Thermodynamics of natural selection II: Chemical Carnot cycles

This is the second in a series of three papers devoted to energy flow and entropy changes in chemical and biological processes, and to their relations to the thermodynamics of computation. In the first paper of the series, it was shown that a general-form dimensional argument from the second law of thermodynamics captures a number of scaling relations governing growth and development across many domains of life. It was also argued that models of physiology based on reversible transformations provide sensible approximations within which the second-law scaling is realized. This paper provides a formal basis for decomposing general cyclic, fixed-temperature chemical reactions, in terms of the chemical equivalent of Carnot's cycle for heat engines. It is shown that the second law relates the minimal chemical work required to perform a cycle to the Kullback-Leibler divergence produced in its chemical output ensemble from that of a Gibbs equilibrium. Reversible models of physiology are used to create reversible models of natural selection, which relate metabolic energy requirements to information gain under optimal conditions. When dissipation is added to models of selection, the second-law constraint is generalized to a relation between metabolic work and the combined energies of growth and maintenance.     

A biomolecular implementation of logically reversible computation with minimal energy dissipation

Energy dissipation associated with logic operations imposes a fundamental physical limit on computation and is generated by the entropic cost of information erasure, which is a consequence of irreversible logic elements. We show how to encode information in DNA and use DNA amplification to implement a logically reversible gate that comprises a complete set of operators capable of universal computation. We also propose a method using this design to connect, or 'wire', these gates together in a biochemical fashion to create a logic network, allowing complex parallel computations to be executed. The architecture of the system permits highly parallel operations and has properties that resemble well known genetic regulatory systems.     

Kinetics of large-ligand binding to one-dimensional lattices: theory of irreversible binding

Exact solutions are obtained for the time dependence of the extent of irreversible binding of ligands that cover more than one lattice site to a homogeneous one-dimensional lattice. The binding may be cooperative or noncooperative and the lattice either finite or infinite. Although the form of the solution is most convenient when the ligand concentration is buffered, exact numerical or approximate analytical solutions, including upper and lower bounds, can be derived for the case of variable ligand concentration as well. The physical reason behind the relative simplicity of the kinetics of irreversible as opposed to reversible binding in such systems is discussed.     

Dissipative Irreversibility from Nosé's Reversible Mechanics

Abstract

Nose's Hamiltonian mechanics makes possible the efficient simulation of irreversible flows of mass, momentum and energy. Such flows illustrate the paradox that reversible microscopic equations of motion underlie the irreversible behavior described by the second law of thermodynamics. This generic behavior of molecular many-body systems is illustrated here for the simplest possible system, with only one degree of freedom: a one-body Frenkel-Kontorova model for isothermal electronic conduction. This model system, described by Nosé-Hoover Hamiltonian dynamics, exhibits several interesting features: (1) deterministic and reversible equations of motion; (2) Lyapunov instability, with phase-space offsets increasing exponentially with time; (3) limit cycles; (4) dissipative conversion of work (potential energy) into heat (kinetic energy): and (5) phase-space contraction, a characteristic feature of steady irreversible flows. The model is particularly instructive in illustrating and explaining a paradox associated with steady-state statistical mechanics: the Gibbs entropy of a nonequilibrium steady state decreases continuously to minus infinity.     

Thermodynamic Costs of Information Processing in Sensory Adaptation

Biological sensory systems react to changes in their surroundings. They are characterized by fast response and slow adaptation to varying environmental cues. Insofar as sensory adaptive systems map environmental changes to changes of their internal degrees of freedom, they can be regarded as computational devices manipulating information. Landauer established that information is ultimately physical, and its manipulation subject to the entropic and energetic bounds of thermodynamics. Thus the fundamental costs of biological sensory adaptation can be elucidated by tracking how the information the system has about its environment is altered. These bounds are particularly relevant for small organisms, which unlike everyday computers, operate at very low energies. In this paper, we establish a general framework for the thermodynamics of information processing in sensing. With it, we quantify how during sensory adaptation information about the past is erased, while information about the present is gathered. This process produces entropy larger than the amount of old information erased and has an energetic cost bounded by the amount of new information written to memory. We apply these principles to the E. coli''s chemotaxis pathway during binary ligand concentration changes. In this regime, we quantify the amount of information stored by each methyl group and show that receptors consume energy in the range of the information-theoretic minimum. Our work provides a basis for further inquiries into more complex phenomena, such as gradient sensing and frequency response.     

