Living organisms from Prigogine’s perspective: an opportunity to introduce students to biological entropy balance

All living structures, from archaea to human, are open thermodynamic systems analysed through nonequilibrium thermodynamics. Nonequilibrium thermodynamics is a field with important applications to life sciences, which is very often left out of life science courses. A three-step method is suggested to make an easy introduction of nonequilibrium thermodynamics to life science students. The first step is to introduce the Prigogine equation dS = d_eS + d_iS, and explain the meaning of the entropy exchange with the surroundings d_eS and internal entropy generation in the system d_iS. The second step is to show that the Prigogine equation is connected to the equilibrium thermodynamics already known to students. This can be done by deriving the Clausius inequality dS ≥ dq/T, from the Prigogine equation applied to reversible and irreversible processes in closed systems. Reversible and irreversible processes are discussed separately and the results are then combined into the Clausius inequality. The third step is to introduce the fact that the Prigogine equation has a variety of applications in life sciences. This would give the students an opportunity to understand the entropy balance of physiological processes in cells and organisms. The import and accumulation of entropy, entropy generation, and entropy export could be made easier for students to adopt.     

Information dynamics in living systems: prokaryotes, eukaryotes, and cancer

Background

Living systems use information and energy to maintain stable entropy while far from thermodynamic equilibrium. The underlying first principles have not been established.

Findings

We propose that stable entropy in living systems, in the absence of thermodynamic equilibrium, requires an information extremum (maximum or minimum), which is invariant to first order perturbations. Proliferation and death represent key feedback mechanisms that promote stability even in a non-equilibrium state. A system moves to low or high information depending on its energy status, as the benefit of information in maintaining and increasing order is balanced against its energy cost. Prokaryotes, which lack specialized energy-producing organelles (mitochondria), are energy-limited and constrained to an information minimum. Acquisition of mitochondria is viewed as a critical evolutionary step that, by allowing eukaryotes to achieve a sufficiently high energy state, permitted a phase transition to an information maximum. This state, in contrast to the prokaryote minima, allowed evolution of complex, multicellular organisms. A special case is a malignant cell, which is modeled as a phase transition from a maximum to minimum information state. The minimum leads to a predicted power-law governing the in situ growth that is confirmed by studies measuring growth of small breast cancers.

Conclusions

We find living systems achieve a stable entropic state by maintaining an extreme level of information. The evolutionary divergence of prokaryotes and eukaryotes resulted from acquisition of specialized energy organelles that allowed transition from information minima to maxima, respectively. Carcinogenesis represents a reverse transition: of an information maximum to minimum. The progressive information loss is evident in accumulating mutations, disordered morphology, and functional decline characteristics of human cancers. The findings suggest energy restriction is a critical first step that triggers the genetic mutations that drive somatic evolution of the malignant phenotype.     

Thermodynamics of stoichiometric biochemical networks in living systems far from equilibrium

The principles of thermodynamics apply to both equilibrium and nonequilibrium biochemical systems. The mathematical machinery of the classic thermodynamics, however, mainly applies to systems in equilibrium. We introduce a thermodynamic formalism for the study of metabolic biochemical reaction (open, nonlinear) networks in both time-dependent and time-independent nonequilibrium states. Classical concepts in equilibrium thermodynamics-enthalpy, entropy, and Gibbs free energy of biochemical reaction systems-are generalized to nonequilibrium settings. Chemical motive force, heat dissipation rate, and entropy production (creation) rate, key concepts in nonequilibrium systems, are introduced. Dynamic equations for the thermodynamic quantities are presented in terms of the key observables of a biochemical network: stoichiometric matrix Q, reaction fluxes J, and chemical potentials of species mu without evoking empirical rate laws. Energy conservation and the Second Law are established for steady-state and dynamic biochemical networks. The theory provides the physiochemical basis for analyzing large-scale metabolic networks in living organisms.     

Thermodynamic of Water Sorption of Grape Seed: Temperature Effect of Sorption Isotherms and Thermodynamic Characteristics

After determination of sorption isotherms of grape seeds using gravimetric method, five models with temperature effect were used to fit water sorption isotherms of grape seeds to investigate temperature effect on sorption isotherms and its thermodynamic characteristics. Halsey model had minimum mean relative percentage error (M _e ) and all other models used were good in fitting experimental data (with M _e of less than 10 %). Differential parameters such as net isosteric heat, isosteric heat, differential entropy and integral function such as equilibrium heat, net equilibrium heat, integral entropy and surface potential have been calculated. The net isosteric heat, isosteric heat and differential entropy decreased with moisture content. The net equilibrium enthalpy, equilibrium enthalpy and integral entropy decreased with moisture content. The surface potential at four temperatures (35, 45, 55 and 65 °C) was estimated, and low temperature effect was reported.     

