Refined second law of thermodynamics for fast random processes

We establish a refined version of the Second Law of Thermodynamics for Langevin stochastic processes describing mesoscopic systems driven by conservative or non-conservative forces and interacting with thermal noise. The refinement is based on the Monge-Kantorovich optimal mass transport and becomes relevant for processes far from quasi-stationary regime. General discussion is illustrated by numerical analysis of the optimal memory erasure protocol for a model for micron-size particle manipulated by optical tweezers.

Macroscopic motion and gravitation in thermodynamics

A series of examples rarely presented to students is discussed to illustrate a property of thermodynamic equilibrium: small parts of a fully isolated system move as if points of a rigid body, so as to minimize the macroscopic (kinetic) energy EM. Most examples lie in the fields of astronomy and astrophysics, EM then including the gravitational energy. The paradoxical behaviour of gravitation, in particular in the extreme case of black holes,is discussed.

A characterization of conserved quantities in non-equilibrium thermodynamics

The well-known Noether theorem in Lagrangian and Hamiltonian mechanics associates symmetries in the evolution equations of a mechanical system with conserved quantities. In this work, we extend this classical idea to problems of non-equilibrium thermodynamics formulated within the GENERIC (General Equations for Non-Equilibrium Reversible-Irreversible Coupling) framework. The geometric meaning of symmetry is reviewed in this formal setting and then utilized to identify possible conserved quantities and the conditions that guarantee their strict conservation. Examples are provided that demonstrate the validity of the proposed definition in the context of finite and infinite dimensional thermoelastic problems.

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.

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.

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.

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.

Thermodynamics,

Supplementary note (p. S1-24) has caption title: Thermodynamics of gas mixtures, a lecture delivered at Brown university, August 23, 1945.

The general theory of thermodynamics; an introduction to the study of thermodynamics,

"Items of Revision of the General Theory of Thermodynamics, by J. E. Trevor", 1936, (15 leaves) bound in the front.

Foundations of thermodynamics.

Mode of access: Internet.