Chem 4311- Chapter3

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Reginald H. GarrettCharles M. Grisham

www.cengage.com/chemistry/garrett

Reginald Garrett & Charles Grisham University of Virginia

Chapter 3Thermodynamics of Biological

Systems

Chapter 3The sun is the source of energy for virtually alllife. We even harvestits energy in the form of electricity generated bywindmills. Wind is themovement of air thathas been heated by the

sun.

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Essential Question What are the laws and principles of thermodynamics that allow

us to describe the flows and interchanges of heat, energy, andmatter in biochemical systems?

BSIC CONCEPT OF Temperature

Energy System

3.1 What Are the Basic Concepts of Thermodynamics? The system : the portion of the universe with which we are

concerned The surroundings : everything else Isolated system cannot exchange matter or energy Closed system can exchange energy Open system can exchange either or both

Figure 3.1 The characteristics of isolated, closed, and open systems. Isolated systemsexchange neither matter nor energy with their surroundings. Closed systems mayexchange energy, but not matter, with their surroundings. Open systems mayexchange either matter or energy with the surroundings.

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The First Law The Total Energy of an IsolatedSystem is Conserved

E (or U) is the internal energy - a function that keeps track of heattransfer and work expenditure in the system

E is heat exchanged at constant volume E is independent of path E2 - E 1 = E = q + w q is heat absorbed BY the system w is work done ON the system Thus both q and w are positive when energy flows into a system

State Function- The E is dependant on the systemw = -PV

Enthalpy

Enthalpy a better function for constant pressure

H = E + PV If P is constant, H = q H is the heat absorbed at constant P Volume is approximately constant for biochemical reactions (in

solution) So H is approximately the same as E for biochemical reactions

CH4 + O2 CH2O + H2O (H = -319.7 kJ.mol -1) ExothermicCH2O + H2O CH4 + O2 (H = +319.7 kJ.mol -1) Endothermic

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3.1 What Are the Basic Concepts of Thermodynamics?

Figure 3.2 Theenthalpy change for areaction can bedetermined from theslope of a plot of R lnK eq versus 1/ T .

3.1 What Are the Basic Concepts of Thermodynamics?

Positive values of H would be expected for the breaking of hydrogen bondsas well as for the exposure of hydrophobic groups from the interior of anative, folded protein during the unfolding process. Such events raise theenergy of the solution.

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The Second Law Systems Tend Toward Disorder and Randomness

Systems tend to proceed from ordered to disordered states

The entropy change for (system + surroundings) is unchanged inreversible processes and positive for irreversible processes

All processes proceed toward equilibrium - i.e., minimum potentialenergy

S= k ln W; S = k ln W final -k ln W initial ( W= microstate)

k is Boltzmanns constant (1.38x10 -23J/K)

A measure of disorder An ordered state is low entropy A disordered state is high entropy dSreversible = dq/T , dq= heat transferred, T = Temperature

What is Life?

, asked Erwin Schrdinger, in 1944.

A disorganized array of letterspossesses no information contentand is a high-entropy state,compared to the systematic arrayof letters in a sentence.

Erwin Schrdinger

s term

negentropy

describes thenegative entropy changes thatconfer organization andinformation content to livingorganisms. Schrdinger pointedout that organisms must

acquirenegentropy

to sustain life.

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Energy dispersion Entropy can be defined as S = k ln W And S = k ln W final k ln W initial Where W final and W initial are the final and initial number of

microstates of a system, and k is Boltzmann

s constant. Viewed in this way, entropy represents energy dispersion

the dispersion of energy among a large number of molecularmotions relatable to quantized states (microstates).

The definition of entropy above is engraved on the tombstoneof Ludwig Boltzmann in Vienna, Austria

If microstate is one ( i.e. no degree of freedoms, S= 0) dSreversible = dq/T

The Third Law Why Is

Absolute Zero

So Important?

The entropy of any crystalline, perfectly ordered substance mustapproach zero as the temperature approaches 0 K

At T = 0 K, entropy is exactly zero

For a constant pressure process (heat capacity Cp) :

C p = dH/dT

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Free Energy

Hypothetical quantity - allows chemists to asses whether reactions will occur

G = H TS (H, enthalpy or total energy, S= entropy)

For any process at constant P and T : G = H - T S

If G = 0, reaction is at equilibrium

If G < 0, reaction proceeds as written (spontaneous backward

reaction) (Endergonic)

G > 0 , spontaneous reaction (Exergonic)

G and Go

- The Effect of Concentration on G

How can we calculate the free energy change for reactions not atstandard state? Consider a reaction: A + B C + D Then:

At equilibrium G = 0 and [C][D]/[A][B]= Keq G =-RT ln Keq G =--2.3 RT log 10 Keq

Keq = 10 -

G/2.3RT

Thus concentrations at other than 1 M will change the value of G This is Equation 3.13. It is used frequently throughout this text.

