Differences between non-specific and bio-specific, and between equilibrium and non-equilibrium, interactions in biological systems

The interaction forces between biological molecules and surfaces are much more complex than those between non-biological molecules or surfaces, such as colloidal particle surfaces. This complexity is due to a number of factors: (i) the simultaneous involvement of many different molecules and different non-covalent forces - van der Waals, electrostatic, solvation (hydration, hydrophobic), steric, entropic and 'specific', and (ii) the flexibility of biological macromolecules and fluidity of membranes. Biological interactions are better thought of as 'processes' that evolve in space and time and, under physiological conditions, involve a continuous input of energy. Such systems are, therefore, not at thermodynamic equilibrium, or even tending towards equilibrium. Recent surface forces apparatus (SFA) and atomic force microscopy (AFM) measurements on supported model membrane systems (protein-containing lipid bilayers) illustrate these effects. It is suggested that the major theoretical challenge is to establish manageable theories or models that can describe the spatial and time evolution of systems consisting of different molecules subject to certain starting conditions or energy inputs.     

Thermodynamically feasible kinetic models of reaction networks

The dynamics of biological reaction networks are strongly constrained by thermodynamics. An holistic understanding of their behavior and regulation requires mathematical models that observe these constraints. However, kinetic models may easily violate the constraints imposed by the principle of detailed balance, if no special care is taken. Detailed balance demands that in thermodynamic equilibrium all fluxes vanish. We introduce a thermodynamic-kinetic modeling (TKM) formalism that adapts the concepts of potentials and forces from irreversible thermodynamics to kinetic modeling. In the proposed formalism, the thermokinetic potential of a compound is proportional to its concentration. The proportionality factor is a compound-specific parameter called capacity. The thermokinetic force of a reaction is a function of the potentials. Every reaction has a resistance that is the ratio of thermokinetic force and reaction rate. For mass-action type kinetics, the resistances are constant. Since it relies on the thermodynamic concept of potentials and forces, the TKM formalism structurally observes detailed balance for all values of capacities and resistances. Thus, it provides an easy way to formulate physically feasible, kinetic models of biological reaction networks. The TKM formalism is useful for modeling large biological networks that are subject to many detailed balance relations.     

Controlling composition of coexisting phases via molecular transitions

Phase separation and transitions among different molecular states are ubiquitous in living cells. Such transitions can be governed by local equilibrium thermodynamics or by active processes controlled by biological fuel. It remains largely unexplored how the behavior of phase-separating systems with molecular transitions differs between thermodynamic equilibrium and cases in which the detailed balance of the molecular transition rates is broken because of the presence of fuel. Here, we present a model of a phase-separating ternary mixture in which two components can convert into each other. At thermodynamic equilibrium, we find that molecular transitions can give rise to a lower dissolution temperature and thus reentrant phase behavior. Moreover, we find a discontinuous thermodynamic phase transition in the composition of the droplet phase if both converting molecules attract themselves with similar interaction strength. Breaking the detailed balance of the molecular transition leads to quasi-discontinuous changes in droplet composition by varying the fuel amount for a larger range of intermolecular interactions. Our findings showcase that phase separation with molecular transitions provides a versatile mechanism to control properties of intracellular and synthetic condensates via discontinuous switches in droplet composition.     

生物分子网络弹性研究进展

弹性是生物分子网络重要且基础的属性之一,一方面弹性赋予生物分子网络抵抗内部噪声与环境干扰并维持其自身基本功能的能力,另一方面,弹性为网络状态的恢复制造了阻力。生物分子网络弹性研究试图回答如下3个问题：a. 生物分子网络弹性的产生机理是什么？b. 弹性影响下生物分子网络的状态如何发生转移？c. 如何预测生物网络状态转换临界点,以防止系统向不理想的状态演化？因此,研究生物分子网络弹性有助于理解生物系统内部运作机理,同时对诸如疾病发生临界点预测、生物系统状态逆转等临床应用具有重要的指导意义。鉴于此,本文主要针对以上生物分子网络弹性领域的3个热点研究问题,在研究方法和生物学应用上进行了系统地综述,并对未来生物分子网络弹性的研究方向进行了展望。     

