The three-state model for the elementary process of energy conversion in muscle

A three-state model for the elementary process of energy conversion in striated muscle is analysed; in two of the three states, the crossbridge is attached to an actin site, while the third is a detached state. This model accounts for the mechanical properties of steady shortening and lengthening processes as well as those of isometric and isotonic transient processes in a quantitative way. Moreover, qualitative agreement is obtained for the total energy liberation from muscle. Biochemical properties are also computed for transient processes. Comparisons are made with other models with “three states”.     

Evidence from insect fibrillar muscle about the elementary contractile process

Bundles of myofibrils prepared from the dorsal longitudinal flight muscles of giant water bugs show oscillatory contractile activity in solutions of low ionic strength containing ATP and 10^-8-10^-7 M Ca²⁺. This is due to delay between changes of length and changes of tension under activating conditions. The peculiarities of insect fibrillar muscle which give rise to this behavior are (1) the high elasticity of relaxed myofibrils, (2) a smaller degree of Ca²⁺ activation of ATPase activity in unstretched myofibrils and extracted actomyosin, and (3) a direct effect of stretch on ATPase activity. It is shown that the cross-bridges of striated muscle are probably formed from the heads of three myosin molecules and that in insect fibrillar muscle the cycles of mechanochemical energy conversion in the cross-bridges can be synchronized by imposed changes of length. This material is more suitable than vertebrate striated muscle for a study of the nature of the elementary contractile process.     

A three-state model for energy trapping and chlorophyll fluorescence in photosystem II incorporating radical pair recombination

The multiphasic fluorescence induction kinetics upon a high intensity light pulse have been measured and analyzed at a time resolution of 10 micros in intact leaves of Peperomia metallica and Chenopodium album and in chloroplasts isolated from the latter. Current theories and models on the relation between chlorophyll fluorescence yield and primary photochemistry in photosystem II (PSII) are inadequate to describe changes in the initial phase of fluorescence induction and in the dark fluorescence level F(0) caused by pre-energization of the system with single turnover excitation(s). A novel model is presented, which gives a quantitative relation between the efficiencies of primary photochemistry, energy trapping, and radical pair recombination in PSII. The model takes into account that at least two turnovers are required for stationary closure of a reaction center. An open reaction center is transferred with high efficiency into its semiclosed (-open) state. This state is characterized by Q(A) and P680 in the fully reduced state and a lifetime equal to the inverse of the rate constant of Q(A)(-) oxidation (approx. 250 micros). The fluorescence yield of the system with 100% of the centers in the semiclosed state is 50% of the maximal yield with all centers in the closed state at fluorescence level F(m). A situation with approximately 100% of the centers in the semiclosed state is reached after a single turnover excitation in the presence of 3-(3',4'-dichlorophenyl)-1,1-dimethylurea (DCMU). The lifetime of this state under these conditions is approximately 10 s. Closure of a semiclosed (-open) center occurs with low efficiency in a second turnover. The low(er) efficiency is caused by the rate of P(+) reduction by the secondary donor Y(Z) being competitive with the rate of radical pair recombination in second and following turnovers. The single-turnover-induced alterations in the initial kinetics of the fluorescence concomitantly with a 15-25% increase in F(o) can be simulated with the present so called three-state model of energy trapping. The experimental data suggest evidence for an electrostatic effect of local charges in the vicinity of the reaction center affecting the rate of radical pair recombination in the reaction center.     

A three-state model for inactivation of sodium permeability

The inactivation of Na⁺ permeability in single myelinated motor nerve fibres of Rana esculenta was investigated under voltage and current clamp conditions at 20°C in Ringer's solution and under blocked K⁺ currents. Development of inactivation and its recovery was described by two potential-dependent time constants: The smaller time constant followed the usual bell-shaped function of membrane potential, whereas the larger one was monotone-increasing with more negative potentials. Several three-state models for inactivation were investigated. The experiments could best be approximated by a model with two open and one closed state for inactivation following: open ? closed ? open. Rate constants were determined for all transitions shown from the voltage clamp experiments. The action potentials computed by means of the proposed model were in good agreement with those measured, both in Ringer's solution and under blocked K⁺ current conditions.     