G = Go + RT ln

[C ][ D ]

[ A ][ B ]

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G

Can Be Temperature Dependent

Figure 3.3 The dependence of G on temperature for the denaturationof chymotrypsinogen.

S

Can Be Temperature Dependent

Figure 3.4 The dependence of S on temperature for the denaturationof chymotrypsinogen.

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3.3 What is the Effect of pH on Standard State FreeEnergies?

A standard state of 1 M for H+ is not typical for biochemical reactions. It makes more sense to adopt a modified standard state i.e., 1 M for

all constituents except protons, for which the standard state is pH 7. This standard state is denoted with a superscript

For reactions in which H + is produced: G

= G

+ RT ln [H+] And for reactions in which H + is consumed:

G

= G

- RT ln [H+]

3.4 What Can Thermodynamic Parameters Tell Us AboutBiochemical Events?

A single thermodynamic parameter is not very useful Comparison of several thermodynamic parameters can

provide meaningful insights about a process Heat capacity values can be useful A positive heat capacity change for a process indicates that

molecules have acquired new ways to move (and thus to storeheat energy)

A negative heat capacity change means that the process hasresulted in less freedom of motion for the molecules involved

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Figure 3.5 Unfolding of a soluble protein exposes significant numbers of nonpolar groups to water, forcing order on the solvent and resulting in anegative entropy change.


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3.5 What are the Characteristics of High-EnergyBiomolecules?

Energy Transfer - A Biological Necessity

Energy acquired from sunlight or food must be used to driveendergonic (energy-requiring) processes in the organism

Two classes of biomolecules do this: Reduced coenzymes (NADH, FADH 2) High-energy phosphate compounds with free energy of

hydrolysis more negative than -25 kJ/mol

High-Energy Biomolecules

Table 3.3 is important

Note what's high - PEP and 1,3-BPG Note what's low - sugar phosphates, etc. Note what's in between - ATP Note difference (Figure 3.6) between overall free energy

change - noted in Table 3.3 - and the energy of activationfor phosphoryl-group transfer

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3.5 What are the Characteristics of High-EnergyBiomolecules?

3.5 What Are the Characteristics of High-EnergyBiomolecules?

Figure 3.6 The activation energiesfor phosphoryl group transferreactions are substantially largerthan the free energy of hydrolysisof ATP.

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Group Transfer Potentials Quantify the Reactivity of Functional Groups

Group transfer is analogous to ionization potential and reductionpotential. All are specific instances of free energy changes.

ATP

An Intermediate Energy Shuttle Device

PEP and 1,3-BPG are created in the course of glucose breakdown Their energy (and phosphates) are transferred to ADP to form ATP But ATP is only a transient energy carrier - it quickly passes its energy

to a host of energy-requiring processes

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ATP Contains Two Pyrophosphate Linkages

Figure 3.7 ATP contains two pyrophosphatelinkages. The hydrolysis of phosphoric acidanhydrides is highly favorable.

Phosphoric Acid Anhydrides

How ATP does what it does

ADP and ATP are examples of phosphoric acid anhydrides Note the similarity to acyl anhydrides Large negative free energy change on hydrolysis is due to:

electrostatic repulsion stabilization of products by ionization and resonance entropy factors

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Hydrolysis of Phosphoric Anhydrides is Highly Favorable

Figure 3.8 Electrostatic repulsion and resonance in acetic anhydride

3.5 What Are the Characteristics of High-EnergyBiomolecules?

Figure 3.9 Hydrolysis of ATP to ADP(and hydrolysis of ADP to AMP)relieves electrostatic repulsion.

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Phosphoric-Carboxylic Anhydrides

These mixed anhydrides - also called acyl phosphates - arevery energy-rich

Acetyl-phosphate: G

= 43.3 kJ/mol 1,3-BPG: G

= 49.6 kJ/mol Bond strain, electrostatics, and resonance are responsible

Acetyl Phosphate and 1,3-Bisphosphoglycerate Are Phosphoric-Carboxylic Anhydrides

Figure 3.10 The hydrolysis reactions of acetyl phosphate and 1,3-bisphosphoglycerate.