Observation of broken detailed balance in polymorphic transformation of bacterial flagellar filament

Living systems operate far from thermodynamic equilibrium, which usually manifests as broken detailed balance at the molecular scale. At larger scales with collective function of many molecules, the presence of non-equilibrium thermodynamics may not be evident. In bacterial motility, the switching dynamics of the flagellar rotary motor was recently discovered to be operating in non-equilibrium. However, the resulting motility pattern at the mesoscale, the run-and-tumble behavior, was normally considered to be a Poisson process that can be described by a two-state equilibrium model. Here, we studied the details of the run-and-tumble behavior by following the polymorphic transformation of the flagellar filaments, observing broken detailed balance that reveals its non-equilibrium nature. Evaluation of entropy production provided a direct measure of the lack of detailed balance and a quantification of the rate of energy dissipation for bacterial run-and-tumble regulation.     

Thermodynamic perspectives on genetic instructions, the laws of biology and diseased states

This article examines in a broad perspective entropy and some examples of its relationship to evolution, genetic instructions and how we view diseases. Living organisms are programmed by functional genetic instructions (FGI), through cellular communication pathways, to grow and reproduce by maintaining a variety of hemistable, ordered structures (low entropy). Living organisms are far from equilibrium with their surrounding environmental systems, which tends towards increasing disorder (increasing entropy). Organisms free themselves from high entropy (high disorder) to maintain their cellular structures for a period of time sufficient to allow reproduction and the resultant offspring to reach reproductive ages. This time interval varies for different species. Bacteria, for example need no sexual parents; dividing cells are nearly identical to the previous generation of cells, and can begin a new cell cycle without delay under appropriate conditions. By contrast, human infants require years of care before they can reproduce. Living organisms maintain order in spite of their changing surrounding environment that decreases order according to the second law of thermodynamics. These events actually work together since living organisms create ordered biological structures by increasing local entropy. From a disease perspective, viruses and other disease agents interrupt the normal functioning of cells. The pressure for survival may result in mechanisms that allow organisms to resist attacks by viruses, other pathogens, destructive chemicals and physical agents such as radiation. However, when the attack is successful, the organism can be damaged until the cell, tissue, organ or entire organism is no longer functional and entropy increases.     

Stochastic thermodynamic limit on E. coli adaptation by information geometric approach

Biological systems process information under noisy environment. Sensory adaptation model of E. coli is suitable for investigation because of its simplicity. To understand the adaptation processing quantitatively, stochastic thermodynamic approach has been attempted. Information processing can be assumed as state transition of a system that consists of signal transduction molecules using thermodynamic approach, and efficiency can be measured as thermodynamic cost. Recently, using information geometry and stochastic thermodynamics, a relationship between speed of the transition and the thermodynamic cost has been investigated for a chemical reaction model. Here, we introduce this approach to sensory adaptation model of E. coli, and examined a relationship between adaptation speed and the thermodynamic cost, and efficiency of the adaptation speed. For increasing external noise level in stimulation, the efficiency decreased, but the efficiency was highly robust to external stimulation strength. Moreover, we demonstrated that there is the best noise to achieve the adaptation in the aspect of thermodynamic efficiency. Our quantification method provides a framework to understand the adaptation speed and the thermodynamic cost for various biological systems.     

Photobiosynthesis of isoprene as an example of leaf excretory function in the light of contemporary thermodynamics

Various aspects in photobiosynthesis of isoprene and its release from leaves into the environment are presently well known. The release of isoprene from the cell can be regarded as dissipation of excess energy (entropy). The systemic release of metabolites into the external medium should be considered as a result of cell excretory activity, one of the most important functions of living systems. Energy dissipation terminates the sustained passage of thermodynamic flows and regulates the overall stability of cell stationary condition. These issues are considered in this review from the standpoint of contemporary thermodynamics. It is concluded that the excretory capacity of living cell is based on thermodynamic dissipation of entropy during irreversible processes that provide for stability and sustainable development of the living organism.     

