Please help me about this Biomedical Engineering question. Q1. a) In a few sente

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Please help me about this Biomedical Engineering question.

Q1. a) In a few sentences, explain the reason why space clamp and voltage experiments are conducted? b) Assume that a membrane is permeable to Ca and CI but not to a large cation R. The Inside concentration are [RCI]-100mM and [CaCl2]-200mM, and the outside concentration is (CaCl21-400mM. Derive the Donnan Equilibrium and find the steady state equilibrium concentration for Ca2+. What is the membrane voltage at the steady state? e) Suppose a membrane has an active Na-K pump with Rx-2.727 k, RNA 94.34 k2, Re = 3.33 ks2. E,--72mV, EN.-55mV, Ec =-49.5mV and Cm =1 F as shown in Fig.1. i) Find the direction and the magnitude of the current for sodium ion, Na", when the membrane is in equilibrium. ii) Find the direction and value of currents INa and IK generated by the active pump related to part (a). ii) Find the current pulse magnitude and duration that will drive Vm to threshold at 3 ms. Assume that the threshold potential is -40mV and time reference of the current application is to-0, iv) Find and sketch Ic for this active behaviour of membrane for t20. v) After the membrane is activated, what would you expect on the changes of the parameters like Vm, RK, RNA of the membrane? (F-96487 C/gram equivalent, R-83141/Ko mole at 27 oC, T-270C) Outaide Px Cm Inside Figure 1

Explanation / Answer

Voltage Clamp Technique:

The voltage clamp is a classic electrophysiological technique to measure ion currents across the cell membrane. Under voltage clamp conditions, voltage-gated ion channels open and close as normal, but the voltage clamp apparatus compensates for the changes in the ion current to maintain a constant membrane potential. The investigator sets a desired holding membrane potential, also referred to as holding voltage or command potential, and the voltage clamp uses negative feedback to maintain the cell at this desired holding potential.

The voltage clamp was first applied by Cole in the 1930s to 1940s, and then further developed by Hodgkin and Huxley. The original two electrodes that Cole, Hodgkin, and Huxley used were fine wires that could be inserted only into extremely large cells such as the squid giant axon, which are as large as 1 mm in diameter. Hodgkin and Huxley used the squid giant axon to determine the ionic basis of the action potential, as described in a landmark set of papers in 1952.

The voltage-clamp technique is applicable only to spherical cells. In nonspherical cells, such as neurons, the membrane potential is not clamped distal to the voltage-clamp electrode. This means that the current recorded by the voltage-clamp electrode is the sum of the local current and of axial currents from locations experiencing different membrane potentials. Furthermore, voltage-gated currents recorded from a nonspherical cell are, by definition, severely distorted due to the lack of space clamp. Justifications for voltage clamping in nonspherical cells are, first, that the lack of space clamp is not severe in neurons with short dendrites. Second, passive cable theory may be invoked to justify application of voltage clamp to branching neurons, suggesting that the potential decay is sufficiently shallow to allow spatial clamping of the neuron. Here, using numerical simulations, we show that the distortions of voltage-gated K(+) and Ca(2+) currents are substantial even in neurons with short dendrites. The simulations also demonstrate that passive cable theory cannot be used to justify voltage clamping of neurons due to significant shunting to the reversal potential of the voltage-gated conductance during channel activation. Some of the predictions made by the simulations were verified using somatic and dendritic voltage-clamp experiments in rat somatosensory cortex.

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