introduction and literature survey copyrighted … · 2020. 2. 17. · a living organism, operates...

P1: OTA/XYZ P2: ABCc01 JWBS019-Filo November 4, 2009 7:29 Printer Name: Sheridan

1INTRODUCTION ANDLITERATURE SURVEY

1.1 INTRODUCTION

Both living organisms and computers are “information-processing machines”that operate on the basis of internally stored programs, but the differencesbetween these systems are also quite large. In the case of living organisms,self-assembly occurs following an internal program, and the nervous systemand brain formed in this way function as an autonomous information ma-chine. Unlike traditional computers which must be “driven” from the outside,biological systems have somehow incorporated within them rules on howto function. Moreover, in the case of biological entities for which there isno external blueprint, the design plan is entirely internal and is thought toundergo changes both in the evolution of species and in the development ofindividuals. These similarities and differences have drawn the attention ofcomputer scientists as well as of life scientists.

In order to revolutionize the current world of computers, three roads, orany combinations of them, are clearly visible [1]

1. Changing the physical elements at the foundations of the computercomponents

2. Changing the architecture of computers3. Devising new software and computing algorithms

Information Processing by Biochemical Systems: Neural Network–Type Configurations, By Orna Filo and Noah LotanCopyright C© 2010 John Wiley & Sons, Inc.

1

COPYRIG

HTED M

ATERIAL


2 INTRODUCTION AND LITERATURE SURVEY

It is, however, true that a biological computer (or biocomputer) of a com-pletely different nature from today’s electronic computers already exists in theform of the fundamental phenomenon of life. The most advanced machinery,a living organism, operates with functional elements that are of moleculardimensions and actually exploits the quantum-size effects of its components[1]. Yet the quintessentially biological functions of living forms: autonomy,self-organization, self-replication, and development, as witnessed in both evo-lution and individual ontogeny, are completely absent from current computingmachines [1].

Two major approaches to the construction of a biocomputer are reviewedhere:

1. Study of the operational mechanism of biological systems, particularlythose of the living brain, and the use of these results in the redesign ofcomputer software and hardware architecture based on semiconductortechnology (Section 1.2).

2. Development of biocomponents that are similar to and/or composed ofbiological macromolecules, the development of biochips that make useof these components, and ultimately, the construction of biocomputers(Section 1.3).

1.2 COMPUTATIONAL PROCESSES BASEDON BIOLOGICAL PRINCIPLES

1.2.1 Modeling Biological Processes

The involvement of biology might lead to new computational processes basedon those found in natural systems. Multiple modes of processing contributeto the information-processing functions of biological systems, and these havebeen investigated and modeled extensively [2–8]. In his pioneering work,Rosen [9,10] introduced a two-factor model based on the idea that the fun-damental dynamic behavior of physiological and biochemical systems isregulated by the combined action of two factors, one excitatory and the otherinhibitory. Kampfner, Kirby, and Conrad [11–13] introduced theoretical mod-els of enzymic neuron systems for learning processes, based on the conceptof a hypothetic enzyme called excitase. Based on the same concept, a com-prehensive mathematical model of the enzymic neuron as a logical circuit hasbeen introduced by Neuschl and Menhart [14].

1.2.2 Artificial Neural Networks

The nerve cell has proved to be an extremely valuable source of ideas aboutnetworks of automata. A fundamentally different approach to computation


COMPUTATIONAL PROCESSES BASED ON BIOLOGICAL PRINCIPLES 3

is represented by artificial neural networks (ANNs), which are designedto mimic the basic organizational features of biological nervous systems[15–22]. The building brick of any neural computing system is some sort ofrepresentation of the fundamental cell of the brain: the neuron. Thus, ANNsconsist of a large number of simple interconnected processing elements whichare simplified models of neurons, and the interconnections between the pro-cessing elements are simplified models of the synapses between neurons.The processing of information in such networks occurs in parallel and isdistributed throughout each unit composing the network [15–22].

There has been a steady development of neuronal analogs over the past50 years. An important early model was proposed in 1943 by McCullochand Pitts [23]. They described the neuron as a logical processing unit, andthe influence of their model set the mathematical tone of what is being donetoday. Adaption or learning is a major focus of neural net research. Thedevelopment of a learning rule that could be used for neural models waspioneered by Hebb, who proposed the famous Hebbian model for synapticmodification [24]. Since then, many alternative quantitative interpretations ofsynaptic modification have been developed [15–22].

There is no universally accepted definition of an artificial neural network.However, some definitions can be found in the literature, and examples arecited here.

� Robert Hecht-Nielsen, the inventor of one of the first commercial neuro-computers, defined [17] a neural network as “a computing system madeup of a number of simple, highly interconnected processing elements,which process information by its dynamic state response to externalinputs.”

� According to the DARPA Neural Network Study [18]: “A neural networkis a system composed of many simple processing elements operatingin parallel whose function is determined by network structure, connec-tion strengths, and the processing performed at computing elements ornodes.”

� According to Aleksander and Morton [19], neural computing can bedefined as “the study of networks of adaptable nodes which, through aprocess of learning from task examples, store experiential knowledgeand make it available for use.”

� According to Zurada [20], artificial neural systems, or neural networks,are “physical cellular systems which can acquire, store, and utilize ex-periential knowledge.”

� According to Nigrin [21], “a neural network is a circuit composed ofa very large number of simple processing elements that are neurallybased. Each element operates only on local information. Furthermore



each element operates asynchronously; thus, there is no overall systemclock.”

� Haykin [22] offers a definition based on Aleksander and Morton [19]:“A neural network is a massively parallel distributed processor that hasa natural propensity for storing experiential knowledge and making itavailable for use. It resembles the brain in two respects:� Knowledge is acquired by the network through a learning process.� Interneuron connection strengths known as synaptic weights are used

to store the knowledge.”

Significant progress in neural network research has been made in recentdecades [15–22,25]. Presently, the neural network strategy is implemented ateither the software or hardware level. The VLSI (very large scale integration)version of neural network implementation is a technology that has approacheda certain degree of maturity [22]. Although the VLSI version serves as animpressive demonstration of the power of the new computer architecture ofneural networks, it falls short of a radical design departure that is capable ofcapturing the structural and functional flexibility inherent in biosystems [25].Many experts believe that neural network technology will be more robust andmore powerful when its implementation becomes possible in a molecular-based “hardware” environment [25].

1.3 MOLECULAR AND BIOMOLECULAR ELECTRONICS

1.3.1 Motivation

The high-technology revolution that made the personal computer standardequipment was fueled primarily by astonishing advances in microelectronicsthat allow more and more circuit elements to be packed into a small integratedcircuit (IC). The number of device components packaged into a single IC hasgrown exponentially with the passage of time [25–28]. Moreover, we witnessincreasing capability of each IC, increasing speed of operation, reduced con-sumption of energy, reduction in sizes and weights of the finished products,and reduced prices. Will this trend continue so that the device size eventuallyreaches the atomic scale? To many experts the answer is “not if using con-ventional microelectronics technology,” which exploits mainly macroscopicproperties of inorganic materials, because the ensuing quantum size and thethermal effects will make such devices unreliable [25,28]. Thus, today, theminiaturization and integration of electronic devices are being pushed to theirphysical limits [25–28].


