The thermodynamics of transition 104 3.1 The condition of stability 104 3.2 The variation of Gibbs energy with pressure 105. CASE STUDY 7.1:Fast events in protein folding 269. a) The variation of concentration with time 272 (b) The rate-determining step 273.
8 Complex Biochemical Processes 296 Transport across membranes 296
III Biomolecular Structure 339 9 The Dynamics of Microscopic
Systems 340
10 The Chemical Bond 394 Valence bond theory 394
11 Macromolecules and Self-Assembly 441
12 Statistical Aspects of Structure and Change 502
IV Biochemical Spectroscopy 539 13 Optical Spectroscopy and
14 Magnetic Resonance 604 Principles of magnetic resonance 604
TOOLBOX: Magnetic resonance imaging 624
Quantities and units 643 Appendix 2: Mathematical techniques 645
Concepts of physics 654 Classical mechanics 654
Review of chemical principles 661
Data section 669
Preface
Gentile, Western Washington University Keith Griffiths, University of Western Ontario Jan Gryko, Jacksonville State University Arthur M. Halpern, Indiana State University Mike Jezercak, University of Central Oklahoma Thomas Jue, University of California–Davis Evguenii I.
About the Book
Organizing the information
In some cases, we have judged that a derivation is too long, too detailed, or too difficult in level for it to be included in the text. We have included a set of Appendices to provide a quick survey of some of the information that we draw on in the text.
Mathematics support
Science is a precise activity, and using its language accurately can help you to understand the concepts. We have used this feature to help you to use the language and procedures of science in conformity to interna- tional practice and to avoid common mistakes.
Problem solving
If QK, the reaction step is far from equilibrium and it is so slow that it may be rate-determining. Provide a molecular interpretation for the observation that the reaction is more exergonic than it is exothermic.
You will now explore the work associated with extending a DNA molecule. i)What are the limitations of this model. ii)What is the magnitude of the force that must be applied to extend a DNA molecule with N200 by 90 nm. iii)Plot the restoring force against, noting that can be either positive or negative. How is the variation of the restoring force with end-to-end distance different from that predicted by Hooke’s law. iv)Keeping in mind that the difference in end-to-end distance from an equilibrium value is xnland, consequently, dxldnNld, write an expression for the work of extending a DNA molecule.(v)Calculate the work of extending a DNA molecule from 0 to 1.0.Hint:You must integrate the expression for w.
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Prologue
The structure of physical chemistry
Its principal relevance to biology is its application to the study of the deployment of energy by organisms. We then turn to chemical kinetics, the study of the rates of chemical reac- tions.
Applications of physical chemistry to biology and medicine
The text begins with an investigation of thermodynamics, the study of the transformations of energy and the relations between the bulk properties of matter. Chemical kinetics is a crucial aspect of the study of organisms because the array of reactions that contribute to life form an intricate network of processes occurring at different rates under the control of enzymes.
One exam- ple is the nuclear model of an atom, and in particular a hydrogen atom, which is used as a basis for the discussion of the structures of all atoms. However, decoding genomic DNA will not al- ways lead to accurate predictions of the amino acids present in biologically active proteins.
It is no surprise that physical chemists are important contributors to the solution of the protein folding problem. These trajectories correspond to the conformations that the molecule can sample at the temperature of the simulation.
Many of the sophisticated experimental techniques in chemical kinetics to be discussed in Chapter 6 continue to yield details of the mechanism of protein folding. The drug inhibits an enzyme that is key to the formation of the protein envelope surrounding the genetic material of the human immunodeficiency virus (HIV).
Many of the targets of rational drug design are enzymes, proteins or nucleic acids that act as biological catalysts. Finally, and perhaps most importantly, the computational techniques discussed in Chapter 10 are used extensively in the prediction of the structure and reactivity of drug molecules.
Fundamentals
- The states of matter
- Physical state
- Force
- Energy
- Pressure
- Temperature
- Equations of state
It follows that the faster the molecules travel (and hence the greater their kinetic energy), the greater the total energy of the gas. The magnitude of the velocity vector is the speed,v, given by v(vx2 vy2vz2)1/2, where vx,vy, and vz, are the components of the vector along the x-,y-, and z-axes, respectively (see the illustration).
