notes+to+bio115+l1+2016

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Notes to Bio115 , Winter 2016, Lecture 1

Hinrich Boeger

Introduction

This lecture will provide you with an introduction into molecular biology and, as the title

indicates, we shall focus on eukaryotes whenever necessary, although many fundamentalinsights have been attained by research on bacteria. Indeed, the molecular biology of bacteria

and eukaryotes is essentially the same ! despite many significant differences ! suggesting a

common ancestor for all of life on earth.

I shall not follow any particular text book, for I suppose that you are perfectly capable of

reading a text book on your own, without me. Of course, essentially all of the material presented here is covered by any text book on molecular biology. Several good text books are

available ! e.g . ‘ Molecular biology of the cell ’ by Alberts et al ., ‘ Molecular biology of the gene’ by Watson et al ., or ‘ Molecular biology, principles and practice’ by Cox et al .;‘ Molecular biology’ by Weaver is a rich source for many historical experiments. And I would

like to encourage you to also read the relevant chapters in any text book of your choice;different books work for different people. This lecture, however, is mine; it thus presents

molecular biology as I understand it, from my point of view. All slides of this lecture togetherwith extensive notes will be available via your eCommons account (Resources).

There are four major themes that run through this lecture. Three of which stress thatbiology is chemistry. The enzymes of molecular biology catalyze essentially two types of

chemical reaction mechanism. Two additional principles are important for understanding the biochemistry of these enzymes: thermodynamic coupling and kinetic proofreading ; both will

require us to review some principles of thermodynamics.

The fourth theme is philosophical; namely ! and this is the critical insight Karl R.

Popper’s (1902-1994) ! that knowledge grows by inventing explanatory conjectures andtesting them, logically and experimentally; experimental observations tell us which theoretical possibilities are false; i.e. we learn from experience by trial and error, by refutation of our

mistaken assumptions ('critical rationalism').

Molecular biology has been extraordinarily successful in its first two decades precisely

because many of its founders sought explanatory conjectures, and refutations; they proceededin a manner contrary to inductivism, the mistaken but widespread idea that scientific theories

grow out of and are justifiable by the methodical collection of data (see below). This is the philosophical thesis of my lecture.

I thus hope that this lecture will also inspire you to reflect on questions such as these:What is science? What are its aims? How does it work? What are the logical condition for the

growth of knowledge? The consideration of such questions is virtually absent from scientificcurricula and textbooks. I believe this is a great shortcoming of science education. The few

remarks that I will be able to make in this lecture will hardly suffice to rectify this deficit. Butthere is nothing that stops you from continuing on this path on your own. I hope you will.

Slide 4

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Inductivism. Common sense holds that the human mind, at least initially, is a blank slate, anempty bucket. Knowledge enters it by observation. Truth is manifest to everyone who is

willing and able to see it. Scientific laws or theories are discovered by repeated observation;and therefore reducible to observation. Observed regularities are extended to instances of

which we have no experience; i.e. it is claimed that the future is like the past. And the more

often we have made a specific observation in the past, the more confident we may be that thesame observation will be made in the future. In short, empirical evidence provides(probabilistic) support for conclusions that go beyond the available evidence. This notion is

sometimes called inductive probability or inductive logic. It aims at the verification oftheories (thus, ‘positivism’).

The notion of inductive probability was first introduced by Pierre-Simon Laplace (1749-1827). He calculated the probability that the sun will rise tomorrow, given that it has risen n

number of days in the past. According to Laplace, this probability is given by (n +1) / (n + 2)

(Laplace’ rule of succession).