MOLECULAR AND BIOMOLECULAR ELECTRONICS 5

1.3.2 Molecular Electronics

Molecular electronics is defined broadly as the encoding, manipulation, andretrieval of information at a molecular or macromolecular level [25–29].This approach contrasts with current techniques, in which these functionsare accomplished via lithographic manipulations of bulk materials to gener-ate integrated circuits [28]. A key advantage of the molecular approach isthe ability to design and fabricate devices from the bottom-up, on an atom-by-atom basis. Lithography can never provide the level of control availablethrough organic synthesis or genetic engineering [28]. The molecular prim-itives allow for improvement in a number of information-processing devicecharacteristics compared with similar characteristics of silicon-based devices.Thus, molecular information processing is attractive because it offers [29]:

� Integrability at the atomic scale� High computational speed due to parallel processing, which compensates

for the inherent low processing rate of each elementary device� Self-assembly capability of atomic or molecular processors� Plasticity of the molecular circuit, which can reconfigure itself to op-

timize its performance, taking into account the previous experience(learning)

� Fault-tolerance capability and even self-repair ability of the molecularcircuit

� Reduced power consumption

Since Aviram’s proposal of a molecular rectifier [30,31], a variety ofdesigns of molecular electronic devices have appeared. Molecular-scale de-vices are fabricated on the nanometer scale and are composed of either asingle molecule or several molecules configured into a supramolecular com-plex. Among these devices, molecular rectifiers, molecular switches, molec-ular diodes, molecular photodiodes, and molecular memories are described[30–39]. Studies also deal with assembling the individual components inthin-film configurations [25,40,41], forming artificial membranes [25,42] andestablishing an interface between the molecules and conventional electronicmaterials [43]. Another possibility that has been investigated is the use of elec-troconductive polymers as “molecular wires” for establishing the connectionrequired between molecular elements [43,44].

1.3.3 Biomolecular Electronics

Biomolecular electronics is a subfield of molecular electronics that considersthe use of native and modified biological molecules in electronic or photonic



devices [45–56]. The growing interest in the possibility of utilizing biologicalmolecules in molecular electronics is fostered by the basic understandingthat, in so doing, one may be able to take advantage of the specific charac-teristics and unique capabilities of these natural molecules [44–56]. Amongthe biomolecular devices investigated, protein-based molecular devices havegained increasing attention due to the versatile and highly specific molec-ular functionality of proteins [43,57]. Enzymes [44,58–67], receptors [68],antibodies [43], and bacteriorhodopsin [29,69–73] have been used as eitherelectronic or optical devices. Computation with simple DNA manipulationshas also been demonstrated [74,75].

1.4 BIOCHEMICAL DEVICES BASED ONENZYMIC REACTIONS

In an extensive study, Okamoto and co-workers [76–86] introduced a bio-chemical switching device based on a cyclic enzyme system in which twoenzymes share two cofactors in a cyclic manner. Cyclic enzyme systemshave been used as biochemical amplifiers to improve the sensitivity of enzy-matic analysis [87–89], and subsequently, this technique was introduced intobiosensors [90–93]. In addition, cyclic enzyme systems were also widely em-ployed in enzymic reactors, in cases where cofactor regeneration is required[94–107]. Using computer simulations, Okamoto and associates [77,80–83]investigated the characteristics of the cyclic enzyme system as a switching de-vice, and their main model characteristics and simulation results are detailedin Table 1.1, as is a similar cyclic enzyme system introduced by Hjelmfeltet al. [109,116], which can be used as a logic element.

Subsequently, Okamoto and associates [84–86] investigated the connec-tion of several cyclic enzyme systems in order to construct a network. Intheir models the cyclic enzyme system represents a biochemical neuron thatparticipates in a biochemical neural network. These models are detailed inTable 1.2. Theoretical models of such networks were also proposed byHjelmfelt and co-workers [109–111,116], and these are also presented inTable 1.2.

Models for biochemical switches, logic gates, and information-processingdevices that are also based on enzymic reactions but do not use the cyclicenzyme system were also introduced [76,115,117–122]. Examples of thesemodels are presented in Table 1.3. It should also be mentioned that in otherstudies [108,112–114,116], models of chemical neurons and chemical neuralnetworks based on nonenzymic chemical reactions were also introduced.


Tabl

e1.

1M

odel

sB

ased

onth

eC

yclic

Enz

yme

Syst

em

Mod

elN

o.M

odel

Cha

ract

eris

tics

Res

ults

Con

clus

ions

and

App

licat

ions

Com

men

tsa

Ref

s.

1k 1 k

2

AB

X3

X4

X2

X1

I 2

I 1k 3

k4

I 1,I

2:i

nput

sto

the

syst

em’s

subs

trat

epo

ols

ofX

1an

dX

3,r

espe

ctiv

ely.

Sim

ple

mas

sac

tion

kine

tics.

Irre

vers

ible

reac

tions

.

The

stea

dy-s

tate

conc

entr

atio

nsof

Aan

dB

( A,B

)ch

ange

step

wis

eat

I 2/I

1=

1an

dca

nbe

repr

esen

ted

asA

=f(

I 1,I 2

)=

[1if

I 1≥

I 2;

0if

I 1<

I 2]

The

stea

dy-s

tate

conc

entr

atio

nsof

X2

and

X4

(X2,X

4)

are

also

afu

nctio

nof

I 1an

dI 2

:X

2=

X4

=f(

min

(I2,I 2

))=

[ I 2 kif

I 1≥

I 2;

I 1 kif

I 1<

I 2]

whe

rek

indi

cate

sth

era

teco

nsta

ntof

the

deca

yof

X2

orX

4,k

3or

k 4,r

espe

ctiv

ely.

The

mat

hem

atic

aleq

uatio

nsfo

rth

ism

odel

and

the

follo

win

gon

esag

ree

with

the

case

ofba

tch

reac

tions

,in

whi

chth

ere

isno

mas

sflo

win

toor

outo

fth

esy

stem

.H

owev

er,I

1an

dI 2

cann

otbe

defin

edas

mas

sflo

ws

ifvo

lum

ech

ange

sar

eno

tco

nsid

ered

.

77

2E

1

E2

AB

X3

X4

X2

X1

I 2

I 1k

3

k4

Sam

eas

sum

ptio

nsas

inm

odel

1ex

cept

:Rea

ctio

nm

echa

nism

sar

eas

sum

edto

beor

dere

dbi

–bie

nzym

icre

actio

ns.

Sam

ere

sults

for

X2

and

X4

asob

tain

edin

mod

el1.

77

(con

tinu

ed)

7


Tabl

e1.

1(c

onti

nued

)

Mod

elN

o.M

odel

Cha

ract

eris

tics

Res

ults

Con

clus

ions

and

App

licat

ions

Com

men

tsa

Ref

s.

3Sa

me

assu

mpt

ions

asin

mod

el1

exce

pt:

I 1an

dI 2

chan

gelin

earl

yw

ithtim

esu

chth

at

I 1(t

)=

80+

tI 2

(t)=

100

−t

X2

and

X4

are

dyna

mic

ally

regu

late

dby

the

leve

lsof

I 1an

dI 2

asde

scri

bed

inm

odel

1.Sw

itchi

ngof

depe

nden

ceon

the

inpu

tsat

apo

intb

eyon

dth

esi

mila

rpo

intd

eter

min

edby

the

stea

dy-s

tate

anal

ysis

isob

serv

ed.

Thi

stim

ela

gis

due

toan

accu

mul

atio

nof

X3.

Con

cent

ratio

nsof

A(t

)an

dB

(t)

show

ast

epfu

nctio

nw

ithth

esa

me

time

lag

asX

2an

dX

4.

The

dyna

mic

beha

vior

ofth

ecy

clic

enzy

me

syst

emdi

spla

yca

tast

roph

icbe

havi

orin

resp

onse

tosp

ecifi

cch

ange

sin

exte

rnal

inpu

t.T

hesy

stem

can

real

ize

ane

uron

icm

odel

capa

ble

ofst

orin

gm

emor

y.