Checklist of Key Ideas
Discussion questions
Exercises
What is the relation between temperatures on (a)the Plutonium and Kelvin scales, (b)the Plutonium and Fahrenheit scales. What is the volume of the air space when the bell has been lowered to a depth of 50 m.
Project
Thermodynamics
The First Law
The conservation of energy
- Systems and surroundings
- Work and heat
- Energy conversion in living organisms
- The measurement of work
- The measurement of heat
There- fore, maximum work is obtained when the external pressure is only infinitesimally less than the pressure of the gas in the system. An intensive property is a property that is independent of the amount of substance in the sample.
Internal energy and enthalpy
The internal energy
The change in the value of a state property is independent of the path between the two states. At con- stant volume, q may be replaced by the change in internal energy of the sub- stance, so.
The enthalpy
That is, the enthalpy differs from the internal energy by the addition of the prod- uct of the pressure, p, and the volume, V, of the system. Note that the enthalpy is always greater than the internal energy of the system and that the difference increases with temperature.
The temperature variation of the enthalpy
Note that the heat capacity varies with temperature (in general) and that Cpis greater than CV. Note that this calculation is only approximate, because the heat capacity depends on the temperature, and we have used an average value for the temperature range of interest.
Physical change
The enthalpy of phase transition
The high enthalpy of vaporization of water has profound ecological conse- quences, for it is partly responsible for the survival of the oceans and the generally. The enthalpy change of an overall process is the sum of the enthalpy changes for the steps (observed or hypothetical) into which it may be divided.
Toolbox: Differential scanning calorimetry
A computer controls the electrical power output in order to maintain the same temperature in the sample and reference compartments through- out the analysis. To maintain the same temperature in both compart- ments, excess energy is transferred as heat to the sample during the process.
Chemical change
- The bond enthalpy
- Thermochemical properties of fuels
- The combination of reaction enthalpies
- Standard enthalpies of formation
- OHCH2OH
- The variation of reaction enthalpy with temperature
Estimate the standard enthalpy of combustion of sucrose from the standard enthalpies of formation of the reactants and products. 䊐 18.The standard reaction enthalpy, rH両, is the difference between the standard enthalpies of formation of the products and reactants, weighted.
The Second Law
Entropy
- The direction of spontaneous change
- Entropy and the Second Law
- The entropy change accompanying heating
- The entropy change accompanying a phase transition
- Entropy changes in the surroundings
- Absolute entropies and the Third Law of thermodynamics
- The standard reaction entropy
- The spontaneity of chemical reactions
We can use this formula to calculate the entropy change of the surroundings re- gardless of whether the change in the system is reversible or not. The area is equal to the absolute entropy at the temperatureT. 2.9 The determination of entropy from heat capacity data. a) Variation of Cp/T with the temperature of the sample.
The Gibbs energy
- Focusing on the system
- Spontaneity and the Gibbs energy
- The Gibbs energy of assembly of proteins and biological membranes
- Work and the Gibbs energy change
Therefore, it is a large decrease in the entropy of the system (transferS0) that accounts for the positive change in Gibbs energy. Calculate (a)the entropy of vaporization of methanol at this temperature and (b)the entropy change of the surroundings.
Projects
Provide a molecular interpretation for the observation that Trouton’s rule underestimates the value of the entropy of vaporization of water. Do these electrostatic effects contribute to the rHorrSterms that determine the exergonicity of the reaction.
Phase Equilibria
The thermodynamics of transition
- The condition of stability
- The variation of Gibbs energy with pressure
- The variation of Gibbs energy with temperature
- Phase diagrams
For most substances (water is an important exception), the molar volume of the liquid phase is greater than that of the solid phase. However, as the tem- perature is raised, the molar Gibbs energy of the liquid phase falls below that of the solid phase, and the substance melts.
Phase transitions in biopolymers and aggregates
The stability of nucleic acids and proteins
We can begin by plottingTmagainst fraction of G–C base pairs and examining the shape of the curve. The data also show that increasing the con- centration of ions in solution increases the melting temperature of DNA.
