP hydrolysis and release of bound

nucleotides. This delay clearly points to the ability of myosin

to store chemical energy from ATP hydrolysis and subsequently

perform useful work with this stored energy. This important

finding does not support the widely accepted view that force

generation is directly coupled to the release of bound ligands.

The authors of the work predicted that ‘‘these results will prove

fundamental for understanding the mechanism of mechan-

ochemical energy transduction in molecular motors’’ [39]. The

RUT Mechanism is the only fundamental theory from first

principles that is currently available that explains these powerful

single molecule results. In summary, it can be stated that, taken

together with Nath’s torsional mechanism of energy transduction

and ATP synthesis, the rotation-uncoiling-tilt energy storage

mechanism of muscle contraction solves fundamental molecular

mechanistic problems in bioenergetics and motility and offers

a most detailed, unified and appealing picture of energy

production, transduction, storage and utilization processes in

systems of biological molecular machines.

8. Application of the general principles to other

molecular machines

The above unifying principles have been applied innova-

tively to other molecular machines, for instance the processive

cargo-carrying kinesin and ncd motors on microtubules [1]. The

general principles work for these motors, yet, because their

biological function is different from myosin II, and the nature of

mechanical constraints on the V-shaped kinesin/ncd/myosin V

S. Nath / Process Biochemistry 41 (2006) 2218–22352230

molecule is different, the specific mechanism (the rotation-twist

energy storage mechanism of processive molecular motors) is

not identical to that of myosin II [1]. However, given the detailed

development for myosin motors in Sections 6 and 7, the sense of

rotation of the two heads is opposite to that proposed earlier. Thus

ATP hydrolysis causes a clockwise rotation of the kinesin/ncd

head 1 viewed from the cargo end. The partner head (head 2 that

rotates by the ‘‘physical stroke’’ [1]) will rotate counterclockwise

viewed from the cargo end. This would also make the rotation

sense in accordance with the X-ray structures of kinesin in ATP-

like and ADP-like states and the clockwise rotation (viewed from

the cargo end) that has been proposed upon ATP hydrolysis by

these workers [40]. Such a rotation may uncoil one heptad of the

neck coiled coil. However, according to the rotation-twist energy

storage mechanism, whether there is more uncoiling or only

some (1-heptad) uncoiling, generation of twisting strain and

storage of energy as elastic (primarily twist) energy in the V-

shaped structure up to hinge 1 is similar in either case [1, 1st

column on page 15]. Experiments show that extensive neck

coiled coil unwinding does not occur during kinesin motility

[41]; hence the role of the�1-heptad unwinding may only be to

enable the heads to separate sufficiently to span the distance

between binding sites on the microtubule and bind to them. In any

case, the re-coiling of the heptad does not drive the physical

stroke of head 2 that binds to the a-tubulin site on the

microtubule; rather, the elastic (twisting) strain in the molecule

forces it to regain its resting state (page 15 of Ref. [1]). Finally,

unlike the estimation of relative speeds of the chemical and

physical strokes made for the situation invivo [1], far-sighted and

innovative in vitro experiments show that progressive shortening

of the coiled coil does not alter the time taken by the fast step, but

slows down the time for the slower step [42]. This can be

interpreted as meaning that, in vitro, with these truncated

constructs, the ‘‘physical stroke’’ [1] is the slower step, because

only the physical stroke can be affected by the mechanical/elastic

properties of the kinesin coiled coil (the chemical stroke has no

contribution from the length of coiled coil constructs but depends

only on the motor, and no alteration in the motor domains was

made in the experiments [42]). In fact, the truncated constructs

can be modeled as shorter springs/elastic elements, which do not

have sufficient elasticity on the average to overcome the barrier

for the physical stroke (and also help unbind head 2 from its

microtubule binding site). Hence these truncated constructs show

greater propensity to limp in the experiments of Block and co-

workers [42]. We predict that a higher load (vertical or backward)