Theoretical analysis of Lumry-Eyring models in differential scanning calorimetry

A theoretical analysis of several protein denaturation models (Lumry-Eyring models) that include a rate-limited step leading to an irreversibly denatured state of the protein (the final state) has been carried out. The differential scanning calorimetry transitions predicted for these models can be broadly classified into four groups: situations A, B, C, and C′. (A) The transition is calorimetrically irreversible but the rate-limited, irreversible step takes place with significant rate only at temperatures slightly above those corresponding to the transition. Equilibrium thermodynamics analysis is permissible. (B) The transition is distorted by the occurrence of the rate-limited step; nevertheless, it contains thermodynamic information about the reversible unfolding of the protein, which could be obtained upon the appropriate data treatment. (C) The heat absorption is entirely determined by the kinetics of formation of the final state and no thermodynamic information can be extracted from the calorimetric transition; the rate-determining step is the irreversible process itself. (C′) same as C, but, in this case, the rate-determining step is a previous step in the unfolding pathway. It is shown that ligand and protein concentration effects on transitions corresponding to situation C (strongly rate-limited transitions) are similar to those predicted by equilibrium thermodynamics for simple reversible unfolding models. It has been widely held in recent literature that experimentally observed ligand and protein concentration effects support the applicability of equilibrium thermodynamics to irreversible protein denaturation. The theoretical analysis reported here disfavors this claim.     

Reversible and Irreversible Inhibition of High-Affinity Choline Transport Caused by Ethylcholine Aziridinium Ion

The effect of ethylcholine aziridinium ion (AF64A) on choline transport in hippocampal, striatal, and cerebrocortical synaptosomes was studied. Synaptosomes prepared from these three brain regions were equally sensitive to AF64A. Low concentrations of AF64A produced a reversible inhibition (IC50 values = 1.35-2.25 microM), whereas higher concentrations produced an irreversible inhibition (IC50 values = 25-30 microM), which started as competitive. The irreversible component of the inhibition was independent of extracellular Na+ concentration, a finding suggesting that the choline transporter is alkylated at its outward position. The kinetics of the inhibition were rapid and similar in the three brain regions examined. The high-affinity choline transport was more sensitive to the toxin than the low-affinity choline transport. Based on these results, we propose a kinetic model that explains the reversible and the irreversible inhibitions induced by AF64A. The possible relationships between the concentrations that in vitro produce reversible and irreversible inhibition and those that in vivo produce selective and nonselective cholinergic hypofunction are discussed.     

Entropy involved in fidelity of DNA replication

Information has an entropic character which can be analyzed within the framework of the Statistical Theory in molecular systems. R. Landauer and C.H. Bennett showed that a logical copy can be carried out in the limit of no dissipation if the computation is performed sufficiently slowly. Structural and recent single-molecule assays have provided dynamic details of polymerase machinery with insight into information processing. Here, we introduce a rigorous characterization of Shannon Information in biomolecular systems and apply it to DNA replication in the limit of no dissipation. Specifically, we devise an equilibrium pathway in DNA replication to determine the entropy generated in copying the information from a DNA template in the absence of friction. Both the initial state, the free nucleotides randomly distributed in certain concentrations, and the final state, a polymerized strand, are mesoscopic equilibrium states for the nucleotide distribution. We use empirical stacking free energies to calculate the probabilities of incorporation of the nucleotides. The copied strand is, to first order of approximation, a state of independent and non-indentically distributed random variables for which the nucleotide that is incorporated by the polymerase at each step is dictated by the template strand, and to second order of approximation, a state of non-uniformly distributed random variables with nearest-neighbor interactions for which the recognition of secondary structure by the polymerase in the resultant double-stranded polymer determines the entropy of the replicated strand. Two incorporation mechanisms arise naturally and their biological meanings are explained. It is known that replication occurs far from equilibrium and therefore the Shannon entropy here derived represents an upper bound for replication to take place. Likewise, this entropy sets a universal lower bound for the copying fidelity in replication.     

Models of growth, self-reproduction and autoregulation based on consideration of reaction vessels with distensible, semipermeable walls]

We constructed non-equilibrium thermodynamics of the open physical-chemical irreversible processes in reactors with the strain semipermeable walls. This thermodynamics does not use the reciprocal relations of Onsager, so it may be applied when the stability stationary state is far from equilibrium. One of a general consequences of this thermodynamics is the statement: coordinated growth and self-reproduction are possible near the absolute equilibrium of the dissolvent and near the absolute stability stationary state of all chemicals with the absolute conservation of the differential equations of chemical kinetics. The supposition of ideal mixing is unnecessary; this condition is fulfilled automatically with diffusion. Growth and self-reproduction are not connected with positive eigenvalue of the differential equation of chemical kinetics. It is possible to construct a model of autoregulation and differentiation with this thermodynamics. The uniquness of such autoregulation follows from the mathematical theory [1]. The mathematical foundation of this thermodynamics is given in [1].     