Despite its popularity, inductivism is a mistaken. The reasons are many:

(i) Truth is not manifest whatsoever. Rather, truth is difficult to attain; and even if wewere in its possession, we have no means of knowing so. All observations, including allmeasurements, are impregnated by theory, they are ‘theory-laden’; empirical observations can

be, and often are, false. Thus, inductivism fails before taking its first step (Popper, 1972). Themistaken belief that truth is manifest (the common sense theory of knowledge) begs for

authoritarian answers, for it has to explain falsity (Popper, 1963).(ii) Even if our observations were unproblematic, scientific theories cannot be justified by

empirical evidence. The reason is simple: Proof would require an infinite number ofobservations; but our observations are always finite; and they pertain to the past and present,

but never the future.(iii) Positivists address this latter problem by claiming that repeated past observation

justifies our expectation of future observations (of the same kind). However, this principle ofinduction is untenable. It leads to absurd result. I mention only one here: that I will be alive

tomorrow is, according to Laplace, more probable today than it was 10 years ago, for I have

observed repeatedly over those 10 years ! indeed without exception ! that I was alive the

following day. As desirable as this conclusion might be, nobody seriously believes thisconclusion to be true. The same argument would have applied to many people who are now

dead, revealing that the argument is false. The notion that the future is like the past has beenrefuted many times. The rule of succession, applied to the probability of the sun’s ascension

tomorrow, yields a prediction that contradicts modern physics.(iv) The most important objection against inductivism, perhaps, is that inductivism does

not seek explanation, but data. However, data, no matter how many, don’t explain anything;

theories do, namely the data.Thus, theories can neither be proved or justified, in any way or by any number of

observation. As explanations theories always transcend the data and therefore cannot be

obtained from observation. Theories are inspired guesses. As such, neither observation norreason may be regarded as sources of our knowledge or theories (Popper, 1963). Even

regularities, the object of discovery of induction, are generally observed only after they have

been anticipated ! what we see, or not, is a function of our conscious and unconscious

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expectations. The latter are often innate. Induction, the formation of a believe by repetition, isa myth (Popper, 1972).

If empirical evidence cannot be used to verify hypotheses, or attain theories, then, what is

its role in science? After all, we think of science as a discipline in which empirical

observation play an important role. The solution of this problem is 'critical rationalism'.

Critical rationalism. Briefly, critical rationalism holds that we acquire knowledge by

inventing theories and criticizing them, logically and empirically (by experimental testing), inorder to force decisions between them. Empirical observations do not tell us which theories

are true, but which ones are false. “The growth of knowledge ! or the learning process ! isnot a repetitive or a cumulative process but one of error-elimination. It is Darwinian selection,

rather than Lamarckian instruction” (Popper, 1972).Thus, in as much as our aim, qua scientists, is to attain knowledge, we must propose

explanatory theories and device experimental tests that may falsify them. Becauseexplanations transcend the data, they are generally independently testable; i.e. they allow for

predictions other than the observations that they were originally invented to explain.Only those hypotheses or theories contribute to the growth of knowledge that allow for

the deduction of consequences that potentially can stand in conflict with experimentalobservations; hypotheses must be falsifiable or testable. The larger the set of its predictions

that may clash with observation (the ‘empirical content ’ of a theory), the better the theory.Empirical evidence contributes to the growth of knowledge only by refutation of theoretical

possibilities; we learn from experience by refutation.Falsification, contrary to verification (proof), requires no more but a finite number of

observations that contradict theoretical expectation. (Logically, a single observation issufficient for refutation.) From false conclusions follows the falsehood of one or more their

premises (modus tollens of logic). We must seek falsification, which is possible, and not

verification, which is not.A theory that has withstood critical testing is said to have been corroborated . We mayaccept a corroborated theory, but only tentatively, for it too may be shown to be false and may

be overthrown by a better theory in the future, namely a theory that explains more (because ithas a larger empirical content) and corrects the errors of the earlier theory. (Correction may

even include earlier empirical observations.) All of human knowledge, including textbookknowledge, is conjectural; it consists, at best, of hypotheses that have ‘proved their mettle’,

that have been corroborated experimentally (Popper, 1963).