will make it more difficult for the physical stroke to unbind head

2 from the microtubule and move it to its next binding site on the

microtubule. In vitro, a smaller load will reduce limping, because

the elastic strain can overcome the load and unbinding of head 2

more easily. It should be re-emphasized that the insignificant

hinge and neck/stalk rotation of kinesin/ncd/unconventional

myosin with respect to the �1808 rotation of the head is a

necessary condition for storage of elastic energy (primarily as

twist) in the V-shaped molecule as per the rotation-twist energy

storage mechanism of processive molecular motors, a require-

ment that has been spelled out very clearly [1]. The mechanism is

also consistent with other innovative experiments that showed

<308 relative rotation between microtubule and the neck/stalk of

kinesin [43]. Thus, the inchworm model is not the only

mechanism possible that is consistent with this observation. The

new mechanism is consistent with both ‘‘poles’’ of observations

[42,43]. Hence the statement on page 16 of Ref. [1] still appears

to be an accurate description in the opinion of this researcher.

The unity of the description of these molecular motors with

aspects of conventional myosin is further realized following the

key insight that the elastic strain energy accumulated in the V-

shaped molecule is by itself insufficient to enable the head that

has stepped forward by the chemical stroke (the leading head

after the stepping process) to return back and thereby relieve the

internal strain. Rather, the elastic strain needs to accumulate in

the molecule before the physical power stroke [1] takes place.

Moreover, upon stepping, the leading head, though at the right

axial position for binding to its site on the track, is in the wrong

orientation for tight, stereospecific binding. Only weak binding

of the head to its microtubule/actin track is possible in this

orientation. Hence a conformational change is needed in the

leading head to cause it to bind tightly and stereospecifically to

its binding site. It is proposed here that this occurs after release

of Pi due to microtubule/actin interaction/activation, just as in

the RUT framework for conventional myosin. Possibilities

upon Pi release from the leading head include bending of the

lever along the length of the leading head, a bending about a

pliant point in the leading head, or, most significantly, rotation

of the leading head about its axis/neck linker, or combinations

of these, until the tight binding of head to track progressively

takes place, and both motor heads face the same direction. As

this occurs, the internal elastic strain in the V-shaped molecule

increases. Further, after ATP hydrolysis, the V-shaped molecule

had bent in a second plane by tethering through the trailing

head. This prevents the trailing head from moving forward. It

can be readily visualized that in the bent structure, a component

of the torque acts downward (and hence not in a direction

perpendicular to the track); therefore, it is difficult to detach the

rear head until the motor is perpendicular to the track. This

trigger is provided by ADP release, again as in the RUT

mechanism, and now the bend/block is removed, and the

internal elastic strain applies a torque at the V-junction of the

molecule in a direction opposite to the direction of the torque

due to the ATP-motive process. The leading head, since it is

tightly and stereospecifically bound to its binding site does not

get released. The rear head bound to a-tubulin/actin detaches

and steps forward and binds to its next available binding site

and a resting state configuration of the kinesin/ncd/myosin V

molecule with both heads bound is reached (with the new

leading head containing bound MgADP, and the rear head

empty of bound nucleotide), and a new mechanochemical cycle

can begin.

9. Systems biology/engineering analysis of musclecontraction

A systems biology/engineering analysis of muscle contrac-

tion (at a certain given length) similar to that performed in

Section 3 for ATP synthesis leads to the following result [1 is

S. Nath / Process Biochemistry 41 (2006) 2218–2235 2231

the driving reaction (input), 0 is the driven mechanical

consequence (output)]:

Lwhole11 ¼ nL11 (13)

where n is the number of operating crossbridges. This is

because force on one crossbridge is 1/n times the force pro-

duced by the muscle sarcomere (neglecting internal shear

effects). Further:

Lwhole00 ¼ L00=n (14)

because the velocity of individual operating crossbridge equals

the velocity of shortening muscle in isotonic contraction.