77,8

2

4Sa

me

assu

mpt

ions

asin

mod

el1

exce

pt:

I 1an

dI 2

are

repr

esen

ted

bya

sinu

soid

alfu

nctio

nw

ithtim

et,

such

that

I 1(t

)=

10+

2si

n( 2π 40

t+

π 2

)

I 2(t

)=

10+

2si

n( 2π 40

t−

π 2

)

Con

cent

ratio

nsof

A(t

)an

dB

(t)

follo

wth

epa

ttern

desc

ribe

din

mod

els

1an

d2.

The

time

lag

isob

serv

eddu

eto

accu

mul

atio

nof

X1

and

X3.S

witc

hing

does

not

occu

run

tilth

eac

cum

ulat

ion

ofei

ther

subs

trat

eis

canc

eled

.

The

accu

mul

ated

subs

trat

eis

equi

vale

ntto

a“c

onde

nser

”an

dis

appl

icab

leto

aki

ndof

“mem

ory

stor

age.

”

81

5

k6

k1

k2

AB

X3

X4

X2

I 2

I 1k

3

k4

k5

X1

Sam

eas

sum

ptio

nsas

inm

odel

4ex

cept

:k 5

�=0

and

k 6�=

0.

No

time

lag

isob

serv

ed,a

ndth

eco

nver

sion

from

switc

hed

onto

off

(or

from

off

toon

)oc

curs

rapi

dly

acco

rdin

gto

the

diff

eren

cein

amou

ntbe

twee

nI 1

and

I 2.

The

beha

vior

ofth

esy

stem

iseq

uiva

lent

toth

atof

anel

ectr

onic

switc

hing

circ

uit.

81

8


6

AB

k1

X2

X1

I 1k

3

k2

X3

X4

I 2k

4

k–1 k–2

Sam

eas

sum

ptio

nsas

inm

odel

3ex

cept

:T

here

actio

nsX

1→

X2

and

X3→

X4

are

reve

rsib

le.

Incr

ease

inth

eva

lues

ofth

era

tepa

ram

eter

s,k −

1an

dk −

2,l

eads

toa

mor

egr

adua

lris

eof

A(t

)an

dB

(t),

and

the

step

func

tion

isno

tobt

aine

d.W

hen

the

ratio

ofk 1

/k−1

and

k 2/k

−2is

fixed

at1,

incr

ease

inth

era

tepa

ram

eter

sle

ads

toa

shar

per

rise

ofA

(t)

and

B(t

).

82

7Sa

me

assu

mpt

ions

asin

mod

el3

exce

pt:

Rea

ctio

nm

echa

nism

sar

ere

pres

ente

dby

orde

red

bi–b

ienz

ymic

kine

tics.

All

reac

tion

step

sar

eas

sum

edto

bere

vers

ible

.

The

dyna

mic

char

acte

rist

ics

ofA

(t)

and

B(t

)ar

equ

alita

tivel

ysi

mila

rto

thos

eob

serv

edin

mod

el3.

The

initi

alco

ncen

trat

ions

ofth

een

zym

esan

dco

fact

ors

affe

cted

the

dyna

mic

char

acte

rist

ics

ofth

esy

stem

sign

ifica

ntly

.The

switc

his

obta

ined

only

whe

nth

ese

conc

entr

atio

nsar

eov

era

cert

ain

thre

shol

dva

lue.

The

syst

emca

nbe

used

asa

switc

hing

cont

rolle

rw

hen

itis

coup

led

toth

ere

actio

nS

→P

and

aco

fact

orA

ises

sent

ialt

opr

oduc

eP.

Thu

s,A

can

beco

ntro

lled

byI 1

and

I 2an

dth

esw

itch

prop

ertie

sw

illbe

obta

ined

for

P(t)

.

82

8Sa

me

assu

mpt

ions

asin

mod

el1

exce

pt:T

wo

sinu

soid

alin

puts

with

aph

ase

diff

eren

ceθ

betw

een

them

:

I 1(t

)=

10+

2si

n

(2π 40

t)

I 2(t

)=

10+

2si

n

(2π 40

t−

θ

)

The

conc

entr

atio

npr

ofile

sob

tain

edfo

rA

(t)

and

B(t

)sh

owth

esw

itchi

ngob

serv

edin

mod

el4,

butt

heon

/off

times

depe

ndon

θ.T

hefr

eque

ncy

and

ampl

itude

ofX

1an

dX

3de

pend

onθ

.

Focu

sing

onth

edy

nam

ics

ofX

1(t

)an

dX

3(t

),th

esy

stem

can

play

the

role

ofa

rect

ifier

circ

uit.

The

amou

ntof

rect

ifica

tion

depe

nds

onθ

.

80

(con

tinu

ed)

9


Tabl

e1.

1(c

onti

nued

)

Mod

elN

o.M

odel

Cha

ract

eris

tics

Res

ults

Con

clus

ions

and

App

licat

ions

Com

men

tsa

Ref

s.

9Sa

me

assu

mpt

ions

asin

mod

el4

exce

pt:R

eact

ion

mec

hani

sms

are

repr

esen

ted

byor

dere

dbi

–bi

kine

tics.

All

reac

tion

step

sas

sum

edto

bere

vers

ible

.

As

inm

odel

4.Si

nce

the

reac

tion

invo

lves

seve

ral

step

s,th

eva

lue

ofA

(t)

orB

(t)

whe

nsw

itche

don

was

nott

hein

itial

tota

lco

ncen

trat

ion

ofth

em(1

.0).

80

101 k2

AB

X3

X4

X2

X1

I 2

I 1k

3

k4

I 4I 3

k

k

6k

5

I 1an

dI 2

are

repr

esen

ted

bya

sinu

soid

alfu

nctio

nw

ithtim

et.

I 3an

dI 4

are

exte

rnal

inpu

tsof

Aan

dB

,res

pect

ivel

y.k 5

and

k 6ar

ede

grad

atio

nra

teco

nsta

nts.

k 5=

k 6=

I 3(t

)+

I 4(t

).

The

switc

hing

time

ofth

ecy

clic

syst

emca

nbe

regu

late

dby

I 3,I

4,a

sw

ella

sby

I 1an

dI 2

.W

hen

apu

lse

ofI 3

and

I 4is

intr

oduc

ed,o

neca

nse

lect

the

time

ofin

trod

uctio

nin

orde

rfo

rA

orB

tobe

switc

hed-

onth

erea

fter

.In

trod

uctio

nof

I 3or

I 4af

fect

only

the

switc

hing

time

ofA

and

B,b

utno

tthe

osci

llato

rypa

ttern

ofX

2an

dX

4.

The

com

men

tsco

ncer

ning

I 1an

dI 2

are

appl

icab

leto

I 3an

dI 4

asw

ell.

83

11k 2 k 3

BA

X3

X4

X2

X1

I 2

I 1C k 1

k 4

Con

cent

ratio

nsof

I 1,I

2,X

2,a

ndX

4ar

ehe

ldco

nsta

nt.C

isth

ein

putp

aram

eter

.All

the

reac

tions

are

reve

rsib

le.

Aan

dB

evol

vein

time

toa

uniq

uest

eady

stat

edi

ctat

edby

C.S

tead

y-st

ate

conc

entr

atio

nsof

Aan

dB

show

step

func

tions

inre

spec

tto

C.k

2an

dk 3

dete

rmin

eth

est

eepn

ess

ofth

eju

mp.

Whe

nk 2

�=k 3

the

curv

esof

the

stea

dy-s

tate

conc

entr

atio

nsof

Aan

dB

are

nots

ymm

etri

c.

The

syst

emca

nac

tas

ach

emic

alne

uron

inw

hich

the

conc

entr

atio

nof

Aor

Bde

term

ines

the

stat

eof

the

neur

on(fi

reor

quie

scen

t).

