Equilibrium and steady state thermodynamics of active transport systems studied on simple models simulating Ca2+ transport through sarcoplasmic reticulum membranes

Equilibrium and steady state conditions of primary active transport systems are analyzed in models simulating well known characteristics of calcium transport through sarcoplasmic reticulum membranes. The model for the equilibrium simulations is a closed system with two compartments and a vectorial chemical reaction coupling Ca transport and ATP breakdown. The chemical potential difference for Ca (delta mu Ca) is calculated as a function of the total amount of Ca (Cat) and nucleotides (Nt) in the system. Results are obtained by successive approximations along the thermodynamic pathway of the reaction, up to minimizing free energy of the system, since the solution of the explicit equations cannot be obtained with computers of current precision for data within physiological ranges. delta mu Ca and [Caout] are extremely dependent on Cat and Nt for certain combinations of the variables, i.e. [Caout] can be raised from 10(-8) to 10(-6) M when Cat varies from 0.998 to 1.002 mM, therefore, the running force of the spontaneous reaction is largely shifted by tiny changes in the parameters of the system. For steady state simulations, ATP supply to the system, ADP and Pi drainage, and Ca diffusion through the barrier, are assumed. Again, conditions within physiological ranges can be found where tiny changes in Cat, the rate of ATP supply, diffusion, the ratio between the volumes of the compartments, or a relative uncoupling between the transport and hydrolytic reactions, largely shifts delta mu Ca and [Caout], thus making the steady state highly unstable and therefore well designed to operate as an amplifier of physiological signals. The equilibrium model describes some physicochemical characteristics of the system; the steady state model is more useful to simulate several physiological situations.     

Structural identification of large systems by reduction to subsystems: VLDL triglycerides

The problem of determining whether or not a particular parameter, or the entire compartmental system, is structural identifiable can be extremely difficult if the number of unknown parameters and the number of compartments is large. However, the problem can be considerably simplified if the system can be decomposed into smaller subsystems in such a way that a parameter is structural identifiable with respect to the large system if and only if it is structural identifiable with respect to the subsystem in which it is contained. The paper offers sufficient conditions under which the desired decomposition can be achieved. The conditions are expressed in terms of the digraph of the system so that they are not difficult to verify. Illustrative examples are provided in terms of application to lipoprotein kinetics.     

Epithelial fluid transport: protruding macromolecules and space charges can bring about electro-osmotic coupling at the tight junctions

The purpose of the present work is to investigate whether the idea of epithelial fluid transport based on electro-osmotic coupling at the level of the leaky tight junction (TJ) can be further supported by a plausible theoretical model. We develop a model for fluid transport across epithelial layers based on electro-osmotic coupling at leaky tight junctions (TJ) possessing protruding macromolecules and fixed electrical charges. The model embodies systems of electro-hydrodynamic equations for the intercellular pathway, namely the Brinkman and the Poisson-Boltzmann differential equations applied to the TJ. We obtain analytical solutions for a system of these two equations, and are able to derive expressions for the fluid velocity profile and the electrostatic potential. We illustrate the model by employing geometrical parameters and experimental data from the corneal endothelium, for which we have previously reported evidence for a central role for electro-osmosis in translayer fluid transport. Our results suggest that electro-osmotic coupling at the TJ can account for fluid transport by the corneal endothelium. We conclude that electro-osmotic coupling at the tight junctions could represent one of the basic mechanisms driving fluid transport across some leaky epithelia, a process that remains unexplained.     

Epithelial Fluid Transport: Protruding Macromolecules and Space Charges Can Bring about Electro-Osmotic Coupling at the Tight Junctions

The purpose of the present work is to investigate whether the idea of epithelial fluid transport based on electro-osmotic coupling at the level of the leaky tight junction (TJ) can be further supported by a plausible theoretical model. We develop a model for fluid transport across epithelial layers based on electro-osmotic coupling at leaky tight junctions (TJ) possessing protruding macromolecules and fixed electrical charges. The model embodies systems of electro-hydrodynamic equations for the intercellular pathway, namely the Brinkman and the Poisson-Boltzmann differential equations applied to the TJ. We obtain analytical solutions for a system of these two equations, and are able to derive expressions for the fluid velocity profile and the electrostatic potential. We illustrate the model by employing geometrical parameters and experimental data from the corneal endothelium, for which we have previously reported evidence for a central role for electro-osmosis in translayer fluid transport. Our results suggest that electro-osmotic coupling at the TJ can account for fluid transport by the corneal endothelium. We conclude that electro-osmotic coupling at the tight junctions could represent one of the basic mechanisms driving fluid transport across some leaky epithelia, a process that remains unexplained.     