Finally:

Lwhole01 ¼ L01 (15)

The differences with the chemical output case of Section 3 are

now clarified. In muscle, while each operating crossbridge

produces its own output (force) independently of the other

operating crossbridges, the forces produced by each cross-

bridge are summed up to produce net force output of the

half-sarcomere, which is further summed up to produce the

macroscopic effect in whole muscle. In other words, with

appropriate scaling of the variables above (per unit length,

area or volume), the result for the half-sarcomere can be readily

extended to whole muscle. However, the velocity of each

working crossbridge is equal to the velocity of contraction

of the sarcomere or in whole muscle because of the structural

relationship/arrangement between myosin and actin. Thus, the

final output is force which is summed up, and we need to know

the number of activated crossbridges, n.

The conclusion suggests itself that the overall muscle

performance is the result of two independent phenomena: that

of the individual crossbridge when activated and producing

force (under which conditions the single crossbridge behaves as

a linear energy convertor and, therefore, linear nonequilibrium

thermodynamics analysis is applicable), and the number of

operating crossbridges, n, that are activated and producing

force in the whole system [2]. We propose that the nonlinear

effects observed in the macroscopic system (e.g. whole muscle)

result from the variation in the value of n for a given

experimental condition and that n is a function of force or

velocity of isotonic contraction. We predict that the value of n

decreases with increase in velocity (because the crossbridge

will have to be disconnected faster to sustain higher velocities).

A systems (electrical) analog incorporating the above novel

concepts is shown in Fig. 11. Putting a switch (S) on is akin to

Fig. 11. Systems (electrical) analog of muscle contraction at a given length.

activating a crossbridge and increasing the number of force-

producing crossbridges (C). For a given steady state condition,

a certain number of switches are in the ‘‘on’’ state, i.e., a certain

constant number of crossbridges are activated. This number is a

function of velocity in whole muscle. Thus, Fig. 11 represents a

conservative (non-dissipative) mode of regulation [2] of the

output of the system. Using these concepts it is possible to

employ the systems approach/analog delineated in Fig. 11 and

completely determine the performance of the ‘‘system’’ in the

following progression: from submolecular elements of cross-

bridge (Sections 6 and 7) to crossbridge and actin, from

connections of crossbridge and actin in series to a myosin–actin

filament pair, from a summation of myosin–actin filament pairs

in parallel to a half-sarcomere, from a sum of half-sarcomeres

in series to a myofibril, from several myofibrils in parallel to a

muscle fiber, and finally, from the sum of muscle fibers

connected to each other in parallel to the macroscopic system of

whole muscle. Hence we have shown that the concluding

comment of other researchers on our systems approach to ATP

synthesis that ‘‘such a transition from the local to the global

level in biology is a significant achievement of the torsional

mechanism’’ [44] is applicable to the muscle system and the

RUT mechanism also.

10. Physical, chemical and biological implications

The work has a plethora of far-reaching physical, chemical

and biological implications. Specific implications have already

been dealt with in the detailed development of Sections 3–9.

Some general scientific implications resulting from the research

are discussed below as concisely as possible.

10.1. Microprocess

In various branches of engineering and science, processes

have traditionally been looked at in a macroscopic sense. This

work emphasizes the need to look at the process on a molecular,

submolecular and even microscopic level, and to seek driving

forces also at such a microlevel. The concept of the

microprocess then leads to a mechanistic, ‘‘first principles’’

understanding that can be integrated to understanding the

systems behavior at higher hierarchical levels, knowing the

systems architecture and topology.

10.2. Unity in diversity

The work shows that storage of strain energy as twist in a-

helical or uncoiling/supercoiling in coiled coil protein domains/

elements or as torsional strain in these motifs provides unified

principles for operation of protein molecular machines (and

similar principles, by extension, to DNA- and RNA-based

molecular machines). Yet, the principles manifest diverse types

of motility: the exact type of strain and localized region of energy

storage, and the exact type of motion depend on the mechanical

constraints present on the degree of freedom of the constituents

of the protein macromolecule(s). Diverse experimental observa-

tions from various fields are shown to be explained by the new

S. Nath / Process Biochemistry 41 (2006) 2218–22352232

theory in a natural way, and we have a unity of physical principle

in a diversity of biological function. The work can be seen as one

further step in revealing (in a centuries-old process of scientific

inquiry) that even the most complex processes in nature are

governed by simple, rational physical laws and principles.