Opto-Mechanical Coupling in Interfaces under Static and Propagative Conditions and Its Biological Implications

Fluorescent dyes are vital for studying static and dynamic patterns and pattern formation in cell biology. Emission properties of the dyes incorporated in a biological interface are known to be sensitive to their local environment. We report that the fluorescence intensity of dye molecules embedded in lipid interfaces is indeed a thermodynamic observable of the system. Opto-mechanical coupling of lipid-dye system was measured as a function of the thermodynamic state of the interface. The corresponding state diagrams quantify the thermodynamic coupling between intensity I and lateral pressure π. We further demonstrate that the coupling is conserved upon varying the temperature T. Notably, the observed opto-mechanical coupling is not limited to equilibrium conditions, but also holds for propagating pressure pulses. The non-equilibrium data show, that fluorescence is especially sensitive to dynamic changes in state such as the LE-LC phase transition. We conclude that variations in the thermodynamic state (here π and T, in general pH, membrane potential V, etc also) of lipid membranes are capable of controlling fluorescence intensity. Therefore, interfacial thermodynamic state diagrams of I should be obtained for a proper interpretation of intensity data.     

Was heißt “lebendig”?

“Life” means “being alive” of special entities, which we call “organisms”. From a physical point of view, living entities are open systems, which exchange matter as well as energy with their surroundings. Against disruptive influences permanently present, they maintain actively and autonomously a steady state far from the thermodynamic equilibrium. This dynamic state of living beings represents a functional order, an internal “organization”. That means that the involved processes one and all must be correlated in such a way that they in sum prevent the breakdown of the living state. Organization implies functionality, which in turn requires structural relationships, and structures require information for their specification. Information in turn presupposes a source, which is constituted in living systems by the nucleic acids. Organisms are unique in having a capacity to use information, which is stored in the nucleic acid and yields the basis for their specific internal organization in its perpetuation: Living beings, and only they, show a self‐maintained organization.     

Feller processes: the next generation in modeling. Brownian motion, Lévy processes and beyond

We present a simple construction method for Feller processes and a framework for the generation of sample paths of Feller processes. The construction is based on state space dependent mixing of Lévy processes. Brownian Motion is one of the most frequently used continuous time Markov processes in applications. In recent years also Lévy processes, of which Brownian Motion is a special case, have become increasingly popular. Lévy processes are spatially homogeneous, but empirical data often suggest the use of spatially inhomogeneous processes. Thus it seems necessary to go to the next level of generalization: Feller processes. These include Lévy processes and in particular brownian motion as special cases but allow spatial inhomogeneities. Many properties of Feller processes are known, but proving the very existence is, in general, very technical. Moreover, an applicable framework for the generation of sample paths of a Feller process was missing. We explain, with practitioners in mind, how to overcome both of these obstacles. In particular our simulation technique allows to apply Monte Carlo methods to Feller processes.     

The Critical Roles of Information and Nonequilibrium Thermodynamics in Evolution of Living Systems

Living cells are spatially bounded, low entropy systems that, although far from thermodynamic equilibrium, have persisted for billions of years. Schrödinger, Prigogine, and others explored the physical principles of living systems primarily in terms of the thermodynamics of order, energy, and entropy. This provided valuable insights, but not a comprehensive model. We propose the first principles of living systems must include: (1) Information dynamics, which permits conversion of energy to order through synthesis of specific and reproducible, structurally-ordered components; and (2) Nonequilibrium thermodynamics, which generate Darwinian forces that optimize the system. Living systems are fundamentally unstable because they exist far from thermodynamic equilibrium, but this apparently precarious state allows critical response that includes: (1) Feedback so that loss of order due to environmental perturbations generate information that initiates a corresponding response to restore baseline state. (2) Death due to a return to thermodynamic equilibrium to rapidly eliminate systems that cannot maintain order in local conditions. (3) Mitosis that rewards very successful systems, even when they attain order that is too high to be sustainable by environmental energy, by dividing so that each daughter cell has a much smaller energy requirement. Thus, nonequilibrium thermodynamics are ultimately responsible for Darwinian forces that optimize system dynamics, conferring robustness sufficient to allow continuous existence of living systems over billions of years.     