The

mat

hem

atic

aleq

uatio

nsfo

rth

ism

odel

also

agre

ew

ithth

eca

seof

batc

hre

actio

ns.H

ere

the

step

I 1→

X1

isa

cata

lytic

reac

tion,

and

the

step

I 2→

X3

isa

nonc

atal

ytic

one.

109,

116

aT

hese

obse

rvat

ions

are

thos

eof

the

pres

enta

utho

rs.

10


Tabl

e1.

2M

odel

sof

Bio

chem

ical

Net

wor

ksB

ased

onth

eC

yclic

Enz

yme

Syst

em

Mod

elN

o.M

odel

Cha

ract

eris

tics

Res

ults

Con

clus

ions

and

App

licat

ions

Com

men

tsa

Ref

s.

1k 3 k 4

Y1

Y2

k 5

Y4

Y3

Y5

Y6

X1

X2

k 1

k 6X

4I 2

I 1

X3

k 2

Cou

pled

cycl

icen

zym

esy

stem

:I1

and

I 2ar

ein

puts

toth

esy

stem

’spo

ols

ofsu

bstr

ate

X1

and

X3,r

espe

ctiv

ely;

sim

ple

mas

sac

tion

kine

tics;

irre

vers

ible

reac

tions

.

Ast

epw

ise

chan

gein

the

stea

dy-s

tate

conc

entr

atio

nof

Yi(

t)is

obse

rved

.The

resu

ltsar

esi

mila

rto

thos

eob

tain

edus

ing

am

onoc

yclic

enzy

me

syst

em(d

escr

ibed

inm

odel

1in

Tabl

e1.

1).

The

syst

emca

nbe

appl

ied

for

exam

inat

ion

ofco

ntro

lmec

hani

sms

ofm

etab

olic

coup

led

enzy

me

syst

ems,

such

asth

esu

gar

tran

spor

tsy

stem

inba

cter

ia.

The

mat

hem

atic

aleq

uatio

nsfo

rth

ism

odel

and

for

the

follo

win

gon

esag

ree

with

the

case

ofba

tch

reac

tions

,in

whi

chth

ere

isno

mas

sflo

win

toor

outo

fth

esy

stem

.How

ever

,I1

and

I 2ca

nnot

bede

fined

asm

ass

flow

sif

volu

me

chan

ges

are

not

cons

ider

ed.

79

2k 1

k 5k 2

AA

´

BB

´

k 3

X1

X2 X

3X

4

X6

X5

k 4 k 6I 3I 1

I 2

Bic

yclic

enzy

me

syst

em:A

,A′ ,

B,a

ndB

′

are

cofa

ctor

s;I 1

,I2,a

ndI 3

are

cons

tant

inpu

ts.

The

stea

dy-s

tate

conc

entr

atio

nsof

Aan

dB

(A,B

)ar

ede

term

ined

byth

em

inim

umin

puta

mon

gI 1

,I2

and

I 3:

I 1m

inim

um:A

,B

=0,

1I 2

min

imum

:A,B

=1,

1I 3

min

imum

:A,B

=1,

0I 1

and

I 3m

inim

um:A

,B

=0,

0

Bas

edon

the

resu

ltspr

esen

ted,

the

basi

clo

gic

func

tions

NO

T,A

ND

,OR

can

bebu

iltus

ing

mon

ocyc

licor

dicy

clic

enzy

me

syst

ems.

The

com

men

tsco

ncer

ning

I 1an

dI 2

are

appl

icab

leto

I 3as

wel

l.

81

(con

tinu

ed)

11


Tabl

e1.

2(c

onti

nued

)

Mod

elN

o.M

odel

Cha

ract

eris

tics

Res

ults

Con

clus

ions

and

App

licat

ions

Com

men

tsa

Ref

s.

3k

1,i

k2,

i

Bi

Ai

X3,

iX

4,i

X2,

iX

1,i

I 2,i

I 1,i

k3,

i

k4,

i

k1,

j

k2,

j

Bj

Aj

X3,

jX

4, j

X2,

jX

1, j

I 2, j

I 1, j

k3,

j

k4,

j

Wi

Wj

The

basi

cel

emen

tis

sim

ilar

toth

eon

eas

sum

edin

mod

el1

inTa

ble

1.1.

The

jthel

emen

tis

assu

med

toha

vean

exci

tato

ryor

inhi

bito

ryaf

fect

onth

eith

elem

enta

ccor

ding

toth

efo

llow

ing

optio

ns:

(a)

Exc

itato

ryin

tera

ctio

ns:A

iaf

fect

sX

1,j

dX

1,j

dt

=(I

1,j+

WiA

i)−

k 1,jX

1,jB

j

(b)

Inhi

bito

ryin

tera

ctio

ns:A

jaf

fect

sX

3,i

dX

3,j

dt

=(I

2,i+

WjA

j)−

k 2,i

X3,

iAi

(c)

Rev

ersi

ble

inte

ract

ions

:bot

hex

cita

tory

and

inhi

bito

ry.

The

num

ber

ofex

cite

del

emen

tsin

sequ

entia

llyco

nnec

ted

syst

ems

isre

late

dpr

opor

tiona

llyto

the

valu

esof

the

exci

tato

ryst

imul

us.W

hen

the

intr

oduc

tion

ofth

eex

cita

tory

stim

ulus

isto

ola

te,i

tcan

notb

etr

ansm

itted

.The

exci

tato

ryst

imul

usis

ampl

ified

toa

cert

ain

limit

and

atte

nuat

eddu

ring

prop

agat

ion.

By

assu

min

gse

vera

lexc

itato

ryst

imul

ian

dva

ryin

gth

eir

freq

uenc

ies,

the

long

-ter

mpo

tent

iatio

nph

enom

enon

can

beob

serv

ed.

Supp

osin

gre

vers

ible

inte

ract

ions

betw

een

two

elem

ents

,aco

ntin

uous

switc

hing

patte

rnof

the

outp

utis

obse

rved

.

One

can

inte

rcon

nect

basi

cel

emen

tsex

cita

tora

lly,

inhi

bito

rally

,or

reve

rsib

lyan

dco

nstr

uctl

arge

netw

orks

.

The

spec

ies

Aian

dA

j

play

the

role

ofef

fect

orfo

ran

othe

ren

zym

icre

actio

n,an

dth

eir

conc

entr

atio

nsar

eno

taff

ecte

dby

this

activ

ity.

84,8

5

12


4E

xter

nals

timul

ion

abr

anch

edse

ries

ofex

cita

tory

inte

ract

ions

,men

tione

din

mod

el3.

98

73

4

high

-fre

quen

cy in

put

W1

W2

W3

W4

W5

W6

W7

W8

low

-fre

quen

cy in

put

5

62

1

Hig

h-fr

eque

ncy

exci

tato

ryst

imul

iwhi

chw

ere

intr

oduc

edto

the

first

elem

entw

asam

plifi

edan

dtr

ansm

itted

toth

eni

nth

elem

ent.

Low

-fre

quen

cyex

cita

tory

stim

uliw

hich

was

intr

oduc

edto

the

fifth

elem

entw

asat

tenu

ated

duri

ngpr

opag

atio

nle

adin

gto

sele

ctiv

eel

imin

atio

nof

syna

ptic

conn

ectio

nbe

twee

nth

ese

vent

han

dfo

urth

elem

ents

.

The

syst

emsh

ows

the

phys

iolo

gica

lph

enom

enon

term

edse

lect

ive

elim

inat

ion

ofsy

naps

esge

nera

llypr

oduc

edas

are

sult

ofa

low

-fre

quen

cytr

ain

ofel

ectr

ical

stim

ulit

oth

esy

naps

es.