10.3. First law of thermodynamics

The question was raised [1] that at which step is energy put

into ATP to raise it to a higher energy level vis-a-vis ADP + Pi?

The problem was that Boyer’s binding change mechanism [1–

3,5,8–10,37,44] did not address the questions of how and when

energy got locked into the ATP, unlike in the torsional

mechanism [1–3,4,5,7–11,13–15,44]. In current mechanisms,

the g-subunit rotates freely (e.g. ‘‘spins like a top’’); but nobody

has found a way to date to convert the rotational kinetic energy

of the spinning shaft into the stored internal energy of ATP. In

fact, as we slow the shaft, the energy will be thermalized and

dissipated as heat and not converted to useful work or stored

energy. We are then left with binding energy as the only source

of useful external work. But calculation based on experimental

Kd values [2] for the catalytic sites and use of the expression

DG = RT ln(Kd2/Kd1) reveals that the binding free energy

difference is grossly insufficient to account for the required

stabilization of�60 kJ/mol postulated by the first theory, or, for

that matter, of even the standard state value of �35 kJ/mol.

Moreover, in a tri-site mechanism, the ultra weak binding of

MgATP to site 3 (with a Kd of 23 mM) does not provide

sufficient energy to drive complete rotation of the g-subunit.

Further, binding energy is not stored energy (that is, it is not

energy stored within ATP) but is only the interaction energy of

the enzyme with the ATP. If there exists no other form of energy

storage in these systems, then, for an open system in a steady

state, we can integrate a general differential expression of the

first law involving elemental transfers over any arbitrary time

period Dt [1]. With these caveats, with the molecular machine

as the system, the binding step lies inside the system boundary,

and such a step internal to the system cannot be used to perform

useful external work outside the system boundary surface,

without violating the first law of thermodynamics for open,

steady state systems. Thus, previous theories have not

synthesized ATP but have only made ADP.Pi. It should be

noted that these are problems with the conceptions of the

earlier, first theories of ATP mechanism, and are not related to

the way the ATP synthase enzyme actually works. A clear

distinction should be made between these two. In any case, the

earlier proposals have not been cast in molecular terms and are

not sufficiently detailed to even permit a proper evaluation; the

energy transduction in these proposals remains a black box. The

new paradigm converts the black box of energy transduction

into a white box, and none of these inconsistencies without

exception arise in the new paradigms [1–17]. This work focuses

attention not only on the physics, but also on the chemistry of

the ATP hydrolysis/cleavage reaction and the chemical

hydrolysis reaction-linked conformational changes as the

elementary step at which energy transduction and storage

occurs in biological molecular machines, unlike the purely

physical interaction energies of ATP/ADP/Pi ligand binding/

release to/from the enzyme invoked in every other current

model of biological energy transduction. We can have different

theories depending on how we redistribute energy. It should

however be clearly recognized that whether ATP binding

energy, or ATP hydrolysis, or both cause rotation in the

hydrolysis mode does not really present problems for the

torsional or RUT mechanism. Since the hydrolysis step follows

the binding step on the enzyme in these processes, the

conformational changes postulated in this paper to be caused by

the hydrolysis step can readily be ascribed to the previously

occurred ATP binding step (or, for that matter, to both the ATP

binding and hydrolysis steps), and the rest of the mechanism

remains unchanged, except for a change in language and

semantics.