Calculating thermodynamic data for transitions of any molecularity from equilibrium melting curves

In this paper, we derive the general forms of the equations required to extract thermodynamic data from equilibrium transition curves on oligomeric and polymeric nucleic acids of any molecularity. Significantly, since the equations and protocols are general, they also can be used to characterize thermodynamically equilibrium processes in systems other than nucleic acids. We briefly review how the reduced forms of the general equations have been used by many investigators to evaluate mono- and bimolecular transitions, and then explain how these equations can be generalized to calculate thermodynamic parameters from common experimental observables for transitions of higher molecularities. We emphasize the strengths and weaknesses of each method of data analysis so that investigators can select the approach most appropriate for their experimental circumstances. We also describe how to analyze calorimetric heat capacity curves and noncalorimetric differentiated melting curves so as to extract both model-independent and model-dependent thermodynamic data for transitions of any molecularity. The general equations and methods of analysis described in this paper should be of particular interest to laboratories that currently are investigating association and dissociation processes in nucleic acids that exhibit molecularities greater than two.     

Nonequilibrium linear behavior of biological systems. Existence of enzyme-mediated multidimensional inflection points.

The linear phenomenological equations of nonequilibrium thermodynamics are limited theoretically to near equilibrium although a number of biological systems have been shown to exhibit a "linear" relationship between steady-state flows and conjugate thermodynamic forces outside the range of equilibrium. We have found a multidimensional inflection point which can exist well outside the range of equilibrium around with enzyme-catalyzed reactions exhibit "linear" behavior between the logarithm of reactant concentrations and enzyme catalyzed flows. A set of sufficient conditions has been derived which can be applied to any enzyme mechanism to determine whether a multidimensional inflection point exists. The conditions do not appear overly restrictive and may be satisfied by a large variety of coupled enzyme reactions. It is thus possible that the linearity observed in some biological systems may be explained in terms of enzyme operating near this multidimensional point.     

Osmophobic effect of glycerol on irreversible thermal denaturation of rabbit creatine kinase

Protein stability plays an extremely important role not only in its biological function but also in medical science and protein engineering. Osmolytes provide a general method to protect proteins from the unfolding and aggregation induced by extreme environmental stress. In this study, the effect of glycerol on protection of the model enzyme creatine kinase (CK) against heat stress was investigated by a combination of spectroscopic method and thermodynamic analysis. Glycerol could prevent CK from thermal inactivation and aggregation in a concentration-dependent manner. The spectroscopic measurements suggested that the protective effect of glycerol was a result of enhancing the structural stability of native CK. A further thermodynamic analysis using the activated-complex theory suggested that the effect of glycerol on preventing CK against aggregation was consistent with those previously established mechanisms in reversible systems. The osmophobic effect of glycerol, which preferentially raised the free energy of the activated complex, shifted the equilibrium between the native state and the activated complex in favor of the native state. A comparison of the inactivation rate and the denaturation rate suggested that the protection of enzyme activity by glycerol should be attributed to the enhancement of the structural stability of the whole protein rather than the flexible active site.     

Fluorescent and dispersion experiments on biological membranes under micro-gravity

Almost all biological processes, especially those involved in signal reception and signal transduction, depend on the physical and physiological properties of biological membranes. It has been shown, that neuronal tissue and the speed of the action potential (AP) which is the basic neuronal unit of all nervous activity, is sensitive to changes in gravity as well as to other weak external forces. We strongly suppose the membrane to be the most important factor in gravitational responses although it is very difficult to observe the effects of gravity changes on these fragile thermodynamic systems. Therefore we developed two different experiments to measure the structural changes and the lateral membrane tension of spheroid cells under microgravity.     

