Theory of single-file noise

A general theoretical approach to the analysis of electric fluctuations generated by the so-called single-file diffusion through narrow channels is presented. The formalism is a slight extension of an approach to electric fluctuations in discrete transport systems with negligible interactions between the particles recently developed by one of the authors. In the single-file transport mechanism interactions between the particles must be taken into account. Three main results of principal interest are: (a) the electric fluctuations around stationary states (at equilibrium and non-equilibrium) are determined by the time-dependent solutions of the macroscopic single-file transport equations, (b) as a direct consequence of the interactions between the ions in the single-file transport the macroscopic time-dependent current and the autocorrelation function of the microscopic current fluctuations can exhibit damped oscillatory behavior, and the current noise spectrum can show peaking, (c) the number of binding sites for the ions within the pores seems to have a strong influence on the oscillatory behavior: with increasing number of binding sites the damping of the oscillations decreases and the peaking of the spectrum becomes stronger.     

Theory of single-file noise.

A general theoretical approach to the analysis of electric fluctuations generated by the so-called single-file diffusion through narrow channels is presented. The formalism is a slight extension of an approach to electric fluctuations in discrete transport systems with negligible interactions between the particles recently developed by one of the authors. In the single-file transport mechanism interactions between the particles must be taken into account. Three main results of principal interest are: (a) the electric fluctuations around stationary states (at equilibrium and non-equilibrium) are determined by the time-dependent solutions of the macroscopic single-file transport equations, (b) as a direct consquence of the interactions between the ions in the single-file transport the macroscopic time-dependent current and the autocorrelation function of the microscopic current fluctuations can exhibit damped oscillatory behavior, and the current noise spectrum can show peaking, (c) the number of binding sites for the ions within the pores seems to have a strong influence on the oscillatory behavior: with increasing number of binding sites the damping of the oscillations decreases and the peaking of the spectrum becomes stronger.     

Thermodynamics and bioenergetics

Bioenergetics is concerned with the energy conservation and conversion processes in a living cell, particularly in the inner membrane of the mitochondrion. This review summarizes the role of thermodynamics in understanding the coupling between the chemical reactions and the transport of substances in bioenergetics. Thermodynamics has the advantages of identifying possible pathways, providing a measure of the efficiency of energy conversion, and of the coupling between various processes without requiring a detailed knowledge of the underlying mechanisms. In the last five decades, various new approaches in thermodynamics, non-equilibrium thermodynamics and network thermodynamics have been developed to understand the transport and rate processes in physical and biological systems. For systems not far from equilibrium the theory of linear non-equilibrium thermodynamics is used, while extended non-equilibrium thermodynamics is used for systems far away from equilibrium. All these approaches are based on the irreversible character of flows and forces of an open system. Here, linear non-equilibrium thermodynamics is mostly discussed as it is the most advanced. We also review attempts to incorporate the mechanisms of a process into some formulations of non-equilibrium thermodynamics. The formulation of linear non-equilibrium thermodynamics for facilitated transport and active transport, which represent the key processes of coupled phenomena of transport and chemical reactions, is also presented. The purpose of this review is to present an overview of the application of non-equilibrium thermodynamics to bioenergetics, and introduce the basic methods and equations that are used. However, the reader will have to consult the literature reference to see the details of the specific applications.     

Physical schemata underlying biological pattern formation-examples, issues and strategies

Biological systems excel at building spatial structures on scales ranging from nanometers to kilometers and exhibit temporal patterning from milliseconds to years. One approach that nature has taken to accomplish this relies on the harnessing of pattern-forming processes of non-equilibrium physics and chemistry. For these systems, the study of biological pattern formation starts with placing a biological phenomenon of interest within the context of the proper pattern-formation schema and then focusing on the ways in which control is exerted to adapt the pattern to the needs of the organism. This approach is illustrated by several examples, notably bacterial colonies (diffusive-growth schema) and intracellular calcium waves (excitable-media schema).     

Steady-State Differential Dose Response in Biological Systems

In pharmacology and systems biology, it is a fundamental problem to determine how biological systems change their dose-response behavior upon perturbations. In particular, it is unclear how topologies, reactions, and parameters (differentially) affect the dose response. Because parameters are often unknown, systematic approaches should directly relate network structure and function. Here, we outline a procedure to compare general non-monotone dose-response curves and subsequently develop a comprehensive theory for differential dose responses of biochemical networks captured by non-equilibrium steady-state linear framework models. Although these models are amenable to analytical derivations of non-equilibrium steady states in principle, their size frequently increases (super) exponentially with model size. We extract general principles of differential responses based on a model’s graph structure and thereby alleviate the combinatorial explosion. This allows us, for example, to determine reactions that affect differential responses, to identify classes of networks with equivalent differential, and to reject hypothetical models reliably without needing to know parameter values. We exemplify such applications for models of insulin signaling.     