Against this theory it has been objected that theories cannot be falsified either, because of

the conjectural nature of our observations. (Observations are theory-laden.) If a conflict arises between theoretical prediction and experimental observation it is not known whether our

theory is false, or our observation, or any other ‘background knowledge’ that we used in the process (e.g . the assumption that the scientist who conducted the experiment is competent as

well as honest). Thus, experiments always test the whole system of human knowledge, ratherthan any specific theory. (This is sometimes called the ‘Duhem-Quine problem’.) This

criticism is countered by approaching a scientific problem with two or more competingtheories, i.e. with a plurality of theoretical solutions. Then our experimental tests decide

between competing systems that differ only over the theories at stake (Popper, 1963). If the

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predictions of both theories, say A and B, disagree with the data, then we will have tocritically reanalyze the background knowledge (e.g . the data). But if our test results conform

to the prediction of theory A, but not B, then we consider B refuted, rather than our background knowledge. Thus there may be no falsification before the emergence of a better

theory (Lakatos, 1970). This is always so in the case of probabilistic theories; refutation and

corroboration are closely linked (Boeger, 2014). References

Boeger, H. (2014). Nucleosomes, transcription, and probability. Molecular biology of the cell

25, 3451-3455.

Lakatos, I. (1970). Methodology of Scientific Research Programmes; in Criticism and the

Growth of Knowledge; edit. Lakatos, I. Musgrave, A. (Cambridge University Press).

Popper, K.R. (1963). Conjectures and refutations (New York: Routledge Classics).

Popper, K.R. (1972). Objective knowledge (Oxford: Clarendon Press).

Slide 5 Nothing in molecular biology makes sense without an appreciation of the function of

enzymes ! almost all of which are proteins ! and their structural properties. I shall therefore begin this lecture with considerations about catalysis, and protein structure. Since we start

with proteins rather than DNA, we shall follow, to some extent, the central dogma (shown inthis slide) in reverse order, i.e, from proteins to genes. This order also roughly traces the

historical development of molecular biology.

Slide 6As you will have learned in your cell biology class, all of live is composed of cells, either

of solitary cells, or of many specialized cells derived from a single cell by cell division. (Thisfundamental biological theory was first suggested by the physiologists Theodor Schwann in

1839.)

This lecture is dedicated mostly to one particular type of cell, the eukaryotic cell (gr. !" – proper, !"#$%& – nucleus). As you already know, eukaryotic cells are distinguished from their

prokaryotic relatives by a set of characteristic features; for instance, the cell nucleus fromwhich they derive their name, chromosomes, the Golgi apparatus, mitochondria, the

centrosome, mitosis, and meiosis (sexual reproduction), exo- and endocytosis. The oldestfossils considered eukaryotic cells are about 1.2 billion years old (the earth is about 4.6 billion

years old, and life on earth is older than 3.5 billion years).

Slide 7What do we mean by ‘molecular biology’ ? There are two rather different notions of

molecular biology. Both of them have existed side by side from the very beginning. The firstnotion is very general in character: Molecular Biology is the attempt to understand any

biological problem at the level of atoms and molecules. This broad definition offers little helpto provide us with a central theme for our lecture. Furthermore it may be asked whether it is

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reasonable to examine all biological problems at the level of atoms and molecules.Historically molecular biology has first and foremost been concerned with a specific

molecular problem: what is the chemical nature of biological information and how is itexpressed? The most fundamental aspects of this problem had been solved no later than the

early 1960ies, and many molecular biologists started to apply their tools and paradigms to

other biological problems. By now, Francis Crick’ s tongue in cheek definition of molecular biology as “everything that a molecular biologist is interested in”, has become reality.In parallel, however, the project of understanding at ever greater depth the molecular

mechanisms that govern the flow of biological information has also continued unabated.For the purpose of this lecture, we will adopt the following, narrower, description of

molecular biology: (next slide).

Slide 8 Molecular biology is concerned with the molecular structures and mechanisms that carry

biological information and govern its flow from the gene into the cytoplasm, and from generation to generation.

Central to this description is the notion of biological information. But, what does thisadmittedly vague notion mean? As we shall see, the pursuit into the chemical foundations of

biological inheritance eventually revealed that biological information is ‘sequenceinformation’ .

