3 1 Physics and Decrement As you learned in the last lesson the neuron membrane has many gated channels that make it excitable able to change its potential rapidly However in the dendrites and soma these channels open for a short period then close generating small graded potentials that can sum at the axon hillock but are insufficient to send electrical signals quickly over long distances In this lesson we will learn more about the physics of how these electrical signals decay The axon must have different properties from the dendrites and soma in order to send signals quickly and faithfully over long distances From the axon hillock to the axon terminal there are no ligand or mechanically gated channels Instead the membrane has channels that allow it to actively propagate an electrical signal that does not decay over space or time In the next lesson we will learn about these active membrane properties that allow neurons to communicate in spite of the physical limitations that cause signal decrement When a chemical or mechanical stimulus opens ligand gated or mechanically gated ion channels in the membrane ion flow across the membrane changes Most of these ion channels are specific to Na K or Cl The resulting inward and outward ion currents I cause graded potentials V that passively spread through the cell and sum at the membrane around the axon hillock These passive graded changes in charge spread via electrotonic conduction charged particles will be attracted to others of opposite charge and repel others of like charge pushing the charge along through the cell see figure below For example as Na comes into the cell it will be attracted to negatively charged particles in the cell It will also repel other positively charged particles close to the membrane which will do the same thing in turn to others Recall that all along the neuron membrane there are leak channels for K and Na that are constitutively open As the electrical signal is electrotonically conducted through the cell some Na will leak in and some K will leak out in accordance with their electrochemical gradients and both the ion currents INa and IK and difference in charge across the membrane Vm will decrease in magnitude Thus I and the change in Vm decrease farther from the site of initiation In the figure below a passive electrical signal is traveling from left to right along the neuron membrane We will typically refer to multipolar neurons where many dendrites project directly from the soma However the neuron in the figure is a bipolar neuron with a main dendrite on the left and axon on the right A change in Vm is artificially induced through an electrode on the left The resulting change in Vm is measured by other electrodes inserted along the membrane You can see that as the initial change in potential travels through space and time it decreases Studying how voltage and current are related is difficult as one always changes the other A technique called voltage clamp allows us to see how voltage affects current If we could change the membrane potential to a set value then hold it there while we measure changes in current we could eliminate the constant cycle of voltage current changes This is what voltage clamping allows us to do We can change membrane potential Vm to a set value Vc by injecting a current of positive or negative charges depending on which direction we want to move the membrane potential When this change in electrical gradient changes how ions flow across the membrane I it will change Vm This change Vm Vc is measured and enough current I is injected to adjust for it Now we know exactly how much current it takes to change Vm By clamping Vm at various voltages we can measure how much current corresponds to each of these changes The following animation will illustrate the technique of voltage clamp At this time look only at slides 4 9 http www sumanasinc com webcontent animations content voltage clamp html http www sumanasinc com webcontent animations content voltage clamp html Voltage clamping is used extensively to study the relationship between membrane potential and ion currents We will become more familiar with reading graphs from voltage clamp experiments throughout the next few lessons Now that we have a technique for studying how Vm and I are related let s get back to signal decay and talk about quantifying electrical signal decrement over distance To do this we can relate the cell to an electrical circuit We know that voltage V a difference in charge and current I movement of charge are related to each other As electrical gradients increase the movement of those charges also increases V and I are proportional However movement of charge is limited by resistance in the system R Because the membrane is largely impermeable to ion flow except for through ion channels it has high resistance the flow of charged particles across the membrane is impeded Charged particles diffuse freely throughout the fluid inside and outside the cell so R is much lower in these fluids As R increases and impedes the flow of charged particles I decreases These relationships are defined by Ohm s Law I V R which we can rearrange as V IR What does all this have to do with signal decay The resistance of the membrane is higher than that of the intracellular fluid but some ions will still flow across the membrane through leak channels The neuron can control how much leaks out by controlling Rm As Rm decreases the membrane impedes the flow of ions less so more of the electrical signal flowing through the neuron will be lost to the extracellular fluid This concept is represented by the length constant which indicates the distance a graded signal can travel If the voltage is increasing maximum If the voltage is decreasing is the distance it must go before it reaches 63 of its is the distance it can go before it drops to only 37 of its maximum Because that distance decreases as Rm decreases but increases if intracellular resistance decreases it can be expressed as Rm Ri This is shown in the figure below where two neurons have differing length constants If we artificially induce a change in voltage in the dendrites then measure the change in voltage at the axon hillock the neurons will differ in how much that signal has decayed at that point The resistance of the membrane to ion flow is determined by the number of leak channels If there are more leak channels the membrane is less resistant to ion flow or more conductive G In a
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