We now clearly see that possible violations of the first law of

thermodynamics are only revealed when we consider ATP

synthesis by the F1FO-ATP synthase and ATP utilization by a

molecular machine such as myosin–actin/kinesin/ncd (as in this

paper) together. If we consider ATP synthesis in isolation (and

never connect it with the ATP usage cycle), we can be as

inefficient as we please and simply waste redox/light energy or

the energy of ion gradients and falsely claim that we had made

ATP (e.g. by freely rotating a shaft, as in the binding change

mechanism). Unless we link ATP synthesis with the ATP

hydrolysis/utilization cycle, we would never see possible

violations of the first law of thermodynamics.

10.4. Second law of thermodynamics

From the above and earlier discussion [1–3], the energy for

useful external work must ultimately come wholly, or at least in

part, from energy stored internally (by molecular rearrange-

ments) within ATP vis-a-vis (ADP + Pi), and not only from

interaction energy steps internal to the overall system of the

molecular machine. Thus, all current mechanisms (with the

exception of Nath’s mechanisms) imply that the energy stored

in ATP is first converted into thermal motions and only then

subsequently used to perform useful external work. But this is

impossible because it would mean that useful work has been

done cyclically using heat under isothermal conditions.

According to the second law, heat cannot be an energy source

unless it flows between a source and a sink at different

temperatures.

Given the above, there are two ways to reconcile the second

law of thermodynamics with reversible processes in statistical

physics. Either we say that the second law is only applicable if,

in a volume V, the number of particles, N that have diffused into/

out of Vare greater than the average number of particles Navg in

that volume (or root mean square number of particles present in

that volume). This implies that we have specified the limits of

validity of the second law and that it is a law of large numbers.

But the fact remains that suberb state-of-the-art biological

experiments show that biological machines work as single

molecules, with discrete steps. Hence alternatively, we can say

that the second law is valid for single molecules, but we now

introduce timescales, and state the law such that it is impossible

S. Nath / Process Biochemistry 41 (2006) 2218–2235 2233

to convert energy that has spread over the thermal degrees of

freedom and equilibrated with the surroundings and reached a

Boltzmann distribution very fast (in time t < t) to a longer-

living form of (stored) energy in a (molecular) device that lasts/

stays stored in the device for a time t > t. Thus, the second law

is not violated by single molecules; rather, we have now truly

understood the meaning of the second law. A suitable concise

restatement of the second law of thermodynamics applicable to

single molecules then is, ‘‘Molecules perform useful work by

direct transduction of energy from one form to another;

thermalized energy cannot be transduced into stored energy.’’

What is thus forbidden by the second law is to take a form of

stored energy, allow it to spread over the thermal degrees of

freedom (Q), and then to try and convert this thermalized

energy Q, under isothermal conditions, to another form of

stored energy, i.e. to an energy that remains stored and lasts

longer than the time of thermal exchange. The trick of biology

then is not to allow stored energy to spread over (and exchange

freely) with the thermal (rotational, vibrational and transla-

tional) degrees of freedom of the surrounding reservoir. Such

processes that directly transduce stored energy from one form

to another are reversible too; hence there is no contradiction

with the reversibility of statistical physics.

The old forms of the second law (e.g. Kelvin-Planck and

Clausius statements) are only valid for heat engines. The

ubiquitous biological machines of molecular dimensions do not

work in the same way as heat engines and hence a new

reformulation/restatement of the second law is needed. It shows

that it is not sufficient for a fluctuation (e.g. Brownian motion)

or other perturbation to lift a microscopic (or molecular) load; it

has to keep the load lifted (or store energy in a device) for a time

t > t and not lose it to the surroundings as heat within that time.

These fundamental concepts enable us to achieve a crystal-clear

understanding of the meaning of the second law of thermo-

dynamics and to grasp what is allowed and what really is

forbidden by the second law at the molecular level. This was

chiefly because the concepts discussed in this paper and earlier

[1–3,45] allowed us to make a distinction between heat and

work/stored energy at the molecular level on the basis of

timescales applicable at even a single molecule level.