An elementary kinetic model of energy coupling in biological membranes

The purpose of this work is to contribute to the understanding of the fundamental kinetic properties of the processes of energy coupling in biological membranes. For this, we consider a model of a microorganism that, in its plasma membrane, expresses two electrogenic enzymes (E(1) and E(2)) transporting the same monovalent cation C and electrodiffusive paths for C and for a monovalent anion A. E(1) (E(2)) couples transport C to the reaction S(1)<-->P(1) (S(2)<-->P(2)). We developed a mathematical model that describes the rate of change of the electrical potential difference across the membrane, of the internal concentrations of C and A, and of the concentrations of S(2) and P(2). The enzymes are incorporated via two-state kinetic models; the passive ionic fluxes are represented by classical formulations of electrodiffusion. The microorganism volume is maintained constant by accessory regulatory devices. The model is utilized for stationary and dynamic studies for the case of bacteria employing the electrochemical gradient of Na(+) as energetic intermediate. Among other conclusions, the results show that the membrane potential represents the relevant kinetic intermediate for the overall coupling between the energy donor reaction S(1)<-->P(1) and the synthesis of S(2).     

A three-state model for connexin37 gating kinetics

The gating behavior of human connexin 37 (hCx37) is unaffected by the nature of the bathing monovalent (for Na, K, Rb). It is modified by [Mg] in the millimolar range. For fitting the kinetics, we propose a simple extension to three states of the canonical 2-state model of the hemichannel. The extra closed state allows for some immobilization of a hemichannel at high transjunctional voltages. The model is reasonably efficient at fitting data at various voltage protocols. Interpreting the fits of the data at different [Mg] is consistent with a binding site for Mg.     

A fuel cell model in biological energy conversion

Consideration of the high energy conversion efficiency of biological systems leads to the idea that mechanical energy may arise via a series of steps, of which a rate-determining one occurs in a fuel-cell-like element. The mitochondrion is suggested as the site of such entities. The observed efficiency would be consistent with a potential loss of about 0.5 V. The supposed biological fuel cells would be able to act as an electrical power source, driving chemical reactions against their spontaneous direction.Considerations of electrical conductance in wet proteins shows that ohmic (i.e., non-interfacial) potential differences through mitochondrial membranes could be negligible. The cathodic reaction would be the reduction of oxygen, O₂+4H⁺+4e^–H₂O and the anodic reaction, 2NADH⁺2NAD+2H⁺+4e^–. The anodes are suggested as being molecular, buried in the invaginations of the inner membrane forming the cristae. The cathodes are located on enzymes which are probably on the inner side of the membrane but could be, respectively, on the outer (cathodic), and the inner (anodic) sides. The electron transport occurs though proteins within each membrane. The relation of the so-called fuel cell potentials to potentially observable membrane potentials, and those measured by fluorescent probes, are discussed.The fuel cells produce electrical energy and this energy is transferred to ADP by an electrolytic route, using electric power from the cells to work the endergonic ATP synthesis. Possible electrode reactions are suggested. An exponential dependence of the rate of ATP synthesis upon applied potential has been observed.Biological cells radiate electromagnetically in the 10⁹ to 10¹⁵ Hz region. Such phenomena support a fuel cell model of a biological cell because they demand the presence of mobile electrons.     

An assessment of a coupled three-state kinetic model for sodium conductance changes.

The behavior of a coupled three-state kinetic scheme is examined to see if it might be a viable model for the conductance changes of sodium channels. It is found that for simulations of experiments which determine the properties of the Hodgkin-Huxley m and h gates, the three-state scheme performs approximately equivalently to the Hodgkin-Huxley model. In particular, the three-state scheme successfully simulates those experiments which the Hodgkin-Huxley model successfully simulates, but fails to simulate those newer voltage clamp experiments which give results anomalous to the H-H model. It is concluded that the three-state scheme is probably as good as the H-H model, but is not a viable successor to it.     