On the admittance of membranes associated with channel conduction. Application to channels at non-equilibrium steady state

The small-signal admittance of membranes associated with channel conduction is derived for a general channel model. A general channel model is represented by a set of chemical reactions with each species of the reactions representing a channel state. The membrane admittance is shown to be related to the phenomenological relaxation matrix of the reactions. If the kinetic reactions are at a non-equilibrium steady state, the relaxation matrix may have complex eigenvalues and the equivalent circuit of the membrane admittance may contain RLC or RLC-like branches. For equilibrium kinetic systems, on the other hand, the equivalent circuit contains only RL or RC branches. Thus, the membrane admittance of equilibrium channels is quite different from that of non-equilibrium channels. In particular, we show that the low frequency feature in the admittance of squid axons as observed by Fishman, Poussart, Moore &; Siebenga (1977) can be obtained easily from a non-equilibrium cycling steady-state model.     

缀块性和缀块动态:Ⅰ.概念与机制

缀块性(patchiness)是自然界中最为普遍的现象之一,它存在于各种生态学系统的每一时空尺度上。森林、农田、草地、湖泊等生态系统,通常构成景观缀块(landscape patches),每一景观缀块内部又具有大小、持续时间以及内容都不同的各种缀块。在不同时、空     

Cultures, genes, and neurons in the development of song and singing in brown-headed cowbirds (Molothrus ater)

In brown-headed cowbirds, Molothrus ater, as in many songbird species, vocalizations are fundamental to reproduction. In our studies, experiments utilizing different social housing regimes and geographic comparisons have indicated the social learning of males' vocalizations and associated abilities to use vocalizations effectively during the breeding season. Here, we describe studies indicating roles of cultural and genetic background, and of social influences from females, on male vocal development. These influences can interact with neural regions, including song learning and song control nuclei, but also visual-processing nuclei, in the development of signaling. We argue that a developmental systems approach to the study of vocal behavior provides a structure to organize these different influences and how they may interact with one another over development. A systems approach requires that researchers study the social context in which signals and signalers develop - both the ontogenetic arena in which young animals learn their signals from older animals, and the functional arena in which young and older animals socially interact with one another.     

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.     

Investigating the Principles of Recrystallization from Glyceride Melts

Different lipids were melted and resolidified as model systems to gain deeper insight into the principles of recrystallization processes in lipid-based dosage forms. Solid-state characterization was performed on the samples with differential scanning calorimetry and X-ray powder diffraction. Several recrystallization processes could be identified during storage of the lipid layers. Pure triglycerides that generally crystallize to the metastable α-form from the melt followed by a recrystallization process to the stable β-form with time showed a chain-length-dependent behavior during storage. With increasing chain length, the recrystallization to the stable β-form was decelerated. Partial glycerides exhibited a more complex recrystallization behavior due to the fact that these substances are less homogenous. Mixtures of a long-chain triglyceride and a partial glyceride showed evidence of some interaction between the two components as the partial glyceride hindered the recrystallization of the triglyceride to the stable β-form. In addition, the extent of this phenomenon depended on the amount of partial glyceride in the mixture. Based on these results, changes in solid dosage forms based on glycerides during processing and storage can be better understood.     

Optically monitoring Baker's yeast (Saccharomyces cerevisiae) growing in an air-fluidized/expanded potato starch matrix

Summary In order to study cell behavior in solid fermentation processes, model systems using gelatin and starch have been developed to track Baker's yeast growth. The difficulty in estimating the cell concentration within solid materials arises because both the solid material and the cellular material contribute to the measurement (such as optical resistance). In general, however, the two materials cannot be easily separated, hence the need to measure the cells along with the solid supporting material. A simple spectrophotometric method has previously been shown to work well in both aerated submerged batch cultures and aerated static solid cultures. The optical approach is applied here to monitor a more complex solidified system: cell growth in a novel air-fluidized/expanded bed of yeast growing on a starch matrix. Conventional assays for reducing sugar, total extracellular protein, and extracellular lysine were also applied to monitor yeast behavior in this new system.     

Random environments and stochastic calculus

This paper investigates the use of heuristically derived stochastic differential equations (SDEs) as models in population biology. It is stressed that these equations are best viewed as approximations for more realistic, but often analytically intractable, models. A criterion is presented for determining which interpretation (e.g., Ito or Stratonovich) is likely to serve as the most useful approximation. Several limit theorems are presented which illustrate the use and implications of this criterion. In particular, it is shown that the solutions to sequences of models which approach a given SDE may converge to a diffusion process which corresponds to no solution of the SDE. However, arguing that in population biology the SDEs are generally serving as approximations to stochastic difference equations with autocorrelated noise, it is shown for a variety of models that the Ito calculus may provide a more useful approximation than the Stratonovich. Important limitations of this result and on the use of SDEs are indicated. These findings and observations are compared with those of several papers in the recent literature.     