10.5. Timescales and lengthscales

The above discussion implies that conventional machines

fail when scaled down to the molecular level because the

constraint against which useful work is done is disturbed by

Brownian fluctuations and the machine cannot function at all.

Classical approaches assume the system to be ergodic, i.e. they

only consider statistical thermal degrees of freedom that are fast

enough to exchange energy with each other/with the

surroundings. However, in biological molecular machines,

this assumption is violated, and only certain specific long-

lasting (compared to the time for thermal exchange) degrees of

freedom are excited in localized spatial regions of the device

that exchange only slowly with the thermal degrees of freedom

and do not reach equilibrium with these thermal degrees of

freedom within a certain interval of time, t (these states were

called nonequilibrium conformational states or metastable

states in our earlier analyses [1–3]). Thus, these nonequilibrium

biological systems possess a deep space-time structure based on

timescales and lengthscales and their existence requires a

different, more mechanical approach to understand the

functioning of these machines.

10.6. Technological applications

The work has great potential to realize various new

technologies, including the development of new, highly

efficient (nano)devices that will play an increasingly important

role in the industrial technology of the future, as discussed

earlier in detail [2].

Finally, the major contributions already made to the world

by scientists from emerging economies (and the greater future

role and responsibilities of these societies) in the generation of

new knowledge needs to be further recognized as being

absolutely vital for the progress and future well-being of the

world in science and in all other fields of human endeavor, as

prophesized by the author [46,47]. The question arises: Can the

creative artist–scientist have a premonition of what lies in store

for him?

11. Conclusions

A comprehensive molecular mechanistic analysis of

fundamental energy transduction processes in biology has

been carried out. In particular, the molecular mechanisms of

two of the most fundamental processes in biology – ATP

synthesis and muscle contraction – have been addressed in

consummate detail in all their complexity. Currently believed

models of these fundamental processes have been analyzed and

found to be perpetual motion machines of the first and second

kinds. The former conclusion has been shown to hold because

the free energy released during the chemical ATP hydrolysis

elementary step is not employed for useful external work in

these models, and binding energy changes alone are

insufficient. The latter conclusion of current models being

Maxwell’s demon machines has been proved because, in all

those models, in effect, heat is being converted to work in a

cyclic isothermal process. The new paradigms of the torsional

mechanism of energy transduction and ATP synthesis and the

rotation-uncoiling-tilt energy storage mechanism of muscle

contraction have been shown to solve the problems in

bioenergetics and motility and to offer a most detailed, unified

and appealing picture of energy production, transduction,

storage and utilization processes in systems of biological

molecular machines. The new paradigms are in consonance

with the universal laws of science. A novel mechanism of

energy storage in biological processes different from the usual

entropic mechanism of rubber elasticity has been identified and

suggested to be of great significance in biology. In this new

mechanism, hydrophobic interactions play a very important

role. It has been proposed that upon mechanical deformation,

the extent of interface between hydrophobic protein regions and

water is increased and new protein–water interfaces are created

S. Nath / Process Biochemistry 41 (2006) 2218–22352234

by making the hydrophobic residues of the protein chain more

accessible to water, thereby storing the energy of the

mechanical torque/elastic deformation in submolecular ele-

ments of the protein machine. Free energy changes associated

with this type of hydrophobic interaction have been postulated

to provide a primary driving force for muscular contraction.

The manifold far-reaching physical, chemical, biological,

technological, social, and human implications arising from the

work have been discussed in detail.

Acknowledgements

My research program has been liberally funded by the

Department of Science and Technology, India through the

Swarnajayanti Research Project ‘‘Molecular Machines:

Mechanism and Thermodynamics’’ under the Swarnajayanti

Fellowships for ‘‘promotion of basic research of world

standard.’’ I am grateful to Dr. C. Channakeshava of the

Engineering Mechanics Research Centre, Bangalore, India for

several most helpful discussions on muscle contraction over the

years. Finally, I thank both referees for their long and detailed

reviews that have greatly helped to improve the presentation of

various aspects of the work.

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