System-size resonance for intracellular and intercellular calcium signaling

Dynamical behaviors of unidirectionally, linearly coupled as well as isolated calcium subsystems are investigated by taking into account the internal noise resulting from finite system size and thus small numbers of interacting molecules. For an isolated calcium system, the internal noise can induce stochastic oscillations for a steady state close to the Hopf-bifurcation point, and the regularity of those stochastic oscillations depends resonantly on the system size, exhibiting system-size resonance. For the coupled system consisting of two subsystems, the system-size resonance effect observed in the subsystem subject to coupling is significantly amplified due to the nontrivial effects of coupling.     

Unbuffered and buffered supply chains in human metabolism

The investigation of very complex dynamical systems like the human metabolism requires the comprehension of important subsystems. The present paper deals with energy supply chains as subsystems of the metabolism on the molecular, cellular, and individual levels. We form a mathematical model of ordinary differential equations and we show fundamental properties by Fourier techniques. The results are supported by a transition from a system of ordinary differential equations to a partial differential equation, namely, a transport equation. In particular, the behavior of supply chains with dominant pull components is discussed. A special focus lies on the role of buffer compartments.     

Shear-Induced Migration of a Transmembrane Protein within a Vesicle

Biomembranes feature phospholipid bilayers and serve as the interface between cells or organelles and the extracellular and/or cellular environment. Lipids can move freely throughout the membrane; the lipid bilayer behaves like a fluid. Such fluidity is important in terms of the actions of membrane transport proteins, which often mediate biological functions; membrane protein motion has attracted a great deal of attention. Because the proteins are small, diffusion phenomena are often in play, but flow-induced transport has rarely been addressed. Here, we used a dissipative particle dynamics approach to investigate flow-induced membrane protein transport. We analyzed the drift of a membrane protein located within a vesicle. Under the influence of shear flow, the protein gradually migrated toward the vorticity axis via a random walk, and the probability of retention around the axis was high. To understand the mechanism of protein migration, we varied both shear strength and protein size. Protein migration was induced by the balance between the drag and thermodynamic diffusion forces and could be represented by the Péclet number. These results improve our understanding of flow-induced membrane protein transport.     

Über die Nachrichtenaufnahme durch biologische Receptoren

Summary The Hodgkin-Huxley theory of ion fluxes across membranes during excitation is extended to explain the graduated depolarisation (receptor potential) of sensory cell membranes. Electric circuit equivalents of living membranes are developed. Driving forces and velocity coefficients are represented by means of electric parameters. From this model active and passive ionic fluxes can be calculated quantitatively on the basis of transport equations derived from irreversible thermodynamics. Thus the circuit equivalent may be used as an analog computer. Electric receptor models allow a reproduction of all potential curves which have been derived in electrophysiological experiments on PD-receptors. The results obtained by the use of this model agree with the results obtained in biological experiments under various conditions of stimuli. The significance of solution compartments for intra-and extracellular ions in relation to the time functions of various conditions are discussed in detail. This models are of heuristic value in experimental research. In combination with neuron networks they can be used for the analysis of information theoretical problems.     

Thermodynamic and kinetic studies of a stoichiometric model of energetic metabolism under starvation conditions

Abstract A stoichiometric model of anaerobic glycolysis is presented and the influence on its dynamics by the ATP-consuming membrane transport processes and substrate input rate are studied. The model is represented by a system of four ODE (ordinary differential equations), mass conservation equations and functions of state variables, such as thermodynamic efficiency. A low substrate input rate provokes damped oscillations while a high enrgy load determines sustained oscillations in all the metabolites and in thermodynamic efficiency. Due to the lack of linearity between fluxes and forces in the oscillatory region it may be stated that oscillations appear when the system is kinetically controlled.     

京郊农业生物循环系统生态经济能值评估——以密云尖岩村为例

国内外学术界和决策者对于循环农业给予了相当关注,但关于循环农业研究,从产业经济角度进行定量分析目前仍处于相对匮乏状态.以京郊典型的尖岩村农业生物循环农业范式为案例,采用能值方法,以翔实的数据描述了从种植、养殖到食用菌生产的各个阶段能量输入与输出,通过能值评估指标体系判断在整个循环产业链条中,各生产环节对环境经济产生的影响,结果显示:(1)农业生物循环系统的能值投资率(2.57)较养殖(116.23)、食用菌子系统(158.73)低;环境负荷率(1.40)也较养殖子系统(7.24)、食用菌子系统(13)低,表明,该循环模式可减少对自然资源和外来经济投入的依赖,能够获得自身的资源补偿.(2)农业生物循环系统的净能值产出率和可持续发展指数较高,说明,该模式有较强的获利性,是较理想的产业系统,在北京郊区推广价值较高.     

