Chapter 4 Excitation

Each excitation activates enough crossbridges to produce a twitch. A twitch is the fundamental unit of active tension. However, a single twitch of active tension is not enough tension when the goal of tension is some sort of voluntary movement or stability. The rise and rate of a twitch depends on the amount and spread of $C{a}^{2+}$ released, the available troponin sites, the available crossbridges to activate as well as the amount of elasticity in the series. One mechanism of muscle fatigue is a reduction in the release of $C{a}^{2+}$ from the SR.

Removal of $C{a}^{2+}$ from the sarcoplasm requires active transport with $C{a}^{2+}$ ATPase. This pump is dependent on $M{g}^{2+}$ and moves 2 $C{a}^{2+}$ into the SR while moving one $H^{+}$ out at the cost of 1 ATP. Sarcoplasm levels of $C{a}^{2+}$ can quickly return to resting levels which is necessary for rapid muscle relaxation and therefore muscle tension regulation and coordination. Situations that result in a delay in the removal of $C{a}^{2+}$ from the sarcoplasm can delay muscle relaxation producing extra twitches or spasms (involuntary tetany). Since $C{a}^{2+}$ ATPase is dependent on $M{g}^{2+}$, a deficiency in $M{g}^{2+}$ can create such a situation.

The sarcolemma is a semipermeable phospholipid bilayer membrane that forms a boundary for the muscle fiber. Semi-permeability arises for two reasons. First, because the lipid bilayer prohibits the free passage of many molecules (a unique combination of hydrophobic and hydrophilic components). Second, there are transport proteins within the membrane for selective forms of active, facilitated and passive transport.

Background: Cellular Transport Mechanisms

Active transport utilizes protein machines that require ATP and move very specific molecules, typically, against a concentration gradient. Facilitated transport utilizes protein machines to move very specific molecules across the membrane without the need for ATP. Facilitated transport requires a concentration gradient for at least one molecule, but can be coupled with another molecule that moves against a concentration gradient. Meaning, facilitated transport can utilize the potential energy of one molecule to provide the energy needed to move another molecule against a gradient. Passive transport occurs due to a concentration gradient (such as simple or channel guided diffusion).

The membrane separates the intracellular from the extra cellular space. Through selective transport the membrane establishes the conditions for cellular activities within the cell and thus influences (but does not completely establish) conditions outside the cell. Sarcolemma (all cell membranes) are dynamic structures that adapt in response to the intracellular and extra cellular conditions to meet the needs of the cell.

Components of the sarcolemma that are discussed below play an important role for establishing the resting membrane potential as well as the action potential are depicted in Figure 4.8.

Movement of molecules across the cell membrane is influenced by the concentration gradient of the ion across the membrane, the permeability of the membrane for that ion and the and the electrical equilibrium potential across the membrane. When we describe electrical potentials the convention is to speak from inside the cell (intra cellular). A negative potential means at the membrane inside the cell there is a negative charge. A positive potential means that at the membrane inside the cell there is a positive charge. We can, for the sake of understanding, simply invert this and say a negative potential means that at the membrane OUTSIDE the cell has a positive charge; and that a positive potential means that at the membrane OUTSIDE the cell has a negative charge.

When an ion moves across a membrane it carries a charge and creates an electrical potential. An important point is that the electrical potential created at the membrane is not created by the concentration gradient, but from the movement of ions which is based on the concentration gradients. The $N{a}^{+}$/$K^{+}$ ATPase pumps work at a rate in response to the concentration gradients (speed up if there is a need to, slow down to resting levels when able). But even for long periods of high frequency excitations there is no risk of significant change to the ionic concentrations outside or inside the cell. Thinking that there an absolute change in ionic concentration is required for an action potential is a common misconception about action potentials [silverthorn_uncovering_2002].

Background: Membrane Potentials Created by Primary Ions of Interest

• •

  When $K^{+}$ moves across the membrane (out of the cell) it creates a negative potential.

• •

  When $N{a}^{+}$ moves across the membrane (into the cell) it creates a positive potential.

• •

  When $C{l}^{-}$ moves across the membrane (into the cell) it creates a negative potential.