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Enol Phosphates

Phosphoenolpyruvate (PEP) has the largest free energy of hydrolysis of any biomolecule

Formed by dehydration of 2-phospho-glycerate Hydrolysis of PEP yields the enol form of pyruvate - and

tautomerization to the keto form is very favorable

PEP Hydrolysis Yields -62.2 kJ /mol

Figure 3.11 PEP is produced by the enolase reaction and in turn drivesthe phosphorylation of ADP to form ATP in the pyruvate kinase reaction.

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Enol Phosphates are Potent Phosphorylating Agents

Figure 3.12 Hydrolysis and subsequent tautomerizationaccount for the very large G of PEP.

Ionization States of ATP

ATP has four dissociable protons pK a values range from 0-1 to 6.95 Free energy of hydrolysis of ATP is relatively constant from pH 1 to

6, but rises steeply at high pH Since most biological reactions occur near pH 7, this variation is

usually of little consequence

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3.6 What Are the Complex Equilibria Involved in ATPHydrolysis?

The Free Energy of Hydrolysis for ATP is pH-Dependent

Figure 3.14 The pH dependenceof the free energy of hydrolysis of ATP. Because pH varies onlyslightly in biologicalenvironments, the effect on G isusually small.

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Metal Ions Affect the Free Energy of Hydrolysis of ATP

Figure 3.15 The free energy of hydrolysis of ATP as a functionof total Mg 2+ ion concentrationat 38C and pH 7.0.

Metal Ions Affect the Free Energy of Hydrolysis of ATP

Figure 3.16 Number of Mg 2+ ions bound per ATP as a function of pH and[Mg2+ ].

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Concentration Affects the Free Energy of Hydrolysis of ATP

Figure 3.17 The free energy of hydrolysis of ATP as a function of concentration at 38C, pH 7.0.

The Effect of Concentration

Recall that free energy changes are concentration- dependent So the free energy available from ATP hydrolysis depends on

concentration

We will use the value of 30.5 kJ/mol for the standard free energyof hydrolysis of ATP

At non-standard-state conditions (in a cell, for example), the G isdifferent

Equation 3.13 allows the calculation of G - be sure you can use itproperly

In typical cells, the free energy change for ATP hydrolysis is typically50 kJ/mol

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3.7 Why Are Coupled Processes Important to LivingThings?

Many reactions of cells and organisms run against theirthermodynamic potential that is, in the direction of positive G

Examples synthesis of ATP, creation of ion gradients These processes are driven in the thermodynamically unfavorable

direction via coupling with highly favorable processes

3.7 Why Are Coupled Processes Important to LivingThings?

Figure 3.18 The pyruvate kinase reaction. Hydrolysis of PEP is veryfavorable, and it is used to drive phosphorylation of ADP to form ATP, aprocess that is energetically unfavorable.

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3.8 What is the Daily Human Requirement for ATP?

The average adult human consumes approximately 11,700 kJof food energy per day

Assuming thermodynamic efficiency of 50%, about 5860 kJ of this energy ends up in form of ATP

Assuming 50 kJ of energy required to synthesize one mole of ATP, the body must cycle through 5860/50 or 117 moles of ATP per day

This is equivalent to 65 kg of ATP per day

The typical adult human body contains 50 g of ATP/ADP Thus each ATP molecule must be recycled nearly 1300 times

per day

ATP Changes K eq by 10 8

Consider a process: A B Compare this to A + ATP B + ADP + Pi Assuming typical cellular concentrations of ATP, ADP and P i,

and using the cellular free energy change for ATP hydrolysis, itcan be shown that coupling ATP hydrolysis to the reaction of A B changes the equilibrium ratio of B/A by more than 200million-fold

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ATP Changes K eq by 10 8

3.9 What Are Reduction Potentials?

How Are Reduction Potentials Used to Calculate Free Energy Changesfor Oxidation-Reduction Reactions?

High o' indicates a strong tendency to be reduced Crucial equation: Go' = n o' o' = o'(acceptor) - o'(donor)

Electrons are donated by the half reaction with the more negativereduction potential and are accepted by the reaction with the morepositive reduction potential: o ' positive, Go' negative

If a given reaction is written so the reverse is true, then the o' willbe a negative number and Go' will be positive

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Chem 4311- Chapter3