Slide 9

The most fundamental property of living beings is their ability to reproduce with onlyminor variations, on the basis of information that is bequeathed from cell to cell, and

generation to generation, in the form of distinct units called genes. Living beings are thus notonly subject to the laws of physics and chemistry, but also to the vagaries of history, as the

information is subject to random changes and selection ( Darwin's theory of evolution). This isa unique feature of life, which distinguishes it from unanimated matter.

The picture of this slide shows an adult fruit fly, Drosophila melanogaster . Research onthis little fly, about 2.5 mm in length, has fundamentally shaped our understanding of the

molecular biology of pattern formation of multicellular organisms, including the human being, and we will again return to Drosophila later in this lecture.

As any living being, Drospophila is endowed with elaborate purposive structures; i.e.

structures that serve a specific purpose, but ultimately one goal: reproduction. ! Jacques

Monod (1910-1976) called reproduction the “essential teleonomic project” (gr. #!$%& – end,

purpose), Francois Jacob (*1920), the “dream of all living beings to become two”. ! For instance, Drosophila bears two large complex eyes, each composed of 800

ommatidia, with each ommatidium containing eight photoreceptor cells for visual perception.

About two thirds of the Drosophila nervous system is dedicated to its visual system. On thesecond of its three thorax segments it carries two wings that beat about 220 times per secondduring flight. The following thorax segment is endowed with halteres, little rotating knobs

that serve as stabilizers of flight, and are a unique feature of all flies. Each one of the threethorax segments furthermore carries one pair of legs for walking. All these structures

essentially serve the task of seeking a mating partner.After fertilization the female lays about 400 eggs into rotten fruit or decaying mushrooms

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using a tube like structure, the ovipositor, at the end of its abdomen. Embryogenesis takes nolonger than 24 hours after which a larva hatches from the egg. The larva feeds on

microorganism within the fruit, and on the sugars of the fruit sap. Eating for growth is themain purpose of the larva. Within 4 days the larva molts twice before encapuslation in the

puparium, where it undergoes metamorphosis, a uniquely shared character of all

holometabolic insects. During metamorphosis the adult fly develops, which has littleresemblance with the larva, but looks just like the parent fly. The adult fly initiates a new lifecycle, inheriting its information to the next generation; its members will thus be endowed with

the largely the same properties as their parents.The reduplication and inheritance of biological information is subject to random

mutation, providing the basis for evolution by selection, which gives rise to new specieswhose shared inherited information reflects their phylogenetic relationships. There are about

1450 Drosophila species alone, about 120,000 fly species, and at least 1 million insectspecies.

Slide 10

Flies can be very different in appearance, but they are always recognizable by theirhalteres, inherited from their common ancestor.

Insects belonging to the taxon pterygota (all insect with wings) – moths, butterflies, bees, beetles, bugs, and the dragon flies, for instance – all inherited from their common ancestor

two pairs of wings, the posterior pair of which has been transformed into halteres in flies,whereas the anterior pair hardened into elytra in beetles, protecting their delicate hind wings

and abdomen.Insects belong to a larger group called euarthropods. Other euarthropods, like the

Indonesian millipede or the tropical jumping spider (see slide), don’t have wings, but sharewith insects the segmental organization of their body plan, and an exoskeleton made out of

chitin due to information inherited from a common ancestor. Biological systems containinheritable information.

Slide 11

At the chemical level biological information is expressed in form of precisely definednetworks of chemical reactions, such as the one shown here, where nodes represent chemical

species and connecting edges realized chemical transformations between them. (Transitionshighlighted in bold represent the glycolytic pathway and the citric acid cycle.)

The topology or graph (nodes and edges) of the chemical network determines the properties of the organism, be it a single cell, or a multicellular organism. Although the

number of different chemical reactions that occur in any cell appears staggering, it onlyrepresents a minor fraction of all possible chemical reactions. How then does the cell generate

defined chemical networks that represent only a small subset of all possible chemicalreactions? The answer to this question is catalysis.