85

5E

xter

nals

timul

ion

abr

anch

edse

ries

ofex

cita

tory

inte

ract

ions

,men

tione

din

mod

els

3an

d4

exce

ptin

the

basi

cel

emen

tthe

subs

trat

esX

1,i

and

X3,

ido

nota

ccum

ulat

ean

dar

ere

mov

edw

ithk 5

and

k 6(m

odel

5in

Tabl

e1.

1).

Sele

ctiv

eel

imin

atio

nof

syna

pses

cann

otbe

obse

rved

.

Neu

raln

etw

ork

mod

elco

mpo

sed

offo

rmal

neur

ons

with

outt

heca

paci

tyof

mem

ory

stor

age

cann

otbe

appl

icab

leto

the

stud

yof

info

rmat

ion

proc

essi

ngof

real

neur

alne

twor

ks.

85

(con

tinu

ed)

13


Tabl

e1.

2(c

onti

nued

)

Mod

elN

o.M

odel

Cha

ract

eris

tics

Res

ults

Con

clus

ions

and

App

licat

ions

Com

men

tsa

Ref

s.

6

A

AY

i

β 1

β 2

Yi

f i

k 2

k 2,W

i

k 1, W

i

k 4, W

i

k 4

θ

k 3

outp

ut

Neu

ron

exci

tato

ryin

put s

igna

l

Syn

apse

l

Syn

apse

i

X3

X3,

Wi

k 3,W

i

X1,

Wi

(+)

(+)

X1

k 1

1–A

AW

i1–

AW

i

Wi

θ

AW

1

AY

1

β 1

β 2

Y1

f 1

k 2,W

1

k 3,W

1

k 1,W

1

k 4, W

1

W1

θX

3, W

1

X1,

W1

(+)

(+)

1–A

W1

X1,

Wi:

syna

ptic

effic

acy

for

exci

tato

ryin

putY

iat

syna

pse

iA

(t):

the

outp

utsi

gnal

θ:t

hres

hold

valu

eβ

1,β

2:a

rbitr

ary

coef

ficie

nts

f i:fe

edba

ckfa

ctor

from

outp

utA

f i=

(β1+

β2A

)Yi;

i=

1,2,

...,

nk 3

,k 4

�k 3

,Wi,k 4

,Wi

86

14


7

109

87

3

4in

put 2

inpu

t 1

5

6

2

1

Eac

hel

emen

tis

assu

med

tobe

com

pose

dof

the

basi

csc

hem

ede

scri

bed

inm

odel

6,an

dto

tran

smit

the

sign

alA

i(t)

toth

esu

bseq

uent

one.

Whe

n0

<t<

60,h

igh-

freq

uenc

yin

puti

sin

trod

uced

toth

efir

stel

emen

tand

low

-fre

quen

cyin

puti

sin

trod

uced

toth

efo

urth

.Whe

n60

<t<

120,

low

-fre

quen

cyin

puti

sin

trod

uced

toth

efir

stel

emen

tan

dhi

gh-f

requ

ency

inpu

tis

intr

oduc

edto

the

four

th.

Exc

itato

ryhi

gh-f

requ

ency

stim

uliw

hich

wer

ein

trod

uced

toth

efir

stel

emen

tdur

ing

0<

t<

60ar

eam

plifi

edan

dtr

ansm

itted

succ

essf

ully

toth

ete

nth

elem

ent.

Exc

itato

rylo

w-f

requ

ency

stim

uliw

hich

wer

ein

trod

uced

toth

efo

urth

elem

entd

urin

g0

<t<

60ar

eat

tenu

ated

duri

ngpr

opag

atio

nle

adin

gto

sele

ctiv

eel

imin

atio

nof

syna

ptic

conn

ectio

n.D

urin

g60

<t<

120,

exci

tato

ryhi

gh-f

requ

ency

stim

uliw

hich

wer

ein

trod

uced

toth

efo

urth

elem

entt

urne

dou

tfa

vora

bly,

lead

ing

toth

ere

viva

lof

the

sign

alpa

thfr

omth

efo

urth

toth

ese

vent

h,an

dth

elo

w-f

requ

ency

stim

uli

intr

oduc

edto

the

first

elem

entc

ause

dse

lect

ive

elim

inat

ion

ofsy

napt

icco

nnec

tion

betw

een

the

thir

dan

dth

ese

vent

hel

emen

ts.

Hig

h-fr

eque

ncy

activ

atio

nof

exci

tato

rysy

naps

espr

oduc

esa

long

-las

ting

incr

ease

insy

napt

icef

ficac

y,an

dex

cita

tory

stim

uliw

ithlo

wfr

eque

ncy

are

unfa

vora

ble

for

the

grow

thof

syna

ptic

effic

ienc

y.

86

(con

tinu

ed)

15


Tabl

e1.

2(c

onti

nued

)

Mod

elN

o.M

odel

Cha

ract

eris

tics

Res

ults

Con

clus

ions

and

App

licat

ions

Com

men

tsa

Ref

s.

8A

ssum

ptio

ns1

to6

asin

mod

el6.

The

num

ber

ofsy

naps

esde

note

dby

iis

2.X

1,W

1,X

1,W

2:

syna

ptic

effic

acie

sof

the

test

path

and

cond

ition

ing

path

,res

pect

ivel

y.L

ow-f

requ

ency

test

inpu

tand

noco

nditi

onin

gin

put.

The

test

inpu

tits

elf

has

not

caus

edlo

ng-t

erm

pote

ntia

tion

ofth

esy

napt

icef

ficac

y(X

1,W

1or

X1,

W2).

86

9A

ssum

ptio

ns1

to3

asin

mod

el8.

Low

-fre

quen

cyte

stin

puta

ndhi

gh-f

requ

ency

cond

ition

ing

inpu

tare

posi

tivel

yco

rrel

ated

.Aft

erth

ein

-pha

sein

puts

are

intr

oduc

ed14

times

only

,th

ete

stin

puti

sre

intr

oduc

edan

dth

ech

ange

sin

X1,

W1

and

Aw

ere

inve

stig

ated

.

The

syna

ptic

effic

acy

X1,

W1

ispo

tent

iate

ddu

ring

alo

ngtim

epe

riod

.

86

10A

ssum

ptio

ns1

to3

asin

mod

el9.

Low

-fre

quen

cyte

stin

puta

ndhi

gh-f

requ

ency

cond

ition

ing

inpu

tare

antic

orre

late

d.

The

syna

ptic

effic

acy

X1,

W1

isw

eake

ned

orde

pres

sed,

lead

ing

tolo

ng-t

erm

depr

essi

onof

syna

ptic

stre

ngth

.

86

16


11

X1,

0–A

0A

0X

3.0

w0

w1

w2

wi

w0

w1

w2

wi

0th

laye

r

1st l

ayer

exte

rnal

tim

e-va

rian

tan

alog

sig

nal (

Ext

In)

com

para

tive

part

mul

tila

yere

dst

ruct

ure

2nd

laye

r

ith

laye

r

X1.

1–A

1A

1X

3.1

X1.

2–

A2

A2

X3.

2

α 2α 1α 0 α iX

1.i

–A

iA

iX

3.i

αi:

thre

shol

dva

lue

for

cutti

ngof

fth

esi

gnal

s.A

tthe

0th

laye

r,ex

tern

alan

alog

sign

alE

xtIn

(t)

and

outp

utof

the

first

laye

rA

1(t

)ar

ein

trod

uced

toX

1,0

and

X3,

0re

spec

tivel

y.O

utpu

tsof

the

(i−

1)th

laye

r,ar

eth

ein

puto

fth

eith

laye

r.T

heex

tern

alsi

gnal

,Ext

In(t

),is

repr

esen

ted

bya

step

func

tion

with

time

t:1.

0E

xtIn

(t)

1020

3040

5060

7080

90

αi=

1,i=

0,1,

2,..