Synergistic Combination of Electrolysis and Electroporation for Tissue Ablation

Electrolysis, electrochemotherapy with reversible electroporation, nanosecond pulsed electric fields and irreversible electroporation are valuable non-thermal electricity based tissue ablation technologies. This paper reports results from the first large animal study of a new non-thermal tissue ablation technology that employs “Synergistic electrolysis and electroporation” (SEE). The goal of this pre-clinical study is to expand on earlier studies with small animals and use the pig liver to establish SEE treatment parameters of clinical utility. We examined two SEE methods. One of the methods employs multiple electrochemotherapy-type reversible electroporation magnitude pulses, designed in such a way that the charge delivered during the electroporation pulses generates the electrolytic products. The second SEE method combines the delivery of a small number of electrochemotherapy magnitude electroporation pulses with a low voltage electrolysis generating DC current in three different ways. We show that both methods can produce lesion with dimensions of clinical utility, without the need to inject drugs as in electrochemotherapy, faster than with conventional electrolysis and with lower electric fields than irreversible electroporation and nanosecond pulsed ablation.     

Thermodynamics of Terrestrial Evolution

The causal element of biological evolution and development can be understood in terms of a potential function which is generalized from the variational principles of irreversible thermodynamics. This potential function is approximated by the rate of entropy production in a configuration space which admits of macroscopic excursions by fluctuation and regression as well as microscopic ones. Analogously to Onsager's dissipation function, the potential takes the form of a saddle surface in this configuration space. The path of evolution following from an initial high dissipation state within the fixed constraint provided by the invariant energy flux from the sun tends toward the stable saddle point by a series of spontaneous regressions which lower the entropy production rate and by an alternating series of spontaneous fluctuations which introduce new internal constraints and lead to a higher entropy production rate. The potential thus rationalizes the system's observed tendency toward "chemical imperialism" (high dissipation) while simultaneously accommodating the development of "dynamic efficiency" and complication (low dissipation).     

On the computation of molecular surface correlations for protein docking using fourier techniques

The computation of surface correlations using a variety of molecular models has been applied to the unbound protein docking problem. Because of the computational complexity involved in examining all possible molecular orientations, the fast Fourier transform (FFT) (a fast numerical implementation of the discrete Fourier transform (DFT)) is generally applied to minimize the number of calculations. This approach is rooted in the convolution theorem which allows one to inverse transform the product of two DFTs in order to perform the correlation calculation. However, such a DFT calculation results in a cyclic or "circular" correlation which, in general, does not lead to the same result as the linear correlation desired for the docking problem. In this work, we provide computational bounds for constructing molecular models used in the molecular surface correlation problem. The derived bounds are then shown to be consistent with various intuitive guidelines previously reported in the protein docking literature. Finally, these bounds are applied to different molecular models in order to investigate their effect on the correlation calculation.     

Reversible and irreversible interactions between elastin and plasma lipoproteins

The interactions between radiolabeled, human plasma lipoproteins and elastin derived from bovine ligamentum nuchae were investigated using a washout technique. The interaction was characterised by Ki, a coefficient of irreversible binding, and Kr, the reversible partition coefficient. For both low-density lipoproteins (LDL) and high-density lipoproteins (HDL) the Ki values decreased as total lipoprotein concentration increased, suggesting that the binding is saturable, and were similar in magnitude to those measured by other workers using elastin derived from the human aorta. For both LDL and HDL the Kr values were independent of lipoprotein concentration in the range 0.1 microgram/ml-1.5 micrograms/ml. At a total protein concentration of 1.5 mg/ml in the incubation medium, the reversible interactions were comparable in magnitude to the irreversible.     