Slide 12

As a chemical reaction progresses from its reactants to its products, the free energy (see below) of the system increases until it reaches a maximum. The corresponding molecular

configuration is called the transition state of the reaction. The difference in free energy

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between the transition state and the reactants is referred to as the activation energy. While theequilibrium distribution of the reaction exclusively depends upon the free energy difference

between reactants and products, the rate constant of the reaction, k , depends on the activationenergy of the reaction according to the formula shown, where k B is the Boltzmann constant, h

is Planck’s constant , T is the absolute temperature in Kelvin.

The chemistry of living beings is organic chemistry, i.e. biochemical molecules arecarbon based compounds. From a biological point of view, the most important property oforganic chemistry is that the activation energies of organic reactions are high at ordinary

temperature and pH . In the absence catalysis, organic reactions are, therefore, exceedinglyslow.

Slide 13

Catalysts accelerate reactions by lowering the activation energy of the reaction ; unlikethe reactants, the catalyst is not consumed in the reaction. Catalysts cannot change the

equilibrium of a chemical reaction; since both forward and backward reaction proceedthrough the same transition state, the catalyst necessarily accelerates both reactions equally.

As we shall see, this remarkable symmetry is a consequence of the second law ofthermodynamics. And it is for this reason that organisms evolved enzymes for thermodynamic

(energetic) coupling ! to allow for anabolic processes (see below).

Slide 14Biological catalysts are called ‘enzymes’ (from gr. '& –inside; () µ* –yeast; the term was

coined by Wilhelm Friedrich Kühne, 1837-1900). They recognize chemical compounds with

great specificity; we say that enzymatic catalysis is stereospecific ! enzymes recognizespecific substrates and release specific products. As we shall see that this selectivity is

entailed in the three-dimensional structure of biological catalysts; almost all of which are proteins. Enzymatic catalysis is accomplished essentially by stabilization of the transition

state.

Slide 15The biological purpose of stereospecific catalysis is selection of chemical reactions. This

important notion, without which most of molecular biology cannot be understood, isdemonstrated in this figure by an analogy. Here, a chemical compound is represented by a ball

in a box. We shake the box, imitating the random thermal motion of molecules. The ball canescape the box by jumping over either one of the four confining walls, the walls are analogous

to the activation energy of alternative chemical reactions. Since the walls are high and ofequal height, the ball will jump over a wall only seldom and equal probabilities for all four

walls. Now imagine, we selectively remove wall 1. Upon shaking the box the ball will almost

always escape by taking path 1. Molecules can thus be guided along a precisely defined pathof chemical transitions. Cells generate reaction networks by catalyzing some reactions andnot others.

Text books generally stress the fact that enzymes accelerate chemical reactions. This iscorrect, but the emphasis on acceleration misses the crucial point: enzymatic (stereospecific)

catalysis serves to select specific reactions from the large number of all possible reactions.

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Slide 16

We can use stereospecific catalysis for accelerating ! and thus selecting ! specific

reactions, but it is not possible to accelerate only one of the two directions of a chemicalreaction. To understand this principle and its biological implications, we have to briefly

review some thermodynamics.

We shall see that chemically molecular biology is concerned with the formation of onlytwo types of bonds: the phosphoester bond and the peptide or amide bond . We shall consider

this biochemistry in some detail. For guidance, we shall focus on three theoretical aspects(i) kinetic proofreading

(ii) energetic coupling(iii) reaction mechanism.

Points (i) and (ii) will require some thermodynamic background knowledge.

A brief review of the first and second law of thermodynamicsIn thermodynamics, we call the object of interest 'the system' (circle), and the rest of the

universe its ' surroundings'. The system may be a heat engine, a reaction tube in the laboratory,or a cell. The surroundings are decomposed into idealized reservoirs (colored rectangles) with

which the system may exchange energy.In the 19th century physicists started to realize that heat was another form of energy with

unique properties (see below); they distinguished, therefore, between heat and all other formsof energy, which are collectively called 'work'. Thus, there are two basic types of reservoirs,

the heat reservoir or heat bath with which the system may exchange heat, and the workreservoir , which may be further decomposed into sub-reservoirs depending on the type of

energy that is exchanged – for instance a volume reservoir against which the system mayexpand (or contract) and thus exchange mechanical work, W , with the surroundings according

to W = ! p"V W , where p is the pressure of the reservoir, and !V is the change in system

volume. The heat reservoir or heat bath is considered infinitely large compared to the systemand therefore maintains the same temperature, even when exchanging heat with the system.

