Reginald H. GarrettCharles M. Grisham

Chapter 3Thermodynamics of Biological

Systems

Chapter 3

The sun is the source of energy for virtually all life. We even harvest its energy in the form of electricity using windmills driven by air heated by the sun.

Essential Question

• What are the laws and principles of thermodynamics that allow us to describe the flows and interchanges of heat, energy, and matter in biochemical systems?

Outline

• What are the basic concepts of thermodynamics?• What can thermodynamic parameters tell us about biochemical

events?• what is the effect of pH on standard-state free energies?• What is the effect of concentration on net free energy

Changes?• Why are couples processed important to living things?• What are the characteristics of high-energy biomolecules ? • What are the complex equilibria involved in ATP hydrolysis?• What is the daily human requirement for ATP?

3.1 What Are the Basic Concepts of Thermodynamics?

• Definitions for 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

3.1 What Are the Basic Concepts of Thermodynamics?

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

The First Law – The Total Energy of an Isolated System is Conserved

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

• E is heat exchanged at constant volume

• E is independent of path

• E2 - E1 = 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

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 approx. constant for biochemical reactions (in solution)

• So H is approx. same as E for biochemical reactions

3.1 What Are the Basic Concepts of Thermodynamics?

Figure 3.2 The enthalpy change for a reaction can be determined from the slope of a plot of R ln Keq

versus 1/T.

3.1 What Are the Basic Concepts of Thermodynamics?

Positive values of ∆H would be expected for the breaking of hydrogen bonds as well as for the exposure of hydrophobic groups from the interior of a native, folded protein during the unfolding process. Such events raise the energy of the protein solution.

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 in reversible processes and positive for irreversible processes

• All processes proceed toward equilibrium - i.e., minimum potential energy

Entropy

• A measure of disorder• An ordered state is low entropy• A disordered state is high entropy• dSreversible = dq/T

“What is Life?”, asked Erwin Schrödinger, in 1945.

A disorganized array of letters possesses no information content and is a high entropy state, compared to the systematic array of letters in a sentence.

Erwin Shrödinder’s term “negentropy” describes the negative entropy changes that confer organization and information content to living organisms. Shrödinger pointed out that organisms must “acquire negentropy” to sustain life.

Energy dispersion

• Entropy can be defined as S = k ln W

• And ∆S = k ln Wfinal – k ln Winitial

• Where Wfinal and Winitial 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 molecular motions relatable to quantized states (microstates).

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

The Third Law –Why Is “Absolute Zero” So Important?

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

• At T = 0 K, entropy is exactly zero• For a constant pressure process:

Cp = dH/dT

Free Energy

• Hypothetical quantity - allows chemists to asses whether reactions will occur

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

G = H - TS• If G = 0, reaction is at equilibrium• If G < 0, reaction proceeds as written

G and Go´ - The Effect of Concentration on ∆G

• How can we calculate the free energy change for reactions not at standard state?

• Consider a reaction: A + B C + D

• Then:

• 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.

[ ][ ]ln

[ ][ ]

C DG G RT

A B

∆G° Can Be Temperature Dependent

Figure 3.3 The dependence of ∆G°on temperature for the denaturation of chymotrypsinogen.

∆S° Can Be Temperature Dependent

Figure 3.4 The dependence of ∆S°on temperature for the denaturation of chymotrypsinogen.

3.3 What is the Effect of pH on Standard State Free Energies?• A standard state of 1 M for H+ is awkward 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, we have ∆G°´= ∆G° + RT ln [H+]

• And for reactions in which H+ is consumed, we have ∆G°´ = ∆G° - RT ln [H+]

3.4 What Can Thermodynamic Parameters Tell Us About Biochemical Events?• A single 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 store heat energy)

• A negative heat capacity change means that a process has resulted in less freedom of motion for the molecules involved

3.4 What Can Thermodynamic Parameters Tell Us About Biochemical Events?

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

노란색잔기: 소수성파란색잔기: 친수성

3.4 What Can Thermodynamic Parameters Tell Us About Biochemical Events?

3.5 What are the Characteristics of High-Energy Biomolecules?

Energy Transfer - A Crucial Biological Need

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

• Two classes of biomolecules do this: • Reduced coenzymes (NADH, FADH2) • 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 activation for phosphoryl-group transfer

3.5 What are the Characteristics of High-Energy Biomolecules?

3.5 What Are the Characteristics of High-Energy Biomolecules?

Figure 3.6 The activation energies for phosphoryl group transfer reactions are substantially larger than the free energy of hydrolysis of ATP.

에너지댐

Group Transfer Potentials Quantify the Reactivity of Functional Groups

Group transfer is analogous to ionization potential and reduction potential. All these 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

ATP Contains Two Pyrophosphate Linkages

Figure 3.7 ATP contains two pyrophosphate linkages. The hydrolysis of phosphoric acid anhydrides is highly favorable.

Phosphoric Acid Anhydrides

Why 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 (분해산물의개수가많다)

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-Energy Biomolecules?

Figure 3.9 Hydrolysis of ATP to ADP (and/or of ADP to AMP) leads to relief of electrostatic repulsion.

Phosphoric-Carboxylic Anhydrides

• These mixed anhydrides - also called acyl phosphates - are very 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.

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 drives the phosphorylation of ADP to form ATP in the pyruvate kinase reaction.

Enol Phosphates are Potent Phosphorylating Agents

Figure 3.12 Hydrolysis and subsequent tautomerization account for the very large ∆G° of PEP.

Ionization States of ATP

• ATP has four dissociable protons• pKa 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

3.6 What Are the Complex Equilibria Involved in ATP Hydrolysis?

The Free Energy of Hydrolysis for ATP is pH-Dependent

Figure 3.14 The pH dependence of the free energy of hydrolysis of ATP. Because pH varies only slightly in biological environments, the effect on ∆G is usually small.

Metal Ions Affect the Free Energy of Hydrolysis of ATP

Figure 3.15 The free energy of hydrolysis of ATP as a function of total Mg2+ ion concentration at 38°C and pH 7.0.

Metal Ions Affect the Free Energy of Hydrolysis of ATP

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

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 energy of hydrolysis of ATP

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

• Equation 3.12 is crucial - be sure you can use it properly

• In typical cells, the free energy change for ATP hydrolysis is typically -50 kJ/mol

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 38°C, pH 7.0.

3.7 Why Are Coupled Processes Important to Living Things?• Many reactions of cells and organisms run against

their thermodynamic 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 Living Things?

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

3.8 What is the Daily Human Requirement for ATP?• The average adult human consumes approximately

11,700 kJ of 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 Keq by 108

• Consider a process: A → B

• Compare this to A + ATP → B + ADP + Pi

• Assume typical cellular concentrations of ATP, ADP and Pi, and using the standard state free energy of ATP hydrolysis, it can be shown that coupling of ATP hydrolysis to the reaction of A to B changes the equilibrium ratio of B/A by more than 200 million-fold

ATP Changes Keq by 108