.,6.

The

time

cour

ses

ofE

xtIn

(t)

and

A1(t

)ar

eal

mos

tthe

sam

eex

cept

for

the

osci

llato

rybe

havi

orof

A1(t

).A

0(t

)be

have

sas

aco

ntro

lvar

iabl

ew

hich

chan

ges

inva

lue

soas

tom

inim

ize

the

func

tion

J:J

=∫

t f t 0[E

xtIn

(t)−

A1(t

) ]2

dt

Aft

erth

ese

cond

laye

rth

etim

eco

urse

sof

Ai(t

)ar

efil

trat

edby

the

thre

shol

dva

lue

αi/2

and

grad

ually

settl

edto

atw

o-st

ate,

havi

ngth

eva

lues

0an

d1.

0on

ly,a

ndha

ving

ahi

gher

sign

al-t

o-no

ise

ratio

.

The

bioc

hem

ical

neur

onha

san

othe

rro

leas

a“t

rans

duce

r”of

exte

rnal

anal

ogsi

gnal

sto

impu

lse

sign

als,

whe

reth

eex

tern

alsi

gnal

sar

ere

ceiv

edat

the

rece

ptiv

efie

ldan

dtr

ansd

uced

toim

puls

esi

gnal

sby

cutti

ngof

fat

ace

rtai

nth

resh

old

valu

e.

86

(con

tinu

ed)

17


Tabl

e1.

2(c

onti

nued

)

Mod

elN

o.M

odel

Cha

ract

eris

tics

Res

ults

Con

clus

ions

and

App

licat

ions

Com

men

tsa

Ref

s.

12A

ssum

ptio

ns1

to3

asin

mod

el11

.The

exte

rnal

anal

ogsi

gnal

,Ext

In(t

),ha

sa

unif

orm

rand

omva

lue

betw

een

0an

d1.

Ext

In(t

)10

αi=

1.8,

i=0,

1,2,

...,

5,α

6=

1.0.

Ext

erna

lran

dom

inpu

tsig

nals

are

filtr

ated

byth

eth

resh

old

valu

eα

i/2=

0.9

and

tran

sfor

med

into

impu

lse

sign

als.

By

chan

ging

the

αi

valu

es,a

nytim

e-va

rian

text

erna

lan

alog

sign

alca

nbe

filtr

ated

byan

arbi

trar

yth

resh

old

valu

e.

86

13C

j

Ci,k

Ci

Ck,

j

Ci,

j

Ci,l

I* 1,j

I* 2,i

I* 1,i

X* 4,

i

X* 2,

i

X* 4,

jI* 2,

j

X1,

jX

2,j

X3,

j

X3,

i

X1,

i

Aj

Bj

Bi

Ai

Ei,

j

Ek,

i

Eac

hne

uron

isas

inm

odel

11in

Tabl

e1.

1.N

euro

nsar

ech

emic

ally

dist

inct

.The

effe

ctof

one

neur

onon

the

othe

rsis

cont

aine

din

Ci.

Neu

ron

iis

affe

cted

byne

uron

sja

ndk.

Aj

and

Bjar

eac

tivat

ors

ofan

enzy

me

Ei,

jto

form

Ci,

j.T

heen

zym

e-ac

tivat

orre

actio

nis

fast

and

ateq

uilib

rium

.A

j,A

k:in

puts

;Ci:

outp

ut;

Ei,

j�

1an

dC

i=

∑jC

i,j.

For

exci

tato

ryco

nnec

tions

:

(Ei,

j+

Aj�

Ci,

j):

Ci,

j=

E0 i,

j

1+1

kAj

For

inhi

bito

ryco

nnec

tions

:

(Ei,

j+

Bj�

Ci,

j):

Ci,

j=

E0 i,

j

1+1

k (A

0−A

j)

whe

rek

isth

eeq

uilib

rium

cons

tant

.By

adju

stin

gth

eva

lues

ofE

0 i,j

and

k,ne

uron

ican

perf

orm

logi

cop

erat

ions

onth

est

ate

ofne

uron

sja

ndk.

Var

ious

type

sof

logi

cga

tes

can

beco

nstr

ucte

dw

hen

the

thre

shol

dva

lue

for

Ci

isde

fined

as1:

AN

D,

OR

,NO

R,A

jA

ND

NO

TA

k.

Con

cent

ratio

nsof

Ai

are

seta

tt=

0an

dth

eou

tput

isob

tain

edat

stea

dyst

ate.

No

time

depe

nden

ceis

cons

ider

ed.

109

18


14C

j

Ei,

j

Ek,

i

X3,

i

Ci,l

Ck,

i

Xl,i

Ci

Ci,

j

Ci,k

Bj

Ai

Bj

ε´

´ε

Aj

Bi

Ai

X1,

j

I 2* ,i

I 2* ,j

I* 1,j

I* 1,i

X* 2,

j

X* 2,

i

X* 4,

i

X* 4,

jX

3,j

Ass

umpt

ions

1to

5as

inm

odel

13.T

hest

ate

ofth

ech

emic

alne

uron

isal

low

edto

chan

geon

lyat

disc

rete

times

,dic

tate

dby

anau

tono

mou

sly

osci

llatin

gca

taly

stε.T

heco

ncen

trat

ion

ofε

isve

rysm

alle

xcep

tdur

ing

shor

tint

erva

ls.ε

inte

ract

sw

ithA

jor

Bjof

each

neur

on,a

ndra

pid

equi

libri

umoc

curs

whe

nits

conc

entr

atio

nis

larg

e.C

i,jca

nbe

activ

ated

/in

hibi

ted

bym

ore

than

one

spec

ies:

Ei+

A′ j

�C

i

Ei+

A′ k

�(E

iA′ k

)

By

chan

ging

the

num

ber

ofne

uron

s,th

efo

rmof

the

conn

ectio

nsbe

twee

nth

em,

and

the

defin

ition

sth

eco

ncen

trat

ions

that

repr

esen

tinp

uts

and

outp

uts

toth

esy

stem

,var

ious

finite

-sta

tem

achi

nes

can

besp

ecifi

ed.

Abi

nary

deco

der,

abi

nary

adde

r,an

da

stac

km

emor

yca

nbe

built

.

110

a The

seob

serv

atio

nsar

eth

ose

ofth

epr

esen

taut

hors

.

19


Tabl

e1.

3M

odel

sof

Oth

erB

ioch

emic

alSy

stem

s

Mod

elN

o.M

odel

Cha

ract

eris

tics

Res

ults

Con

clus

ions

and

App

licat

ions

Com

men

tsa

Ref

s.

1K

9

X6

X5

X1

X2

X3

X4

Ea

Ei

k 2

k 5

y 3 y 2

k 3

E0

Ea

K7

K6

K8

k 1

k 4

y 1

y

x

(+)

(+)

(+)

(+)

Ea:a

ctiv

een

zym

eE

i:in

activ

een

zym

ex,

y:ex

cita

tory

and

inhi

bito

ryfa

ctor

s,re

spec

tivel

y;bo

thfa

ctor

sre

mai

nco

nsta

ntdu

ring

the

reac

tion

E0:a

nen

zym

ew

ithco

nsta

ntac

tivity

All

the

reac

tions

are

first

orde

r.In

puts

:xan

dy;

outp

uts:

x 1an

dx 2

.

The

stea

dy-s

tate

conc

entr

atio

nsof

Ea

and

Eish

owst

epfu

nctio

nsw

ithre

spec

tto

the

valu

eof

x/y:

Ea(x

,y)

=[0

;x≥

y,1;

x<

y ]E

i(x,

y)=

[1;x

≥y,

0;x

<y ]

The

conc

entr

atio

nsof

x 1an

dx 2

chan

gein

asi

mila

rw

ayex

cept

for

the

appe

aran

ceof

acu

rved

corn

erw

hose

mag

nitu

dese

ems

tode

pend

onth

eco

ncen

trat

ion

ofE

0.