A state function is a function whose value only depends on the state of the system, i.e., its

chemical composition, temperature, pressure and volume, but not its history. Thus, for anycyclical process, the change in a state function is zero. We may now state the first (i) and

second law (ii) of thermodynamics:

(i) The first law

There is a state function U , called the internal energy of the system, with

!U =Q +W ,

where, by definition, Q > 0 if heat flows into the system, and W > 0 if work is done on the

system. (Both heat flowing out of the system and work done by the system is < 0). The firstlaw implies that the (internal) energy of an isolated system, i.e. a system that does notexchange energy (including matter) with its surroundings, is constant. Thus, the energy of the

universe is constant. For this reason the first law is also called the 'law of energy

conversation'. A critical insight that made its discovery possible ! and is implied by the first

law ! is that heat is energy.

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(ii) The second law

There is a state function S , called the entropy. The total change (system + surroundings =

universe) in S for any process is larger or equal to zero:

!S total

" 0 ;

furthermore, the entropy change in the surroundings is limited to the heat bath and is given by

!S res

= "Q

T ;

the entropy of the work reservoir does not change.

Note that !S res > 0 if heat flows into the reservoir (and thus out of the system), for Q < 0

according to the sign convention in (i); and !S res< 0 if heat flows out of the reservoir (and

thus into the system), for Q > 0.) The equality sign in !S total

" 0 applies only for quasi-static

processes, i.e., processes for which the system is infinitesimally close to thermodynamicequilibrium at all times. We call processes that are not quasi-static spontaneous. All natural

processes are spontaneous and hence, according to the second law, increase the entropy of theuniverse. The surroundings plus the systems together form an isolated system, i.e. no energy

or matter can flow into or out of the system. The entropy of an isolated system ever increasesuntil reaching a maximum.

The word ‘entropy’ was introduced by Rudolf Clausius (1822-1888) in 1865 (Gr.

"#$%&'()* ! transformation content).

Slide 17

As mentioned earlier, catalysts cannot accelerate the forward reaction of a chemicalreaction without accelerating the backward reaction, too; and therefore cannot change the

equilibrium of a chemical reaction. This symmetry is a consequence of the second law of

thermodynamics. We shall prove this statement by assuming the opposite and showing thatour assumption leads to a contradiction with the second law. (That is, we apply the modustollens, see above.)

Our model system encompasses molecules A and B, which can be chemically convertedinto each other and is coupled to the heat reservoir HT at temperature T . Let B have lower

energy than A, the reaction, therefore, releases energy as it proceeds from A to B; i.e., thereaction from A to be B is 'exothermic'. We furthermore assume the reaction is in equilibrium,

i.e. forward and backward reaction proceed at equal speeds:

k 1[ A] = k 2[ B] ,

where k 1,k 2 are the rate constants of the reaction. Thus, in equilibrium the concentration ratio

[ A] / [ B] = k 2 / k 1 assumes a characteristic value at temperature T . Now suppose that one direction of the reaction is catalyzed by a catalyst, C , but not the

other, say the reaction from A to B. Let k 1C be the rate constant for A! B in the presence of

C, where k 1C >> k 1 . Upon removal of C , A! B , but not A! B becomes slower and there

will be a net flow from B to A. This requires absorption of energy from the heat reservoir because the reaction from A to B is exothermic; the opposite reaction, therefore, is

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endothermic; it absorbs heat. We now reintroduce the catalyst, the old equilibrium will beattained, which requires the conversion of some A molecules into B molecules until

[ A] / [ B] = k 2 / k 1 is again obtained, releasing energy, which we harness for work by coupling

the system to a work reservoir. Thus we have obtained a cyclical (chemical) process whose

only effect is the conversion of some heat, Q, into work, W .

