Directionality principles in thermodynamics and evolution

Directionality in populations of replicating organisms can be parametrized in terms of a statistical concept: evolutionary entropy. This parameter, a measure of the variability in the age of reproducing individuals in a population, is isometric with the macroscopic variable body size. Evolutionary trends in entropy due to mutation and natural selection fall into patterns modulated by ecological and demographic constraints, which are delineated as follows: (i) density-dependent conditions (a unidirectional increase in evolutionary entropy), and (ii) density-independent conditions, (a) slow exponential growth (an increase in entropy); (b) rapid exponential growth, low degree of iteroparity (a decrease in entropy); and (c) rapid exponential growth, high degree of iteroparity (random, nondirectional change in entropy). Directionality in aggregates of inanimate matter can be parametrized in terms of the statistical concept, thermodynamic entropy, a measure of disorder. Directional trends in entropy in aggregates of matter fall into patterns determined by the nature of the adiabatic constraints, which are characterized as follows: (i) irreversible processes (an increase in thermodynamic entropy) and (ii) reversible processes (a constant value for entropy). This article analyzes the relation between the concepts that underlie the directionality principles in evolutionary biology and physical systems. For models of cellular populations, an analytic relation is derived between generation time, the average length of the cell cycle, and temperature. This correspondence between generation time, an evolutionary parameter, and temperature, a thermodynamic variable, is exploited to show that the increase in evolutionary entropy that characterizes population processes under density-dependent conditions represents a nonequilibrium analogue of the second law of thermodynamics.

Extension of the thermodynamics of small systems to open metastable states: An example

By using a simplified model of small open liquid-like clusters with surface effects, in the gas phase, it is shown how the statistical thermodynamics of small systems can be extended to include metastable supersaturated gaseous states not too far from the gas–liquid equilibrium transition point. To accomplish this, one has to distinguish between mathematical divergence and physical convergence of the open-system partition function.

Folding thermodynamics of a model three-helix-bundle protein

The calculated folding thermodynamics of a simple off-lattice three-helix-bundle protein model under equilibrium conditions shows the experimentally observed protein transitions: a collapse transition, a disordered-to-ordered globule transition, a globule to native-state transition, and the transition from the active native state to a frozen inactive state. The cooperativity and physical origin of the various transitions are explored with a single “optimization” parameter and characterized with the Lindemann criterion for liquid versus solid-state dynamics. Below the folding temperature, the model has a simple free energy surface with a single basin near the native state; the surface is similar to that calculated from a simulation of the same three-helix-bundle protein with an all-atom representation [Boczko, E. M. & Brooks III, C. L. (1995) Science 269, 393–396].

Magnesium-dependent folding of self-splicing RNA: Exploring the link between cooperativity, thermodynamics, and kinetics

Folding of the Tetrahymena self-splicing RNA into its active conformation involves a set of discrete intermediate states. The Mg2+-dependent equilibrium transition from the intermediates to the native structure is more cooperative than the formation of the intermediates from the unfolded states. We show that the degree of cooperativity is linked to the free energy of each transition and that the rate of the slow transition from the intermediates to the native state decreases exponentially with increasing Mg2+ concentration. Monovalent salts, which stabilize the folded RNA nonspecifically, induce states that fold in less than 30 s after Mg2+ is added to the RNA. A simple model is proposed that predicts the folding kinetics from the Mg2+-dependent change in the relative stabilities of the intermediate and native states.

A meanfield approach to the thermodynamics of a protein-solvent system with application to the oligomerization of the tumor suppressor p53

The thermodynamic stability and oligomerization status of the tumor suppressor p53 tetramerization domain have been studied experimentally and theoretically. A series of hydrophilic mutations at Met-340 and Leu-344 of human p53 were designed to disrupt the hydrophobic dimer–dimer interface of the tetrameric oligomerization domain of p53 (residues 325–355). Meanfield calculations of the free energy of the solvated mutants as a function of interdimer distance were compared with experimental data on the thermal stability and oligomeric state (tetramer, dimer, or equilibrium mixture of both) of each mutant. The calculations predicted a decreasing stability and oligomeric state for the following amino acids at residue 340: Met (tetramer) > Ser Asp, His, Gln, > Glu, Lys (dimer), whereas the experimental results showed the following order: Met (tetramer) > Ser > Gln > His, Lys > Asp, Glu (dimers). For residue 344, the calculated trend was Leu (tetramer) > Ala > Arg, Gln, Lys (dimer), and the experimental trend was Leu (tetramer) > Ala, Arg, Gln, Lys (dimer). The discrepancy for the lysine side chain at residue 340 is attributed to the dual nature of lysine, both hydrophobic and charged. The incorrect prediction of stability of the mutant with Asp at residue 340 is attributed to the fact that within the meanfield approach, we use the wild-type backbone configuration for all mutants, but low melting temperatures suggest a softening of the α-helices at the dimer–dimer interface. Overall, this initial application of meanfield theory toward a protein-solvent system is encouraging for the application of the theoretical model to more complex systems.