The

enzy

mic

conj

ugat

esy

stem

desc

ribe

dca

nre

aliz

eth

etw

o-fa

ctor

mod

el.

The

syst

emw

asin

clud

edas

aco

ntro

lele

men

tin

afe

edba

cksy

stem

.In

this

case

,asp

ecifi

cco

nfigu

ratio

nof

the

cont

role

lem

entc

anm

aint

ain

the

valu

eof

the

end

prod

uct

ata

desi

red

leve

l.

76

2A

∗E

1−→

B−→

P∗T

heco

ncen

trat

ions

ofA

and

Par

ehe

ldco

nsta

nt.T

heco

nver

sion

ofB

toP

follo

ws

Mic

hael

is–M

ente

nki

netic

s.I 1

and

I 2:t

wo

exte

rnal

effe

ctor

sof

E1

Out

put:

stea

dy-s

tate

conc

entr

atio

nof

BIn

put:

conc

entr

atio

nof

I 1an

dI 2

.

Thr

eedi

ffer

entm

echa

nism

sfo

rth

eki

netic

sof

E1

can

beus

edto

cons

truc

tthr

eedi

ffer

ent

logi

cga

tes:

AN

D,O

R,a

ndX

OR

.The

degr

eeof

coop

erat

ivity

inth

ebi

ndin

gof

E1

and

I 1or

I 2de

term

ines

the

stee

pnes

sof

the

tran

sitio

nfr

omlo

wto

high

stea

dy-s

tate

conc

entr

atio

nsof

B.

115

20


3X

* 3X

* 1X

* 2

E1

E3

BC

A

I 1X

* 4

E2

E4I 2

E1

toE

4ar

eir

reve

rsib

leen

zym

esth

atfo

llow

Mic

hael

is–M

ente

nki

netic

s.E

1an

dE

2ar

ein

hibi

ted

byth

eno

ncom

petit

ive

inhi

bito

rsI 1

and

I 2.C

once

ntra

tions

ofX

iar

ehe

ldco

nsta

nt.I

nput

s:co

ncen

trat

ions

ofI 1

and

I 2.O

utpu

t:st

eady

-sta

teco

ncen

trat

ion

ofA

.The

conc

entr

atio

nsof

the

spec

ies

mar

ked

with

(*)

are

fixed

.

Whe

nno

inhi

bito

rsar

epr

esen

t,th

est

eady

-sta

teco

ncen

trat

ions

ofA

,B

,and

Car

eeq

uiva

lent

.Whe

non

eof

the

inhi

bito

rsis

pres

ent,

the

mat

eria

lis

appo

rtio

ned

betw

een

Aan

don

eof

the

othe

rsp

ecie

s.W

hen

both

inhi

bito

rsar

epr

esen

t,co

nver

sion

ofA

toth

eot

her

spec

ies

isbl

ocke

d.T

hest

eepn

ess

oftr

ansi

tion

betw

een

the

high

esta

ndlo

wes

tco

ncen

trat

ions

ofA

,the

valu

esof

thes

eco

ncen

trat

ions

,and

the

sym

met

ryof

the

resp

onse

depe

ndon

the

kine

ticpa

ram

eter

sof

the

enzy

mes

.

The

syst

emca

nfu

nctio

nas

alo

gica

lAN

Dga

te.

115

4I 5

*X

5

E5

E6

*X

6

DE E

5,a

ndE

6ar

eir

reve

rsib

leen

zym

esth

atfo

llow

Mic

hael

is–M

ente

nki

netic

s.E

5is

inhi

bite

dby

the

nonc

ompe

titiv

ein

hibi

tor

I 5.C

once

ntra

tions

ofX

i

are

held

cons

tant

.Inp

uts:

conc

entr

atio

nsof

I 5.

Out

put:

stea

dy-s

tate

conc

entr

atio

nof

D.T

heco

ncen

trat

ions

ofth

esp

ecie

sm

arke

dw

ith(*

)ar

efix

ed.

The

conc

entr

atio

nof

Dis

high

(low

)w

hen

the

conc

entr

atio

nof

I 5is

low

(hig

h).T

hest

eepn

ess

oftr

ansi

tion

betw

een

the

high

est

and

low

estc

once

ntra

tions

ofD

and

the

valu

eof

this

conc

entr

atio

nde

pend

onth

eki

netic

para

met

ers

ofth

een

zym

es.

The

syst

emca

nfu

nctio

nas

alo

gica

lNO

Tga

te.

115

(con

tinu

ed)

21


Tabl

e1.

3(c

onti

nued

)

Mod

elN

o.M

odel

Cha

ract

eris

tics

Res

ults

Con

clus

ions

and

App

licat

ions

Com

men

tsa

Ref

s.

5I 1

I 2X

5,* 1

X* 3

X5,

* 3X

6,* 3

X* 2

X* 4

X* 1

E5,

1

E6,

1

X6,

* 2X

5,* 2

X6,

* 1

D1

E1

E5,

3

E6,

3

D3

E3

E1

E3

E2

E4

AB

C

E5,

2

E6,

2

E2

D2

Thr

eeN

OT

gate

s(m

odel

4),a

ndon

eA

ND

gate

(mod

el3)

.Inp

uts:

conc

entr

atio

nsof

I 1an

dI 2

.O

utpu

t:st

eady

-sta

teco

ncen

trat

ion

ofD

3.

The

outp

utre

ache

sits

max

imum

valu

ew

hen

one

ofth

ein

puts

orbo

thof

them

are

pres

enti

nsi

gnifi

cant

amou

nts.

The

outp

utis

min

imiz

edw

hen

neith

erin

put

chem

ical

ispr

esen

t.

The

syst

emca

nfu

nctio

nas

alo

gica

lOR

gate

.

115

aT

heob

serv

atio

nsar

eth

ose

ofth

epr

esen

taut

hors

.

22


KINETIC CHARACTERISTICS OF CYCLIC ENZYME SYSTEMS 23

The works presented in Tables 1.1 to 1.3 [76–86,109–122] deal only withtheoretical aspects of the enzymic biochemical devices, and the biochemicaldevices were not carried into practice. Moreover, Okamoto [85] suggestsusing silicon technology instead of biomaterials for practical implementationof the device based on the cyclic enzyme system.

This study is also based on the cyclic enzyme system, but its leading conceptis to accomplish practical implementation of this system using biomaterials.In this respect, the analytical models developed here are related to severalbiochemical reactors in which enzymic reactions take place. This practicalapproach cannot be found in the models reviewed [76–86,109–122].

1.5 OSCILLATIONS IN BIOCHEMICAL SYSTEMS

Many oscillatory patterns can be found in biological systems [123–126]. It isgenerally recognized in engineering that encoding information in a frequencyprovides resistance to degradation by noise and enhanced precision of control.Rapp [124] suggested that many biological oscillations can be envisaged toreflect the biochemical implementation of this control strategy.

Intracellular communication often proceeds in a pulsatile, rhythmic manner[126]. Moreover, an increasing number of hormones are found to be secretedin a pulsatile manner, and the physiological efficiency of these signals appearsto be closely related to their frequency [126]. Based on this understanding, anumber of classes of drug therapies have been shown to require a periodic,pulsatile regimen of delivery for efficacy or optimization [131], and severaldelivery strategies have been proposed to respond to this need [127–131].