Detection of interaction between lysionotin and bovine serum albumin using spectroscopic techniques combined with molecular modeling

A combination of fluorescence, UV–Vis absorption, circular dichroism (CD), Fourier transform infrared (FT-IR) and molecular modeling approaches were employed to determine the interaction between lysionotin and bovine serum albumin (BSA) at physiological pH. The fluorescence titration suggested that the fluorescence quenching of BSA by lysionotin was a static procedure. The binding constant at 298 K was in the order of 10⁵ L mol^?1, indicating that a high affinity existed between lysionotin and BSA. The thermodynamic parameters obtained at different temperatures (292, 298, 304 and 310 K) showed that the binding process was primarily driven by hydrogen bond and van der Waals forces, as the values of the enthalpy change (ΔH°) and entropy change (ΔS°) were found to be ?40.81 ± 0.08 kJ mol^?1 and ?35.93 ± 0.27 J mol^?1 K^?1, respectively. The surface hydrophobicity of BSA increased upon interaction with lysionotin. The site markers competitive experiments revealed that the binding site of lysionotin was in the sub-domain IIA (site I) of BSA. Furthermore, the molecular docking results corroborated the binding site and clarified the specific binding mode. The results of UV–Vis absorption, CD and FT-IR spectra demonstrated that the secondary structure of BSA was altered in the presence of lysionotin.     

On the relationship between dissipation and the rate of spontaneous entropy production from linear irreversible thermodynamics

When systems are far from equilibrium, the temperature, the entropy and the thermodynamic entropy production are not defined and the Gibbs entropy does not provide useful information about the physical properties of a system. Furthermore, far from equilibrium, or if the dissipative field changes in time, the spontaneous entropy production of linear irreversible thermodynamics becomes irrelevant. In 2000 we introduced a definition for the dissipation function and showed that for systems of arbitrary size, arbitrarily near or far from equilibrium, the time integral of the ensemble average of this quantity can never decrease. In the low-field limit, its ensemble average becomes equal to the spontaneous entropy production of linear irreversible thermodynamics. We discuss how these quantities are related and why one should use dissipation rather than entropy or entropy production for non-equilibrium systems.     

Driving force of water entry into hydrophobic channels of carbon nanotubes: entropy or energy?

Spontaneous entry of water molecules inside single-wall carbon nanotubes (SWCNTs) has been confirmed by both simulations and experiments. Using molecular dynamics simulations, we have studied the thermodynamics of filling of a (6,6) carbon nanotube in a temperature range from 273 to 353 K and with different strengths of the nanotube–water interaction. From explicit energy and entropy calculations using the two-phase thermodynamics method, we have presented a thermodynamic understanding of the filling behaviour of a nanotube. We show that both the energy and the entropy of transfer decrease with increasing temperature. On the other hand, scaling down the attractive part of the carbon–oxygen interaction results in increased energy of transfer while the entropy of transfer increases slowly with decreasing the interaction strength. Our results indicate that both energy and entropy favour water entry into (6,6) SWCNTs. Our results are compared with those of several recent studies of water entry into carbon nanotubes.     

Thermodynamics of activation gating in olfactory-type cyclic nucleotide-gated (CNGA2) channels

Olfactory-type cyclic nucleotide-gated (CNG) ion channels open by the binding of cyclic nucleotides to a binding domain in the C-terminus. Employing the Eyring rate theory, we performed a thermodynamic analysis of the activation gating in homotetrameric CNGA2 channels. Lowering the temperature shifted the concentration-response relationship to lower concentrations, resulting in a decrease of both the enthalpy ΔH and entropy ΔS upon channel opening, suggesting that the order of an open CNGA2 channel plus its environment is higher than that of the closed channel. Activation time courses induced by cGMP concentration jumps were used to study thermodynamics of the transition state. The activation enthalpies ΔH^‡ were positive at all cGMP concentrations. In contrast, the activation entropy ΔS^‡ was positive at low cGMP concentrations and became then negative at increasing cGMP concentrations. The enthalpic and entropic parts of the activation energies approximately balance each other at all cGMP concentrations, leaving the free enthalpy of activation in the range between 19 and 21 kcal/mol. We conclude that channel activation proceeds through different pathways at different cGMP concentrations. Compared to the unliganded channel, low cGMP concentrations generate a transitional state of lower order whereas high cGMP concentrations generate a transitional state of higher order.     