Bayesian methods for a three-state model for rodent carcinogenicity studies

The objective of a chronic rodent bioassay is to assess the impact of a chemical compound on the development of tumors. However, most tumor types are not observable prior to necropsy, making direct estimation of the tumor incidence rate problematic. In such cases, estimation can proceed only if the study incorporates multiple interim sacrifices or we make use of simplified parametric or nonparametric models. In addition, it is widely accepted that other factors, such as weight, can be related to both dose level and tumor onset, confounding the association of interest. However, there is not typically enough information in the current study to assess such effects. The addition of historical data can help alleviate this problem. In this article, we propose a novel Bayesian semiparametric model for the analysis of data from rodent carcinogenicity studies. We develop informative prior distributions for covariate effects through the use of historical control data and outline a Gibbs sampling scheme. We implement the model by analyzing data from a National Toxicology Program chronic rodent bioassay.     

Theory of excitable membranes. I. A simple model for a three-state artificial membrane.

The effect of the thermal fluctuation on the orientation distribution pattern of globular protein molecules in a two-dimensional lattice was investigated by the method of computer simulation. A set of interaction parameters was assigned to interaction sites on each molecule and the interaction energy between two molecules was given by the product of the parameters of facing sites. Orientation fluctuation was assumed to take place with the probability proportional to the Boltzmann factor. Patterns having different degrees of order appeared with the change of temperature. The entropy and other thermodynamic quantities of these patterns were calculated, and gradual and transitional changes of the pattern were discussed in comparison with the case of simple atoms or molecules.     

The currently accepted model of primary energy conversion in the plant photosystems must be substantially modernized

According to the current model of primary events in plants, electronic excitations generated in antenna chlorophylls (Chl) by the light rapidly migrate within vast Chl ensembles, reach the reaction centres (RCs) and initiate the primary photoreactions of electron transfer from the RC special pairs (P700 and P680 in plant photosystems). A minor portion of electronic excitations is lost en route, in particular, via fluorescence of Chl a. A number of fluorescence parameters in vivo had been reliably established in many independent studies. Based on these parameters, the author calculated a dimensionless value, the ratio of fluorescence yields emitted by PS-2 and PS-1 Chl a ensembles. The ratio proved to differ 5-10 times from that obtained in experiments. Such a divergence seems to indicate an internal discrepancy in the currently used model. The author proposes a substantial modernization of the model by introducing a new subpicosecond state for RCs, which precedes the primary reaction of electron transfer from the RC special pairs.     

Stochastic description of the three-state model of the Na channel

The three-state model of the Na channel is formulated stochastically and various observable quantities calculated from this model. This model assumes that the Na channel can occupy one of three states--resting, open and inactivated--and that each channel is independent. This is a simplified representation of the model proposed by Aldrich et al. (1983) mainly with respect to the neuroblastoma. When the system contains many channels, the probability distribution of the numbers of the channels that occupy each of these states is a time-dependent multinomial distribution and the distribution of the first passage time from resting state to open state becomes an exponential decay function with higher components. The average and variance of the channel current calculated by the distribution show the time course with a single peak and its ratio converges to the current of a single channel. Stochastic treatment of the transient process developed here gives a method of estimating all of the transition rates and the number of channels in the system.     

A model of human muscle energy expenditure

A model of muscle energy expenditure was developed for predicting thermal, as well as mechanical energy liberation during simulated muscle contractions. The model was designed to yield energy (heat and work) rate predictions appropriate for human skeletal muscle contracting at normal body temperature. The basic form of the present model is similar to many previous models of muscle energy expenditure, but parameter values were based almost entirely on mammalian muscle data, with preference given to human data where possible. Nonlinear phenomena associated with submaximal activation were also incorporated. The muscle energy model was evaluated at varying levels of complexity, ranging from simulated contractions of isolated muscle, to simulations of whole body locomotion. In all cases, acceptable agreement was found between simulated and experimental energy liberation. The present model should be useful in future studies of the energetics of human movement using forward dynamic computer simulation.