Thermodynamic calculations for biochemical transport and reaction processes in metabolic networks

Thermodynamic analysis of metabolic networks has recently generated increasing interest for its ability to add constraints on metabolic network operation, and to combine metabolic fluxes and metabolite measurements in a mechanistic manner. Concepts for the calculation of the change in Gibbs energy of biochemical reactions have long been established. However, a concept for incorporation of cross-membrane transport in these calculations is still missing, although the theory for calculating thermodynamic properties of transport processes is long known. Here, we have developed two equivalent equations to calculate the change in Gibbs energy of combined transport and reaction processes based on two different ways of treating biochemical thermodynamics. We illustrate the need for these equations by showing that in some cases there is a significant difference between the proposed correct calculation and using an approximative method. With the developed equations, thermodynamic analysis of metabolic networks spanning over multiple physical compartments can now be correctly described.     

Is a constant low-entropy process at the root of glycolytic oscillations?

We measured temporal oscillations in thermodynamic variables such as temperature, heat flux, and cellular volume in suspensions of non-dividing yeast cells which exhibit temporal glycolytic oscillations. Oscillations in these variables have the same frequency as oscillations in the activity of intracellular metabolites, suggesting strong coupling between them. These results can be interpreted in light of a recently proposed theoretical formalism in which isentropic thermodynamic systems can display coupled oscillations in all extensive and intensive variables, reminiscent of adiabatic waves. This interpretation suggests that oscillations may be a consequence of the requirement of living cells for a constant low-entropy state while simultaneously performing biochemical transformations, i.e., remaining metabolically active. This hypothesis, which is in line with the view of the cellular interior as a highly structured and near equilibrium system where energy inputs can be low and sustain regular oscillatory regimes, calls into question the notion that metabolic processes are essentially dissipative.     

The static head method for determining the charge stoichiometry of coupled transport systems. Applications to the sodium-coupled D-glucose transporters of the renal proximal tubule

The static head method for determining the charge stoichiometry (the number of moles of charge translocated per mole of substrate) of a coupled transport system is presented. The method involves establishing experimental conditions under which a membrane potential exactly balances the thermodynamic driving force of a known substrate gradient. The charge stoichiometry can then be calculated from thermodynamic principles. In contrast to the usual steady-state method for determining charge stoichiometry in cell suspensions and vesicle preparations, the static head method is applicable to systems which are not capable of maintaining a constant membrane potential over time. The charge stoichiometries of two renal sodium coupled D-glucose transporters previously identified in brush-border membrane vesicle preparations from the outer cortex (early proximal tubule) and outer medulla (late proximal tubule) are determined. The charge stoichiometries of these transporters are in good agreement with their sodium/glucose coupling ratios arguing against the possibility that glucose transport is coupled to ions other than sodium in these membranes.     

The static head method for determining the charge stoichiometry of coupled transport systems Applications to the sodium-coupled d-glucose transporters of the renal proximal tubule

The static head method for determining the charge stoichiometry (the number of moles of charge translocated per mole of substrate) of a coupled transport system is presented. The method involves establishing experimental conditions under which a membrane potential exactly balances the thermodynamic driving force of a known substrate gradient. The charge stoichiometry can then be calculated from thermodynamic principles. In contrast to the usual steady-state method for determining charge stoichiometry in cell suspensions and vesicle preparations, the static head method is applicable to systems which are not capable of maintaining a constant membrane potential over time. The charge stoichiometries of two renal sodium coupled d-glucose transporters previously identified in brush-border membrane vesicle preparations from the outer cortex (early proximal tubule) and outer medulla (late proximal tubule) are determined. The charge stoichiometries of these transporters are in good agreement with their sodium/glucose coupling ratios arguing against the possibility that glucose transport is coupled to ions other than sodium in these membranes.     

Theoretical study of flow,pressure and solute concentration in double membrane systems

A model system consisting of two rigidly held membranes in series was investigated through the application of the Kedem and Katchalsky thermodynamic single membrane flow equations. This analysis results in predictions of the steady state flow properties as well as values for the solute concentration and pressure of the internal compartment when the system is under the influence of a constant solute concentration or hydrostatic pressure gradient. It is demonstrated that although the flow properties and internal compartment pressure are complicated functions of the membrane permeability coefficients and driving gradient across the system, the relationships are greatly simplified by the explicit appearance of the internal compartment steady state solute concentration in the equations. It is shown that the steady state volume flow rate depends on the absolute value of the solute concentration in the external compartments, as well as the solute concentration gradient across the system. The properties of non-linear dependence of volume flow on concentration gradient, and rectification of volume flow are discussed and shown to be independent properties of the system. For the system under the influence of a solute concentration gradient, the internal compartment pressure can be greater or less than the ambient pressure, and depends mainly on the order in which the membranes are encountered by the volume flow. These properties are qualitatively correlated with certain available experimental observations in biological systems.     