Gel-free proteomic methodologies to study reversible cysteine oxidation and irreversible protein carbonyl formation

Abstract

Oxidative modifications in proteins have been traditionally considered as hallmarks of damage by oxidative stress and aging. However, oxidants can generate a huge variety of reversible and irreversible modifications in amino acid side chains as well as in the protein backbones, and these post-translational modifications can contribute to the activation of signal transduction pathways, and also mediate the toxicity of oxidants. Among the reversible modifications, the most relevant ones are those arising from cysteine oxidation. Thus, formation of sulfenic acid or disulfide bonds is known to occur in many enzymes as part of their catalytic cycles, and it also participates in the activation of signaling cascades. Furthermore, these reversible modifications have been usually attributed with a protective role, since they may prevent the formation of irreversible damage by scavenging reactive oxygen species. Among irreversible modifications, protein carbonyl formation has been linked to damage and death, since it cannot be repaired and can lead to protein loss-of-function and to the formation of protein aggregates. This review is aimed at researchers interested on the biological consequences of oxidative stress, both at the level of signaling and toxicity. Here we are providing a concise overview on current mass-spectrometry-based methodologies to detect reversible cysteine oxidation and irreversible protein carbonyl formation in proteomes. We do not pretend to impose any of the different methodologies, but rather to provide an objective catwalk on published gel-free approaches to detect those two types of modifications, from a biologist's point of view.     

Purification and characterization of two classes of neurotoxins from the funnel web spider, Agelenopsis aperta

Two classes of paralytic toxins were isolated from the venom of Agelenopsis aperta and their chemical and larvicidal properties characterized. Five acylpolyamine toxins (alpha-agatoxins) of molecular masses 452, 488, 489, 504, and 505 Da produce immediate but reversible paralysis in Manduca sexta following injection. Six insecticidal peptides (mu-agatoxins) produce a gradual but irreversible paralysis. The complete amino acid sequences (36-38 residues) of the mu-agatoxins are presented. These peptides contain eight half-cystines and are quite similar in sequence. At least four of these toxins are amidated at the carboxyl terminus. The secondary structure of one of these toxins (mu-Aga V) was investigated.     

Problems with entropy in biology.

Entropy has been widely referred to as a measure of biological order. The validity of this notion is discussed in conjunction with it's relation to the spontaneous creation of order. Information theory offers a quantitative method for characterization of order, however, it is not fundamentally connected to formalisms of irreversible thermodynamics, and it is severely limited because the meaning and value of the information is neglected. A completely general notation is proposed for including measures of order of a biological system in the entropy balance equation of irreversible thermodynamics. Problems of assigning energetic equivalents to measures of order are indicated, with a final focus on the problem of meaning and value.     

The action of agonists and antagonists at the histamine H1 receptor and receptor protection studies in guinea pig ileum

We have examined the ability of histamine and the competitive reversible antihistamines to protect the histamine H1 receptor against alkylation with the 2-haloalkylamines, phenoxybenzamine and SY-14. In isolated guinea pig ileum these irreversible antagonists produce a parallel shift in the dose-response curve to histamine with retention of the maximum response if they are used at concentrations less than about 10(-6)M. Treatment with these 2-haloalkylamines in the presence of a high concentration of histamine did not alter the blocking activity. Thus histamine appears to be unable to protect its own receptor against irreversible blockade. The competitive reversible antagonists, on the other hand, did provide effective protection against irreversible blockade. It is likely that the competitive reversible H1 receptor antagonists have at least some part of their attachment site in common with irreversible antagonists of the 2-haloalkylamine type, while the inability of histamine to provide self-protection suggests that its primary attachment site is different from that of the antagonists.     

Integrated stoichiometric, thermodynamic and kinetic modelling of steady state metabolism

The quantitative analysis of biochemical reactions and metabolites is at frontier of biological sciences. The recent availability of high-throughput technology data sets in biology has paved the way for new modelling approaches at various levels of complexity including the metabolome of a cell or an organism. Understanding the metabolism of a single cell and multi-cell organism will provide the knowledge for the rational design of growth conditions to produce commercially valuable reagents in biotechnology. Here, we demonstrate how equations representing steady state mass conservation, energy conservation, the second law of thermodynamics, and reversible enzyme kinetics can be formulated as a single system of linear equalities and inequalities, in addition to linear equalities on exponential variables. Even though the feasible set is non-convex, the reformulation is exact and amenable to large-scale numerical analysis, a prerequisite for computationally feasible genome scale modelling. Integrating flux, concentration and kinetic variables in a unified constraint-based formulation is aimed at increasing the quantitative predictive capacity of flux balance analysis. Incorporation of experimental and theoretical bounds on thermodynamic and kinetic variables ensures that the predicted steady state fluxes are both thermodynamically and biochemically feasible. The resulting in silico predictions are tested against fluxomic data for central metabolism in Escherichia coli and compare favourably with in silico prediction by flux balance analysis.