ELECTRONICS MODELS OF MEMBRANE AND SYNAPTIC JUNCTIONS

Abstract

An ionic model is proposed to understand and predict the behaviour of nerve and synaptic junction. The various characteristics of the excitable membrane are studied under steady-state and transient conditions. Under steady-state, current-voltage character istic of the proposed model is obtained. The built-involtage, which is a cause of negative resistance region in voltage current characteristic, is estimated for a membrane dipped in equimolar solution of potassium ions. The voltage-current characteristic obtained by Hamel and Zimmerman, using dipcle theory is compared. Using ionic model, the width of ionic region, the effect of polyvalent ions such as calcium ions and the effect of injected ions on membrane are discussed. The distribution of charged ions in membrane under transient condition is found and an ionic transistor model is used to understand the behaviour of nerve under different excitation voltages. The amplification factor of an equivalent ionic transistor using planar and circular • • • -Vlllgeometry of nerves is estimated separately* The time delay for starting of potassium current is also obtained by using this model. Results thus obtained are very near to the values known experimentally. A step response of an ionic transistor is obtained theoretically using Laplace transform technique. The sodium and potassium currents with their conductances f0r a step excitation voltage, are computed and compared with the results obtained by Hodgkin- Huxley's mathematical model and that of voltage-clamp experiment results. The currents, voltages and conductances of sodium and potassium are compared for three different excitation voltages. Further for three different excitation voltages various waveforms of ionic currents are obtained using this proposed model. The behaviour of ionic currents of nerves under hydro-static pressure is predicted using this model and is compared with experimental results. It is observed that the predicted results are very similar to the results available for nerve under hydro-static pressure. A comparison is made by computing the currents for a semi conductor transistor under hydrostatic pressure. The behaviours of ionic and semiconductor transistor are very much similar, suggesting that the laws governing an electronic flow are applicable in both physical and physiological domains. F0r different excitation voltages the concept of membrane conductivity modulation is used to calculate various parameters of an ionic transistor. -ix- The concept of ionic models is extended to study synaptic junctions- between nerves and muscles. A new model is proposed to calculate the time lag of current build-up in post-synaptic junction. The voltage-current characteristic of synaptic junction is obtained using this model. This characteristic has a negative resistance region. The firing potential, at which a spike is generat ed in post-synaptic intracellular solution is estimated for the case of cat and frog separately. Results are very near to available experimental data. Special properties of synapses are explained using this model. The generation of the spike at post-synaptic membrane and miniature endplate potential are also studied. An explanation of repetitive discharge of synapse is given using this model. A diffusion equation together with proper boundary conditions is solved to calculate the flux of ions to reach the other end of pre-synaptic membrane before a release of transmitter to generate a spike in post synaptic membrane. The latency period obtained mathe matically agrees with the known experimental value. Finally some suggestions along with the critical discussions are given for further work. Many problems could be solved using this proposed model.