Phase transitions of biological membranes
On the other hand, positive ions, such as Na in Self-test 3.3, bind electrostatically to the surface of DNA and mitigate repulsive interactions between phosphate groups. Answer:Insertion of lipids with unsaturated chains lowers the plasma membrane’s melting temperature to a value that is close to the lower ambient temperature.
The thermodynamic description of mixtures
- Measures of concentration
- The chemical potential
- Ideal solutions
- Ideal-dilute solutions
- Real solutions: activities
Note that the chemical potential of the solvent is lower in the mixture than for the pure liquid (for an ideal system). Note that the chemical potential of the solute is lower in the mixture than for the pure solute (for an ideal system).
Colligative properties
The modification of boiling and freezing points
SELF-TEST 3.10 Estimate the lowering of the freezing point of the solution made by dissolving 3.0 g (about one cube) of sucrose in 100 g of water. A solute lowers the chemical potential of the solvent but leaves that of the solid unchanged.
Osmosis
The presence of a solute lowers the chemical potential of the solvent in the right-hand compartment, but the application of pressure raises it. The osmotic pressure is the pressure needed to equalize the chemical potential of the solvent in the two compartments.
The osmotic pressure of solutions of biopolymers
The molar concentration [B] of the solute is re- lated to the mass concentration cBmB/Vby. Therefore, by locating the intercept by extrapolation of the data to cB0, we can find the molar mass of the solute.
䊐 19.The molar masses of biological polymers can be determined by measurements of the osmotic pressure of their solutions. Derive an expression for the equilibrium constant K[A2]/[A]2in terms of the depression in vapor pressure caused by a given concentration of compound.
Chemical Equilibrium
Thermodynamic background
- The reaction Gibbs energy
- The variation of r G with composition
- Reactions at equilibrium
- The standard reaction Gibbs energy
Each change contributes to the change in the total Gibbs energy of the mixture, and the overall change is. SELF-TEST 4.6 Calculate the standard reaction Gibbs energy of the oxidation of ammonia to nitric oxide according to the equation 4 NH3(g)5 O2(g)ˆl 4 NO(g)6 H2O(g).
The response of equilibria to the conditions
The presence of a catalyst
They are a measure of the “thermody- namic altitude” of a compound above or below a “sea level” of stability represented by the elements in their reference states (Fig. 4.8). Exergonic compounds lie below the thermodynamic sea level of the el- ements (under standard conditions).
The effect of temperature
As before, we use the approximation that the standard reaction enthalpy and entropy are independent of temperature over the range of interest, so the entire temperature dependence of rG両stems from the TinrG両 rH両TrS両. The opposite is true when rH両0, so we can con- clude that the equilibrium constant of an exothermic reaction decreases with an increase in temperature.
Coupled reactions in bioenergetics
The function of adenosine triphosphate
On account of its exergonic charac- ter, the ADP-phosphate bond has been called a “high-energy phosphate bond.” The name is intended to signify a high tendency to undergo reaction and should not be confused with “strong” bond in its normal chemical sense (that of a high bond en- thalpy). In fact, even in the biological sense it is not of very “high energy.” The action of ATP depends on the bond being intermediate in strength.
The oxidation of glucose
Metabolism continues in the form of the citric acid cycle, in which pyruvate ions are oxidized to CO2, and ends with oxidative phosphorylation, in which O2is reduced to H2O. In the presence of O2, pyruvate is oxidized further during the citric acid cycle and oxidative phosphory- lation, which occur in the mitochondria of cells.
Proton transfer equilibria
Brønsted-Lowry theory
Overall, we write the oxidation of glucose as a result of glycolysis and the citric acid cycle as. As will be familiar from introductory chemistry, the hydronium ion concen- tration is commonly expressed in terms of the pH, which is defined formally as.
Protonation and deprotonation
The extent of deprotonation of a weak acid in solution depends on the acid- ity constant and the initial concentration of the acid, its concentration as prepared. The initial molar concentrations of the species, ignoring any contributions to the concentration of H3Oor OHfrom autoprotolysis of water.
