Resting membrane state as an interplay of electrogenic transporters with various pumps.

In this study, a new idea that electrogenic transporters determine cell resting state is presented. The previous assumption was that pumps, especially the sodium one, determine it. The latter meets difficulties, because it violates the law of conservation of energy; also a significant deficit of pump activity is reported. The amount of energy carried by a single ATP molecule reflects the potential of the inner mitochondrial membrane, which is about -200 mV. If pumps enforce a resting membrane potential that is more than twice smaller, then the majority of energy stored in ATP would be dissipated by each pump turning. However, this problem could be solved if control is transferred from pumps to something else, e.g., electrogenic transporters. Then pumps would transfer the energy to the ionic gradient without losses, while the cell surface membrane potential would be associated with the reversal potential of some electrogenic transporters. A minimal scheme of this type would include a sodium-calcium exchanger as well as sodium and calcium pumps. However, note that calcium channels and pumps are positioned along both intracellular organelles and the surface membrane. Therefore, the above-mentioned scheme would involve them as well as possible intercellular communications. Such schemes where various kinds of pumps are assumed to work in parallel may explain, to a great extent, the slow turning rate of the individual members. Interaction of pumps and transporters positioned at distant biological membranes with various forms of energy transfer between them may thus result in hypoxic/reperfusion injury, different kinds of muscle fatigue, and nerve-glia interactions.

An approach to expand description of the pump and co-transporter steady-state current.

The membrane transporters (pumps and co-transporters) are the main players in maintaining the cell homeostasis. Models of various types, each with their own drawbacks, describe transporter behavior. The aim of this study is to find the link between the biophysically based and empirical models to face and solve their specific problems. Instead of decreasing the number of states and using few complex rate constants as is usually done, we use the number of states as great as possible. Then, each transition in the cycle can represent an elementary process and we can apply the mass action law, according to which if rate constants depend on concentrations the dependence is linear. Thus, the expression for the steady state transporter current can be transformed from a function of rate constants into a function of concentrations. When transporter states form a single cycle, it can be characterized by two modes of action - forward and backward ones. Specific mode is realized depending on the available free energy. Each mode of action is characterized by a set of transporter affinities together with a parameter that describes the maximal turning rate. Except standard affinities corresponding to the substances that are binding to the transporter, affinities for the substances that are released are also defined. Such scheme provides great possibilities to construct approximations as each individual affinity could be estimated from experiments as precisely as possible. The approximations may be used for not only description and study of the transporter current but also in cellular models that attempt to describe wide variety of processes in excitable cells.

Calculation of spatially filtered signals produced by a motor unit comprising muscle fibres with non-uniform propagation.

Simulation of actual muscle potentials is necessary to understand processes that underlie changes in electromyographic signals. The work reported aims to analyse existing methods and suggest new ways of calculating precisely the signals (MUS) detected by a multielectrode from motor units (MUs) consisting of homogeneous or inhomogeneous (functionally and geometrically) fibres. Simulation (based on cable equations) of intracellular action potential (IAP) in a muscle fibre with a moderate geometrical inhomogeneity demonstrates that considerable changes in propagation velocity (more than 3.5 times) are accompanied by insignificant changes in the IAP amplitude (< 5%) and IAP shape in the temporal domain. MUS can therefore be considered as the output signal of a timeshift-invariant system whose input signal is the first temporal derivative of the IAP. As a result, calculation of MUS is reduced to a single convolution in the case of muscle composed of both homogeneous and inhomogeneous fibres. The suggested approach is valid for simulation of recordings obtained with points or rectangular plates leading off surfaces from muscles consisting of fibres that are parallel or inclined to the skin surface. The MUS terminal phases are prolonged because of fibre inhomogeneities. The presence of geometrical inhomogeneities results in additional positive-negative phases in MUS.

Analyzing sensory systems with the information distortion function.

The nature and information content of neural signals have been discussed extensively in the neuroscience community. They are important ingredients in many theories on neural function, yet there is still no agreement on the details of neural coding. There have been various suggestions about how information is encoded in neural spike trains: by the number of spikes, by temporal correlations, through single spikes, or by spike patterns in one, or across many neurons. The latter scheme is most general and encompasses many others. We present an algorithm which can recover a coarse representation of a pattern coding scheme, through quantization to a reproduction set of smaller size. Among many possible quantizations, we choose one which preserves as much of the informativeness of the original stimulus/response relation as possible, through the use of an information-based distortion function. This method allows us to study coarse but highly informative models of a coding scheme, and then to refine them when more data becomes available. We shall describe a model in which full recovery is possible and present example for cases with partial recovery.

Neural coding and decoding: communication channels and quantization.

We present a novel analytical approach for studying neural encoding. As a first step we model a neural sensory system as a communication channel. Using the method of typical sequence in this context, we show that a coding scheme is an almost bijective relation between equivalence classes of stimulus/response pairs. The analysis allows a quantitative determination of the type of information encoded in neural activity patterns and, at the same time, identification of the code with which that information is represented. Due to the high dimensionality of the sets involved, such a relation is extremely difficult to quantify. To circumvent this problem, and to use whatever limited data set is available most efficiently, we use another technique from information theory--quantization. We quantize the neural responses to a reproduction set of small finite size. Among many possible quantizations, we choose one which preserves as much of the informativeness of the original stimulus/response relation as possible, through the use of an information-based distortion function. This method allows us to study coarse but highly informative approximations of a coding scheme model, and then to refine them automatically when more data become available.

Calculation of extracellular potentials produced by an inclined muscle fibre at a rectangular plate electrode.

Generally the anatomy of muscles is rather complex, and the fibres have various inclination angles within the muscles. We suggest a fast and reliable way to calculate extracellular potentials produced at a point or rectangular plate electrode by a muscle fibre of finite length with an arbitrary inclination. A muscle fibre was considered to be a linear timeshift-invariant system of potential generation. Then, similar to the fibre without inclination, the extracellular potential produced by an inclined fibre was represented as the output signal of the system; it was calculated as the convolution of the input signal and impulse response. Irrespective of the inclination, the input signal of the system was the first temporal derivative of the intracellular action potential. The impulse response of the system differed for the fibres with inclination. This required a new method of analytical integration over the rectangular electrode area. The approach provides a chance to simulate and analyze motor unit potentials or F-, H- or M-responses produced by muscles of complicated anatomy (circum-pennate or complex pennate type) at electrodes of actual size and location in normals and patients with neuro-muscular disorders.