1.6 KINETIC CHARACTERISTICS OF CYCLICENZYME SYSTEMS

Many examples of enzymatic cyclic systems have been developed in prac-tice [87–107]. These systems can be utilized to construct the biochemicaldevice proposed by Okamoto et al. [76–86]. The kinetic properties of fiveenzymes that catalyze reactions in which cofactors are required, and there-fore can participate in a cyclic enzyme system, are summarized in Table 1.4[132–144]. These enzymes are glucose-6-phosphate dehydrogenase (G6PDH,E.C. 1.1.1.49), glutathione reductase (GR, E.C. 1.6.4.2), glucose dehydroge-nase (GDH, E.C. 1.1.1.47), l-lactate dehydrogenase (LDH, E.C. 1.1.1.27),and alcohol dehydrogenase (ADH, E.C. 1.1.1.1).


Tabl

e1.

4K

inet

icPr

oper

ties

ofE

nzym

esU

sed

inC

yclic

Syst

ems

Enz

yme

Proc

ess

Km

valu

esC

ondi

tions

Rea

ctio

nM

echa

nism

Oth

erFi

ndin

gsR

efs.

G6P

DH

From

brew

er’s

yeas

t

Glu

cose

-6-p

hosp

hate

+N

AD

P→

gluc

onat

e-6-

phos

phat

e+

NA

DPH

Km

,G6P

=6.

9×

10−5

MK

m,N

AD

P=

3.3

×10

−5M

Inth

epr

esen

ceof

MgC

l 20.

01M

:K

m,G

6P=

5.8

×10

−5M

Km

,NA

DP

=2.

0×

10−5

M

0.06

3M

Tri

sbu

ffer

,pH

8at

25◦ C

The

enzy

me

isin

hibi

ted

byN

AD

PH,w

hich

isco

mpe

titiv

ew

ithN

AD

P.T

hein

hibi

tion

cons

tant

KI=

2.7

×10

−5M

.T

here

actio

nis

reve

rsib

lean

dth

eeq

uilib

rium

cons

tant

is6

±0.

7×

10−7

Mat

28◦ C

.

132

From

Can

dida

util

isK

m,G

6P=

2.3

×10

−4M

Km

,NA

DP

=6.

7×

10−5

M93

mM

glyc

ine–

NaO

Hbu

ffer

pH9.

1,al

soco

ntai

ning

9.3

mM

MgC

l 2an

d0.

93m

ME

DTA

133

GR Fr

omba

ker’

sye

ast

Oxi

dize

dgl

utat

hion

e+

NA

DPH

→re

duce

dgl

utat

hion

e+

NA

DP

Km

,GSS

G=

6.1

×10

−5M

Km

,NA

DPH

=7.

6×

10−6

MPh

osph

ate

buff

er,p

H7.

6at

25◦ C

134

From

sea

urch

ineg

gK

m,G

SSG

=1

×10

−4M

Km

,NA

DPH

=5

×10

−6M

0.1

Mpo

tass

ium

–ph

osph

ate

buff

er,

pH7.

2,co

ntai

ning

1m

ME

DTA

Add

ition

of1

mM

ED

TAin

crea

ses

the

enzy

me

activ

ity.

Furt

her

addi

tion

ofE

DTA

show

sno

furt

her

effe

ct.

135

24


GD

H From

beef

liver

Glu

cose

+N

AD

→gl

ucon

o-δ-l

acto

ne+

NA

DH

Km

,NA

D=

4.3

×10

−6M

0.05

Mph

osph

ate

buff

er,p

H7.

6at

21–2

2◦ C

The

reac

tion

isre

vers

ible

and

the

equi

libri

umco

nsta

ntis

2.9–

3.3

×10

−7M

.

136

pHK

m,g

luco

se(M

)

6.28

34.9

×10

−2

7.00

3.13

×10

−2

8.92

32.6

×10

−2

From

oxliv

erK

m,g

luco

se=

15×

10−2

MK

m,N

AD

=1.

5×

10−5

M0.

05M

phos

phat

ebu

ffer

,pH

7T

here

actio

nis

reve

rsib

lean

dth

eeq

uilib

rium

cons

tant

is30

×10

−7M

atpH

7.

137

Km

,glu

cose

=7

×10

−2M

0.05

Mph

osph

ate

buff

er,p

H7.

6

From

ratl

iver

Km

,glu

cose

=0.

3–0.

7M

Km

,NA

D=

0.38

µM

Km

,NA

DP

=0.

45µ

M

Phos

phat

ebu

ffer

,pH

8.2

138

From

Bac

illu

sM

egat

eriu

mK

m,g

luco

se=

47.5

×10

−3M

Km

,NA

D=

4.5

×10

−3M

Ki,

NA

D=

69×

10−5

M

Ace

tate

–bor

ate

buff

er,p

H9

at25

◦ C

Ord

ered

Bi–

Bi

139

LD

H From

rabb

itm

uscl

e

Pyru

vate

+N

AD

H→

lact

ate

+N

AD

Km

,pyr

uvat

e=

5.2

×10

−5M

140

(con

tinu

ed)

25


Tabl

e1.

4K

inet

icPr

oper

ties

ofE

nzym

esU

sed

inC

yclic

Syst

ems

(con

tinu

ed)

Enz

yme

Proc

ess

Km

valu

esC

ondi

tions

Rea

ctio

nM

echa

nism

Oth

erFi

ndin

gsR

efs.

LD

H From

rabb

itm

uscl

e

Pyru

vate

+N

AD

H→

Lac

tate

+N

AD

Km

,pyr

uvat

e=

15×

10−6

MK

m,N

AD

H=

35×

10−7

MK

PN=

6.5

×10

−12

M2

0.05

Mso

dium

phos

phat

ebu

ffer

,pH

6.8

at25

◦ C

Ord

ered

Bi–

Bi.

Vm V

=1

+K

m,P

[P]

+K

m,N

[NA

DH

]

+K

PN

[P][

NA

DH

]

The

reac

tion

isre

vers

ible

and

the

equi

libri

umco

nsta

ntis

2.76

×10

−12

Mat

pH7

and

25◦ C

.Pyr

uvat

eis

anin

hibi

tor.

141

Km

,pyr

uvat

e=

1.64

×10

−4M

Km

,NA

DH

=1.

07×

10−5

MK

PN=

1.38

×10

−9M

2

0.25

Mph

osph

ate

buff

er,p

H6.

8at

25◦ C

Pyru

vate

and

lact

ate

inhi

bitt

heen

zym

ew

ithK

I,py

ruva

te=

2.02

×10

−4M

KI,

lact

ate=

0.20

9M

142

From

Lac

toba

cill

uspl

anta

rum

Pyru

vate

+N

AD

H→

lact

ate

+N

AD

Km

,pyr

uvat

e=

3.7

×10

−4M

0.1

MT

ris

buff

er,p

H8

143

AD

H From

bake

r’s

yeas

t

Eth

anol

+N

AD

→ac

etal

dehy

de+

NA

DH

pHK

m,N

AD

(mM

)K

m,E

th.

(mM

)K

i,N

AD

(mM

)0.

01M

acet

icac

id–s

odiu

mac

etat

ebu

ffer

,pH

4.9

Ord

ered

Bi–

Bi

The

reac

tion

isre

vers

ible

and

the

equi

libri

umco

nsta

ntis

0.98

×10

−11

Mat

25◦ C

144

4.9

0.22

410

70.

390

5.95

0.10

643

0.34

00.

1M

phos

phat

ebu

ffer

,pH

5.95

,7.

05,8

.17.

050.

108

260.

270

8.1

0.11

818

.50.

385

8.9

0.15

010

0.86

00.

01M

glyc

ine-

NaO

Hbu

ffer

,pH

8.9,

9.9

9.9

0.20

05

2.40

26

introduction and literature survey copyrighted … · 2020. 2. 17. · a living organism, operates...

Documents