Thermodynamic principles of the behavior of biological systems

A theory of the behavior of biological systems is proposed which is an extension of the conception of biological evolution (Gladyshev, 1977, Gladyshev, 1978) based on classical (equilibrium) thermodynamics. A thermodynamic theory of homeostasis is presented, in accordance with which homeostatic mechanisms of regulation are connected with a compensative shift of a fundamental quasi-equilibrium. The principle of least compulsion is formulated on the basis of thermodynamic laws and describes behavior of biological systems. A fundamental thermodynamic equation of behavioral processes is introduced. The Weber-Fechner law is shown to be a corollary of the fundamental thermodynamic equation.     

Biosynthetic potentials of metabolites and their hierarchical organization

A major challenge in systems biology is to understand how complex and highly connected metabolic networks are organized. The structure of these networks is investigated here by identifying sets of metabolites that have a similar biosynthetic potential. We measure the biosynthetic potential of a particular compound by determining all metabolites than can be produced from it and, following a terminology introduced previously, call this set the scope of the compound. To identify groups of compounds with similar scopes, we apply a hierarchical clustering method. We find that compounds within the same cluster often display similar chemical structures and appear in the same metabolic pathway. For each cluster we define a consensus scope by determining a set of metabolites that is most similar to all scopes within the cluster. This allows for a generalization from scopes of single compounds to scopes of a chemical family. We observe that most of the resulting consensus scopes overlap or are fully contained in others, revealing a hierarchical ordering of metabolites according to their biosynthetic potential. Our investigations show that this hierarchy is not only determined by the chemical complexity of the metabolites, but also strongly by their biological function. As a general tendency, metabolites which are necessary for essential cellular processes exhibit a larger biosynthetic potential than those involved in secondary metabolism. A central result is that chemically very similar substances with different biological functions may differ significantly in their biosynthetic potentials. Our studies provide an important step towards understanding fundamental design principles of metabolic networks determined by the structural and functional complexity of metabolites.     

生态学研究中的分析与能值分析理论

与能值是研究生态系统自组织过程的两个重要的目标函数。分析与能值分析理论在 2 0世纪 70年代开始应用于生态学研究 ,它们有各自的理论起点 ,在应用上从不同的角度表现生态系统功能 ,两者的互补关系受到了生态学家的关注 ,并在实际应用中取得了有益的研究成果。从与能值各自的理论基础与研究成果出发 ,概述了两者在描述生态系统功能上的互补关系 ,并分析了其在生态学理论研究及实际应用上的重要意义     

The temperature jump relaxation technique.

The temperature jump relaxation technique is a convenient and general means of studying rapid reversible reactions of biological macromolecules. Recent advances in automatic data acquisition and the introduction of different optical detection systems will soon allow us to exploit the full potential of kinetic measurements near equilibrium. On the other hand, the kinetic approach can be quite limited if not accompanied by detailed structural and thermodynamic studies. Finally, we must accept the fact that one can rarely demonstrate a reaction mechanism to the exclusion of all plausible alternative models.     

Molecular simulations of protein dynamics: new windows on mechanisms in biology

Recent advances in computer hardware and software have led to the development of increasingly successful molecular simulations of protein structural dynamics that are intrinsic to biological processes. These simulations have resulted in models that increasingly agree with experimental observations, suggest new experiments and provide insights into biological mechanisms. Used in combination with data obtained with sophisticated experimental techniques, simulations are helping us to understand biological complexity at the atomic and molecular levels and are giving promising insights into the genetic, thermodynamic and functional/mechanistic behaviour of biological processes. Here, we highlight some examples of such approaches that illustrate the current state and potential of the field of molecular simulation.