ADP-ribosylation factor and coatomer couple fusion to vesicle budding

The coat proteins required for budding COP-coated vesicles from Golgi membranes, coatomer and ADP-ribosylation factor (ARF) protein, are shown to be required to reconstitute the orderly process of transport between Golgi cisternae in which fusion of transport vesicles begins only after budding ends. When either coat protein is omitted, fusion is uncoupled from budding-donor and acceptor compartments pair directly without an intervening vesicle. Coupling may therefore results from the sequestration of fusogenic membrane proteins into assembling coated vesicles that are only exposed when the coat is removed after budding is complete. This mechanism of coupling explains the phenomenon of "retrograde transport" triggered by uncouplers such as the drug brefeldin A.     

The Balance of Fluid and Osmotic Pressures across Active Biological Membranes with Application to the Corneal Endothelium

The movement of fluid and solutes across biological membranes facilitates the transport of nutrients for living organisms and maintains the fluid and osmotic pressures in biological systems. Understanding the pressure balances across membranes is crucial for studying fluid and electrolyte homeostasis in living systems, and is an area of active research. In this study, a set of enhanced Kedem-Katchalsky (KK) equations is proposed to describe fluxes of water and solutes across biological membranes, and is applied to analyze the relationship between fluid and osmotic pressures, accounting for active transport mechanisms that propel substances against their concentration gradients and for fixed charges that alter ionic distributions in separated environments. The equilibrium analysis demonstrates that the proposed theory recovers the Donnan osmotic pressure and can predict the correct fluid pressure difference across membranes, a result which cannot be achieved by existing KK theories due to the neglect of fixed charges. The steady-state analysis on active membranes suggests a new pressure mechanism which balances the fluid pressure together with the osmotic pressure. The source of this pressure arises from active ionic fluxes and from interactions between solvent and solutes in membrane transport. We apply the proposed theory to study the transendothelial fluid pressure in the in vivo cornea, which is a crucial factor maintaining the hydration and transparency of the tissue. The results show the importance of the proposed pressure mechanism in mediating stromal fluid pressure and provide a new interpretation of the pressure modulation mechanism in the in vivo cornea.     

A microscale model of bacterial and biofilm dynamics in porous media

A microscale model for the transport and coupled reaction of microbes and chemicals in an idealized two-dimensional porous media has been developed. This model includes the flow, transport, and bioreaction of nutrients, electron acceptors, and microbial cells in a saturated granular porous media. The fluid and chemicals are represented as a continuum, but the bacterial cells and solid granular particles are represented discretely. Bacterial cells can attach to the particle surfaces or be advected in the bulk fluid. The bacterial cells can also be motile and move preferentially via a run and tumble mechanism toward a chemoattractant. The bacteria consume oxygen and nutrients and alter the profiles of these chemicals. Attachment of bacterial cells to the soil matrix and growth of bacteria can change the local permeability. The coupling of mass transport and bioreaction can produce spatial gradients of nutrients and electron acceptor concentrations. We describe a numerical method for the microscale model, show results of a convergence study, and present example simulations of the model system.     

Life cycle assessment in urban territories: a case study of Dalian city,China

The International Journal of Life Cycle Assessment - A city comprises different subsystems, such as an industry subsystem, agriculture subsystem, building subsystem, and transport subsystem. With...     

Ansätze zur quantitativen Analyse der Nachrichtenaufnahme und -verarbeitung in biologischen Rezeptoren

The flux equilibrium theory, used for interpretating active and passive ion transport, can explain the generation of receptor potentials. In a model, driving forces and velocity coefficients are represented by the parameters of electric circuits. From these membrane models ionic fluxes can be calculated quantitatively on the basis of transport equations. These equations are derived from the theory of irreversible thermodynamic processes. Receptor models allow a simulation and prediction of the bioelectric potentials which were recorded by other authors in neuro-physiological experiments under various stimulus conditions. The information capacity of a single receptor channel is determined by the ionic flux and the stimulus parameters. In combination with the network of neuron models, receptor models can be used in a perception. The problems of on-off-activation and lateral inhibition were investigated with such a network.