According to the second law, this is impossible: Since entropy is a state function and thesystem ( A, B) is in the same state at the beginning and end of the process, !S sys = 0 . In

contrast, because heat Q was absorbed by the system (Q > 0), the change in entropy of HT,

!S res

= "Q / T , is negative. Hence, the total change in entropy !S res

+ !S sys is negative, in

contradiction of the second law of thermodynamics; the notion that a catalyst may catalyzeonly one direction of a chemical reaction and thus affect the equilibrium of the reaction,stands in contradiction to the second law. Note that fundamentally the same argument may be

used to prove the following general result:

Slide 18

No process is possible whose sole result is the absorption of heat from a reservoir andthe conversion of this heat into work .

This is the Kelvin-Planck statement of the second law of thermodynamics. It establishes

the unique status of heat energy among all forms of energy. While every other form of energy(i.e., work) can be completely converted into heat, heat can never be completely converted

into work.(The Kelvin-Planck statement is equivalent to our formulation of the second law. It is

easily derived from our formulation of the second law; as we have seen. The reverse howeveris hard.)

Slide 19

The second law does not imply that heat cannot be converted into work whatever; afterall, this is what a steam engine does. However, conversion of heat into work by some

(cyclically operating) engine requires two heat baths, one colder than the other, for we cancompensate for the loss of entropy in the warmer heat bath, !Q H /T H , by transfer of a

smaller amount of heat, QC <Q H , to the colder heat bath, fulfilling the second law's

requirement that

!Q H

T H !QC

T C " 0 .

The difference between these two, QC !Q H , can be used for work. (Note that work done by

the system is negative by sign convention.) From this inequality, it is easily seen that thethermal efficiency of the engine ! !W /Q H ! i.e., the amount of work that can be done per

unit of heat absorbed from the heat reservoir ! obeys the following law:

! !1" T C

T H

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Thus, 1!T C /T

H is the upper limit for the efficiency of the engine and only depends on the

temperatures of the two heat baths. It thus applies to any engine; and is therefore a universal

upper bound for the efficiency of a heat engine. This upper bound is approached only for idealquasi-static processes. (The actual efficiency of realistic engine is much smaller.) The greater

the temperature difference between the two reservoirs, the greater the maximal efficiency of

the engine.

Slide 20

By considering the reversal of the process shown in this slide, transfer of heat from a coldreservoir to a hot reservoir, we may infer that

No process is possible whose sole result is the transfer of heat from a cooler to a hotterreservoir .

This is the Clausius statement of the second law of thermodynamics. (It can be provedthat it is equivalent to the Kelvin-Planck statement.) The process shown is that of a heat pump

(refrigerators are heat pumps). Thus, work energy needs to be converted into heat in order to

cool a body. A refrigerator requires energy (i.e., work). Now, consider the problem of heating your house. The second law allows you to heatyour house by using energy to pump heat from the surroundings, the cold heat bath, into your

house, the hot reservoir; i.e. by running a heat pump. The energy eventually added to yourhouse per unit of work 'consumed' by the heat pump is

Q H

W =QC + (Q H !QC )

W =QC +W

W =QC

W +1 .

The ratio ! =QC /W is called the coefficient of performance for the heat pump. Its

theoretical upper limit is given by

! !

T C

T H "T C .

(Derive this inequality.) Thus, for an outside temperature of 5°C (273°K; a cold winter at the

coast of California) and 25°C (298°K) for your house, the maximal coefficient of performanceis 273 / 20 =13.65 . This value is obtainable only, if the engine runs quasi-statically or

'reversibly', which practically is impossible. Nonetheless, the coefficient of performance of

modern heat pumps ranges between 2 and 7. Hence, Q H /W , the amount of heat generated

per unit of work, can range between 3 and 8, as opposed to 1 for the direct conversion of work

(e.g. oil or coal) into heat. According to the U.S. Energy Information Administration 42% ofenergy spent in American households is used for space heating, another 18% for water

heating. We could cut the total amount of energy 'consumption' by at least 40%, if we usedheat pumps for heating. (The question of why we don't do this must be discussed elsewhere.)