Specific features in realization of the principle of minimum energy dissipation during individual development

Realization of the principle of minimum energy dissipation (Prigogine??s theorem) during individual development has been analyzed. This analysis has suggested the following reformulation of this principle for living objects: when environmental conditions are constant, the living system evolves to a current steady state in such a way that the difference between entropy production and entropy flow (?? _u function) is positive and constantly decreases near the steady state, approaching zero. In turn, the current steady state tends to a final steady state in such a way that the difference between the specific entropy productions in an organism and its environment tends to be minimal. In general, individual development completely agrees with the law of entropy increase (second law of thermodynamics).     

Development of thermodynamic optimum searching (TOS) to improve the prediction accuracy of flux balance analysis

Flux balance analysis (FBA) has been widely used in calculating steady‐state flux distributions that provide important information for metabolic engineering. Several thermodynamics‐based methods, for example, quantitative assignment of reaction directionality and energy balance analysis have been developed to improve the prediction accuracy of FBA. However, these methods can only generate a thermodynamically feasible range, rather than the most thermodynamically favorable solution. We therefore developed a novel optimization method termed as thermodynamic optimum searching (TOS) to calculate the thermodynamically optimal solution, based on the second law of thermodynamics, the minimum magnitude of the Gibbs free energy change and the maximum entropy production principle (MEPP). Then, TOS was applied to five physiological conditions of Escherichia coli to evaluate its effectiveness. The resulting prediction accuracy was found significantly improved (10.7–48.5%) by comparing with the ¹³C‐fluxome data, indicating that TOS can be considered an advanced calculation and prediction tool in metabolic engineering. Biotechnol. Bioeng. 2013; 110: 914–923. © 2012 Wiley Periodicals, Inc.     

Temperature-Dependent Estimation of Gibbs Energies Using an Updated Group-Contribution Method

Reaction-equilibrium constants determine the metabolite concentrations necessary to drive flux through metabolic pathways. Group-contribution methods offer a way to estimate reaction-equilibrium constants at wide coverage across the metabolic network. Here, we present an updated group-contribution method with 1) additional curated thermodynamic data used in fitting and 2) capabilities to calculate equilibrium constants as a function of temperature. We first collected and curated aqueous thermodynamic data, including reaction-equilibrium constants, enthalpies of reaction, Gibbs free energies of formation, enthalpies of formation, entropy changes of formation of compounds, and proton- and metal-ion-binding constants. Next, we formulated the calculation of equilibrium constants as a function of temperature and calculated the standard entropy change of formation $\left({\mathit{\Delta }}_{\text{f}}{S}^{°}\right)$ using a model based on molecular properties. The median absolute error in estimating ${\mathit{\Delta }}_{\text{f}}{S}^{°}$ was 0.013 kJ/K/mol. We also estimated magnesium binding constants for 618 compounds using a linear regression model validated against measured data. We demonstrate the improved performance of the current method (8.17 kJ/mol in median absolute residual) over the current state-of-the-art method (11.47 kJ/mol) in estimating the 185 new reactions added in this work. The efforts here fill in gaps for thermodynamic calculations under various conditions, specifically different temperatures and metal-ion concentrations. These, to our knowledge, new capabilities empower the study of thermodynamic driving forces underlying the metabolic function of organisms living under diverse conditions.     

Preferential binding of fisetin to the native state of bovine serum albumin: spectroscopic and docking studies

We have investigated the binding of the biologically important flavonoid fisetin with the carrier protein bovine serum albumin using multi-spectroscopic and molecular docking methods. The binding constants were found to be in the order of 10⁴ M^?1 and the number of binding sites was determined as one. MALDI-TOF analyses showed that one fisetin molecule binds to a single bovine serum albumin (BSA) molecule which is also supported by fluorescence quenching studies. The negative Gibbs free energy change (?G°) values point to a spontaneous binding process which occurs through the presence of electrostatic forces with hydrophobic association that results in a positive entropy change (+51.69 ± 1.18 J mol^?1 K^?1). The unfolding and refolding of BSA in urea have been studied in absence and presence of fisetin using steady-state fluorescence and lifetime measurements. Urea denaturation studies indicate that fisetin is gradually released from its binding site on the protein. In the absence of urea, an increase in temperature that causes denaturation of the protein results in the release of fisetin from its bound state indicating that fisetin binds only to the native state of the protein. The circular dichroism (CD) and Fourier transform infrared (FTIR) spectroscopic studies showed an increase in % α-helix content of BSA after binding with fisetin. Site marker displacement studies in accordance with the molecular docking results suggested that fisetin binds in close proximity of the hydrophobic cavity in site 1 (subdomain IIA) of the protein. The PEARLS (Program of Energetic Analysis of Receptor Ligand System) has been used to estimate the interaction energy of fisetin with BSA and the results are in good correlation with the experimental findings.     