Self-organization in dissipative structures: A thermodynamic theory for the emergence of prebiotic cells and their epigenetic evolution

This paper presents a discussion on self-organization processes in dissipative structures, in order to highlight the general conditions for raising complexity and generate order. In particular, some concepts were introduced from non-equilibrium thermodynamics and from the Molecular Anamorphic Evolution Theory, especially concerning processes of matter randomization.     

Distributed state simulation of endogenous processes in biological wastewater treatment

Distributed state-type simulations (based on modeling of individual bacteria as they move through a reactor system) predicted a greater sensitivity of enhanced biological phosphorus removal (EBPR) performance to endogenous degradation than did conventional, "lumped"-type simulations (based on average biomass compositions). Recent research has indicated that the variable hydraulic residence times experienced by individual microbial storage product accumulating bacteria in systems with completely mixed reactors tend to produce populations with diverse microbial storage product contents (distributed states). Endogenous degradation in EBPR systems is of particular interest because the polyphosphate accumulating organisms (PAOs) responsible for EBPR rely on the accumulation of three different storage products that may be endogenously degraded. Simulations indicated that as endogenous degradation rates of microbial storage products were increased, EBPR performance decreased more rapidly according to the distributed approach than according to the lumped approach. State profile analysis demonstrated that as these rates increased, the population fraction with depleted storage products also increased, and this tended to increase the error in calculated biokinetic rates by the lumped approach. Simulations based on recently reported endogenous rate coefficients also suggested large differences between distributed and lumped predictions of EBPR performance. These results demonstrated that endogenous decay processes may play a more important role in EBPR than predicted by the lumped approach. This suggests a need for further research to determine endogenous process rates, and for incorporation of this information to distributed-type simulators, as this should lead to improved accuracy of EBPR simulations.     

Current noise around steady states in discrete transport systems

Subject of this paper is the transport noise in discrete systems. The transport systems are given by a number (n) of binding sites separated by energy barriers. These binding sites may be in contact with constant outer reservoirs. The state of the system is characterized by the occupation numbers of particles (current carriers) at these binding sites. The change in time of the occupation numbers is generated by individual “jumps” of particles over the energy barriers, building up the flux matter (for charged particles: the electric current). In the limit n → ∞ continuum processes as e.g. usual diffusion are included in the transport model. The fluctuations in occupation numbers and other quantities linearly coupled to the occupation numbers may be treated with the usual master equation approach. The treatment of the fluctuations in fluxes (current) makes necessary a different theoretical approach which is presented in this paper under the assumption of vanishing interactions between the particles. This approach may be applied to a number of different transport systems in biology and physics (ion transport through porous channels in membranes, carrier mediated ion transport through membranes, jump diffusion e.g. in superionic conductors). As in the master equation approach the calculation of correlations and noise spectra may be reduced to the solution of the macroscopic equations for the occupation numbers. This result may be regarded as a generalization to non-equilibrium current fluctuations of the usual Nyquist theorem relating the current (voltage) noise spectrum in thermal equilibrium to the macroscopic frequency dependent admittance.The validity of the general approach is demonstrated by the calculation of the autocorrelation function and spectrum of current noise for a number of special examples (e.g, pores in membrances, carrier mediated ion transport).     

Studying the Unfolding Kinetics of Proteins under Pressure Using Long Molecular Dynamic Simulation Runs

The usefulness of computational methods such as molecular dynamics simulation has been extensively established for studying systems in equilibrium. Nevertheless, its application to complex non-equilibrium biological processes such as protein unfolding has been generally regarded as producing results which cannot be interpreted straightforwardly. In the present study, we present results for the kinetics of unfolding of apomyoglobin, based on the analysis of long simulation runs of this protein in solution at 3 kbar (1 atm = 1.01325, bar = 101 325 Pa). We hereby demonstrate that the analysis of the data collected within a simulated time span of 0.18 μs suffices for producing results, which coincide remarkably with the available unfolding kinetics experimental data. This not only validates molecular dynamics simulation as a valuable alternative for studying non-equilibrium processes, but also enables a detailed analysis of the actual structural mechanism which underlies the unfolding process of proteins under elusive denaturing conditions such as high pressure.     