As mentioned earlier, almost all biological catalysts are proteins. The importance of

biological catalysis, and therefore of proteins, is not understood without the concept ofenergetic coupling . We first briefly review the concept of 'Gibbs free energy'.

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Slide 21Most systems of interest to chemists and biologists are systems that may be viewed as

systems coupled to a volume reservoir and a thermal reservoir, an open reaction tube in thelaboratory for instance. For such a system the second law of thermodynamics may be

expressed in terms of state functions of the system only, because in this instance heat

exchanged with the heat reservoir is also a state function, called enthalpy. This can be easilyseen as follows:Since the only work reservoir is the volume reservoir, the only work done on the system

is volume-pressure work, - p!V , where p is the pressure of the reservoir and the system (sincethey are coupled). Thus, the first law of thermodynamics becomes

!U =Q " p!V for constant p.

With H !U + pV , it follows

! H =Q for constant p.

Since U , p, and V are state functions, H is a state function, too. From the second law it thus

follows

!S total

= !S sys+ !S

res

= !S sys

" ! H /T

# 0

(for constant p)

and hence, with G ! H "TS

!G " 0

for all processes at constant p and T (i.e., coupled to heat and volume reservoir). G is calledGibbs free energy (after Josiah Williard Gibbs, 1839-1903). For every naturally occurring (i.e

spontaneous) process at constant p and T

!G < 0.

Note that this statement is nothing else but the second law of thermodynamics again, for thespecial case of a system that is coupled to a heat and a volume reservoir (and no other

reservoir).

Slide 22Processes for which !G < 0 are called exergonic. Thus, all naturally occurring processes

(in systems coupled to a heat and temperature reservoir) are exergonic. ‘Exergonic’ must not

be confused with ‘exothermic’ , which means ! H > 0 . Processes for which !G > 0 are called

endergonic (not to be confused with endothermic, i.e. ,! H < 0 ).

Many important biochemical reactions, for example polymerization reactions, which will

be at the center stage of this lecture, are endergonic, and hence do not occur spontaneously.And yet nucleic acids (DNA and RNA) and protein molecules (all are polymers) are

continually synthesized inside cells. How is this possible?

Slide 23As we have seen, the second law of thermodynamics implies the impossibility of a

catalyst that catalyzes the forward direction but not the backward direction of a chemical

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13

reaction, or vice versa. And yet biological catalysts, enzymes, can promote endergonicreactions.

This remarkable feat is accomplished by the mechanistic coupling of two chemicalreactions. This coupling allows for endergonic reactions to proceed when coupled to a

sufficiently exergonic reaction (energetic or thermodynamic coupling ) ! the total change in

free energy is the sum of the partial free energy changes ! to assures that the total change inGibbs free energy is negative.

One of the most often used reactions by cells to drive energetically unfavorable,endergonic, reaction is the hydrolysis of ATP to ADP, which under cellular conditions is

highly exergonic. Thus, in every reaction that involves ATP hydrolysis we observe biology paying its dues to the second law of thermodynamics. In 3.5 billion years of evolution, life did

not manage to invent a 'unidirectional catalyst' that could subvert, i.e. invalidate, the secondlaw of thermodynamics. The second law is a well-tested and corroborated theory, by biology.

Slide 24

The preceding discussion is summarized in this slide. It shows that energetic coupling

allows to decrease entropy within the cell (in the course of polymerization reactions, forinstance) at the expense of generating entropy in the surroundings, which means the export ofenergy from the cells into its surroundings in the form of heat (i.e. random molecular motion).

Slide 25

Enzymes are, with very few (but important) exceptions, proteins. As Francis Crick (1916-2004) pointed out in his famous 1957 essay 'On protein synthesis', which laid down the

foundations for molecular biology: “the main function of proteins is to act as enzymes”. If wewant to understand biological information, we have to start with an exploration of the

chemical nature of proteins.

notes+to+bio115+l1+2016

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