Structure-assisted design of mechanism-based irreversible inhibitors of human rhinovirus 3C protease with potent antiviral activity against multiple rhinovirus serotypes

Human rhinoviruses, the most important etiologic agents of the common cold, are messenger-active single-stranded monocistronic RNA viruses that have evolved a highly complex cascade of proteolytic processing events to control viral gene expression and replication. Most maturation cleavages within the precursor polyprotein are mediated by rhinovirus 3C protease (or its immediate precursor, 3CD), a cysteine protease with a trypsin-like polypeptide fold. High-resolution crystal structures of the enzyme from three viral serotypes have been used for the design and elaboration of 3C protease inhibitors representing different structural and chemical classes. Inhibitors having α,β-unsaturated carbonyl groups combined with peptidyl-binding elements specific for 3C protease undergo a Michael reaction mediated by nucleophilic addition of the enzyme’s catalytic Cys-147, resulting in covalent-bond formation and irreversible inactivation of the viral protease. Direct inhibition of 3C proteolytic activity in virally infected cells treated with these compounds can be inferred from dose-dependent accumulations of viral precursor polyproteins as determined by SDS/PAGE analysis of radiolabeled proteins. Cocrystal-structure-assisted optimization of 3C-protease-directed Michael acceptors has yielded molecules having extremely rapid in vitro inactivation of the viral protease, potent antiviral activity against multiple rhinovirus serotypes and low cellular toxicity. Recently, one compound in this series, AG7088, has entered clinical trials.

Kinetics and thermodynamics of T cell receptor– autoantigen interactions in murine experimental autoimmune encephalomyelitis

In the current study, cellular and molecular approaches have been used to analyze the biophysical nature of T cell receptor (TCR)–peptide MHC (pMHC) interactions for two autoreactive TCRs. These two TCRs recognize the N-terminal epitope of myelin basic protein (MBP1–11) bound to the MHC class II protein, I-Au, and are associated with murine experimental autoimmune encephalomyelitis. Mice transgenic for the TCRs have been generated and characterized in other laboratories. These analyses indicate that the mice either develop encephalomyelitis spontaneously (172.10 TCR) or only if immunized with autoantigen in adjuvant (1934.4 TCR). Here, we show that the 172.10 TCR binds MBP1–11:I-Au with a 4–5-fold higher affinity than the 1934.4 TCR. Consistent with the higher affinity, 172.10 T hybridoma cells are significantly more responsive to autoantigen than 1934.4 cells. The interaction of the 172.10 TCR with cognate ligand is more entropically unfavorable than that of the 1934.4 TCR, indicating that the 172.10 TCR undergoes greater conformational rearrangements upon ligand binding. The studies therefore suggest a correlation between the strength and plasticity of a TCR–pMHC interaction and the frequency of spontaneous disease in the corresponding TCR transgenic mice. The comparative analysis of these two TCRs has implications for understanding autoreactive T cell recognition and activation.

Persistent confusion of total entropy and chemical system entropy in chemical thermodynamics.

The change in free energy with temperature at constant pressure of a chemical reaction is determined by the sum (dS) of changes in entropy of the system of reagents, dS(i), and the additional entropy change of the surroundings, dS(H), that results from the enthalpy change, W. A faulty identification of the total entropy change on reaction with dS(i) has been responsible for the attribution of general validity to the expressions (d deltaG/dT)p = -deltaS(i) and d(deltaG/T)/d(1/T)= deltaH, which are found in most textbooks and in innumerable papers.

Irreversible inactivation of interleukin 2 in a pump-based delivery environment.

The physical stability of pharmaceutical proteins in delivery environments is a critical determinant of biological potency and treatment efficacy, and yet it is often taken for granted. We studied both the bioactivity and physical stability of interleukin 2 upon delivery via continuous infusion. We found that the biological activity of the delivered protein was dramatically reduced by approximately 90% after a 24-hr infusion program. Only a portion of these losses could be attributed to direct protein deposition on the delivery surfaces. Analysis of delivered protein by size exclusion chromatography gave no indication of insulin-like, surface-induced aggregation phenomena. Examination of the secondary and tertiary structure of both adsorbed and delivered protein via Fourier-transform infrared spectroscopy, circular dichroism, and fluorescence spectroscopy indicated that transient surface association of interleukin 2 with the catheter tubing resulted in profound, irreversible structural changes that were responsible for the majority of the biological activity losses.

Large electrostatic differences in the binding thermodynamics of a cationic peptide to oligomeric and polymeric DNA.

Results presented here demonstrate that the thermodynamics of oligocation binding to polymeric and oligomeric DNA are not equivalent because of long-range electrostatic effects. At physiological cation concentrations (0.1-0.3 M) the binding of an oligolysine octacation KWK6-NH2 (+8 charge) to single-stranded poly(dT) is much stronger per site and significantly more salt concentration dependent than the binding of the same ligand to an oligonucleotide, dT(pdT)10 (-10 charge). These large differences are consistent with Poisson-Boltzmann calculations for a model that characterizes the charge distributions with key preaveraged structural parameters. Therefore, both the experimental and the theoretical results presented here show that the polyelectrolyte character of a polymeric nucleic acid makes a large contribution to both the magnitude and the salt concentration dependence of its binding interactions with simple oligocationic ligands.