Kinetic Mechanisms of Biological Regulation in Photosynthetic Organisms

Principles of regulation on different levels of photosynthetic apparatus are discussed. Mathematical models of isolated photosynthetic reaction centers and general system of energy transduction in chloroplast are developed. A general approach to model these complex metabolic systems is suggested. Regulatory mechanisms in plant cell are correlated with the different patterns of fluorescence induction curve at different internal physiological states of the cells and external (environmental) conditions. Light regulation inside photosynthetic reaction centers, diffusion processes in thylakoid membrane, generation of transmembrane electrochemical potential, coupling with processes of CO₂ fixation in Calvin Cycle are considered as stages of control of energy transformation in chloroplasts in their connection with kinetic patterns of fluorescence induction curves and other spectrophotometric data.     

Phenomenon of Life: Between Equilibrium and Non-Linearity

A model of ordering applicable to biological evolution is presented. It is shown that a steady state (more precisely approaching to a steady state) system of irreversible processes, under conditions of disproportionation of entropy, produces a lower-entropy product, that is, ordering. The ordering is defined as restricting of degrees of freedom: freedom of motion, interactions etc. The model differs from previous ones in that it relates the ordering to processes running not far from equilibrium, described in the linear field of non-equilibrium thermodynamics. It is shown that a system, which includes adenosine triphosphate (ATP) to adenosine diphosphate (ADP) conversion meets the demands of the physical model: it provides energy maintaining steady state conditions, and hydrolysis of ATP proceeding with consumption of water can be tightly conjugated with the most important reactions of synthesis of organic polymers (peptides, nucleotide chains etc.), which proceed with release of water. For these and other reasons ATP seems to be a key molecule of prebiotic evolution. It is argued that the elementary chemical reaction proceeding under control of an enzyme is not necessarily far from equilibrium. The experimental evidence supporting this idea, is presented. It is based on isotope data. Carbon isotope distribution in biochemical systems reveals regularity, which is inherent to steady state systems of chemical reactions, proceeding not far from equilibrium. In living organisms this feature appears at the statistical level, as many completely irreversible and non-linear processes occur in organisms. However not-far-from-equilibrium reactions are inherent to biochemical systems as a matter of principle. They are reconcilable with biochemical behavior. Extant organisms are highly evolved entities which, however, show in their basis the same features, as the simplest chemical systems must have had been involved in the origin of life. Some consequences following from the model, which may be significant for understanding the origin of life and the mechanism of biological evolution, are pointed out.     

A study of instability to electrical symmetry breaking in unicellular systems

The formation of a transcellular electric potential by an initially homogeneous and symmetric unicellular system is treated as the result of a non-equilibrium transition of the homogeneous cellular state to a patterned state. A mathematical theory is set forth which incorporates effects due to ion binding by membraneous structures in the cell interior, nonlinearity in the membrane transport of ions and a membrane-localized, mobile ion transport mechanism. This is a general theory, applicable to any unicellular system, for which a stability criterion giving the response of the system to non-spherically symmetric perturbations can be calculated. The general theory is applied to a specific model of the Fucus egg cell system. The model is found to be unstable to non-spherically symmetric perturbations under experimental conditions which lead to the formation of a net transcellular electric field and accompanying ionic currents. This study shows that the Fucus phenomenon can be thought of as a self-organization event, the result of nonlinear, non-equilibrium processes occurring in the cell membrane.     

Advantage of storage in a fluctuating environment

We will elaborate the evolutionary course of an ecosystem consisting of a population in a chemostat environment with periodically fluctuating nutrient supply. The organisms that make up the population consist of structural biomass and energy storage compartments. In a constant chemostat environment a species without energy storage always out-competes a species with energy reserves. This hinders evolution of species with storage from those without storage. Using the adaptive dynamics approach for non-equilibrium ecological systems we will show that in a fluctuating environment there are multiple stable evolutionary singular strategies (ss's): one for a species without, and one for a species with energy storage. The evolutionary end-point depends on the initial evolutionary state. We will formulate the invasion fitness in terms of Floquet multipliers for the oscillating non-autonomous system. Bifurcation theory is used to study points where due to evolutionary development by mutational steps, the long-term dynamics of the ecological system changes qualitatively. To that end, at the ecological time scale, the trait value at which invasion of a mutant into a resident population becomes possible can be calculated using numerical bifurcation analysis where the trait is used as the free parameter, because it is just a bifurcation point. In a constant environment there is a unique stable equilibrium for one species following the "competitive exclusion" principle. In contrast, due to the oscillatory dynamics on the ecological time scale two species may coexist. That is, non-equilibrium dynamics enhances biodiversity. However, we will show that this coexistence is not stable on the evolutionary time scale and always one single species survives.