Living in Sofia is associated with a risk for antibiotic resistance in Helicobacter pylori: a Bulgarian study

The aim of the retrospective study was to evaluate geographic regions and residence places as possible risk factors for primary Helicobacter pylori antibiotic resistance in Bulgaria. Data from Sofia region, exhibiting the highest living density, were compared to those from other residence places. In total, 588 H. pylori strains from untreated adults who filled a questionnaire were evaluated. Strain susceptibility was assessed by a breakpoint susceptibility test. Resistance rates to metronidazole and clarithromycin have been found to increase, and that to tetracycline has been found to decrease over years. Clarithromycin resistance was 1.7-fold higher in Sofia inhabitants (23.5 %) than elsewhere (13.8 %) and 4.7-fold higher than that in villages (5.0 %). Moreover, the clarithromycin resistance rate was 2.6-fold lower in northern region (8.2 %) than in southern region (21.7 %). On multivariate analysis, sex and residence place were independent predictors for metronidazole resistance. Men were at lower risk for metronidazole resistance compared with women [odds ratio (OR) 0.703; 95 % confidence interval (CI) 0.499–0.990]. Importantly, Sofia inhabitants were at higher risk for the resistance compared with those living elsewhere (OR 1.453; 95 % CI 1.009–2.093). In conclusion, living in Sofia was associated with a risk for antibiotic resistance in H. pylori-positive adults. Living density could be associated with H. pylori resistance rates.     

Efficiency of energy conversion in model biological pumps: Optimization by linear nonequilibrium thermodynamic relations

Experimental investigations showed linear relations between flows and forces in some biological energy converters operating far from equilibrium. This observation cannot be understood on the basis of conventional nonequilibrium thermodynamics. Therefore, the efficiencies of a linear and a nonlinear mode of operation of an energy converter (a hypothetical redox-driven H⁺ pump) were compared. This comparison revealed that at physiological values of the forces and degrees of coupling (1) the force ratio permitting optimal efficiency was much higher in the linear than in the nonlinear mode and (2) the linear mode of operation was at least 10⁶-times more efficient that the nonlinear one. These observations suggest that the experimentally observed linear relations between flows and forces, particularly in the case of oxidative phosphorylation, may be due to a feedback regulation maintaining linear thermodynamic relations far from equilibrium. This regulation may have come about as the consequence of an evolutionary drive towards higher efficiency.     

Purification and Characterization of Cold Adapted Trypsins from Antarctic krill (Euphausia superba)

Three trypsins (TRY-ES) were purified from Antarctic krill (Euphausia superba) by ammonium sulfate precipitation, ion-exchange and gel-filtration chromatography, with relative molecular mass of 28.7, 28.8 and 29.2 kDa respectively. The TRY-ES was inhibited by specific trypsin inhibitors (benzamidine, STI, CHOM and TLCK), with optimum temperature at 40 (Trypsin I), 45 (Trypsin II) and 40 °C (Trypsin III) repetitively. The TRY-ES was stabled between 5 and 40 °C, which was consistent with the red shift in fluorescence intensity peak at 40 °C (Trypsin I) and 45 °C (Trypsin II and Trypsin III) and blue shift at 40 °C (Trypsin II and Trypsin III). The K _cat/K _m values of the TRY-ES was 14.28, 9.46 and 5.93 mM^?1s^?1 respectively, 1.1–10.2 folds higher than trypsins from other crustacean and mammal, which was supported by the differences in thermodynamics parameters, the free energy, enthalpy, and entropy of benzamidine and the TRY-ES system.     

Effect of temperature on functional properties of carp hemoglobin

Precise oxygen equilibrium curves of carp hemoglobin have been obtained in 0·1 m-phosphate from 10 to 25 °C. The equilibrium data were analyzed according to the stepwise oxygenation model of Adair (1925) to obtain the enthalpy change (ΔH_i), entropy change (ΔS_i) and free energy change (ΔG_i) for the i (= 1, 2, 3, 4) individual oxygenation steps. The values of ΔH_i are definitely non-uniform with dependencies on i and the pH of the medium. The co-operative effects in carp hemoglobin are due mainly to enthalpic contributions under the conditions studied here. The thermodynamic properties suggest a structural transition with pK ~8·5 as was also seen in other functional and spectroscopic measurements.