To generalize these facts. When a positive ion moves into the cell it creates a positive potential (+in+); when it moves out of the cell it creates a negative potential (+out-). When a negative ion moves into a cell it creates a negative potential (-in-); when it moves out of a cell it creates a positive potential (-out+). Notice that when an ion moves ”in” there is a direct relationship between the charge of the ion and its impact on the membrane potential. But when an ion moves out of a cell there is an indirect (or inverse) relationship between the charge of the ion and its impact on the membrane potential. It is always important to remember that the membrane potentials are based on the movement of the ions, not on their concentration.

The electrical potential created at the membrane by the movement of an ion has an influence on the movement of ions. The negative electrical potential created at the membrane by the movement of $K^{+}$ out of the cell will eventually resist the continued movement of $K^{+}$ out of the cell. How negative that negative potential needs to be to stop the movement of $K^{+}$ out of the cell is dependent on the concentration gradient and how permeable the membrane is to $K^{+}$.³³3It is also dependent on the temperature (which is kept within tight boundaries in the body), Faraday’s constant, and the universal gas constant. From these variables the potential generated by any ion can be determined with the Nernst Equation, which is not be covered here at this time. The electrical potential that stops the movement of an ion is called the equilibrium potential. Figure 4.9 shows the concentration gradient and resultant equilibrium potential for our primary ions of interest ($N{a}^{+}$, $K^{+}$, $C{l}^{-}$). Each equilibrium potential in 4.9 is based on the assumption that it is the only ion moving across the membrane. In reality they are all moving across the membrane with varying rates based on the permeability of the membrane to each ion at any moment in time.⁴⁴4The Goldman-Hodgkin-Katz (GHK) Equation (model) allows the estimation of the membrane potential based on $N{a}^{+}$, $K^{+}$, $C{l}^{-}$ concentration gradients and membrane permeability (along with several other relevant variables. A calculator for the GHK Equation can be found at https://www.physiologyweb.com/calculators/ghk_equation_calculator.html.

The resting membrane potential is an equilibrium potential. It is the consequence of two physiological situations. First, the presence of large concentration gradients for $K^{+}$, $N{a}^{+}$ and $C{l}^{-}$ across the membrane. Second, the relative permeability of the membrane to these ions. For example, based on Figure 4.9, if $K^{+}$ was the only ion that the membrane was permeable to at rest the RMP would be equal to the $K^{+}$ equilibrium potential (about -97 mV). The concentration gradients for $K^{+}$ and $N{a}^{+}$ are established primarily by the $N{a}^{+}$-$K^{+}$-ATPase pumps. The concentration gradient maintains a large outwardly directed $K^{+}$ gradient, and a large inwardly directed $N{a}^{+}$ gradient. The concentration gradient for $C{l}^{-}$ is maintained primarily through the actions of a $K^{+}$ - $C{l}^{-}$ co-transporter known as KCC2. Relative to the other ions, there is a moderate inwardly directed $C{l}^{-}$ gradient.

Since these ions do not pass through the lipid bi-layer of the cell membrane the permeability of the membrane to each ion is tuned by the presence of ion specific channels. Therefore, the relative permeability of the plasma membrane to $N{a}^{+}$, $K^{+}$ and $C{l}^{-}$ is dependent on the number and state (open or closed) of ion-selective membrane channels. Different membranes display different degrees of permeability to different ions, and due to gating mechanisms on many of the ion-selective channels the permeability can be changed. This is an important point considering the entire purpose of an RMP (polarization) is to have the opportunity to generate an AP (depolarization). In resting conditions the membrane of nerve and muscle cells are most permeable to $K^{+}$. In addition to KCC2 allowing movement of $K^{+}$ out of the cell, there are also non-gated $K^{+}$ ion channels. When combined with the relatively high permeability of $K^{+}$, the concentration gradient results in a $K^{+}$ flow out of the cell. As $K^{+}$ flows out it creates a negative electrical potential (+out-). However, the negative electrical potential resists further flow of $K^{+}$ outside of the cell (and eventually reaches an equilibrium potential). Since $K^{+}$ has the highest permeability at rest, the resting membrane potential is primarily influenced by the equilibrium potential of $K^{+}$. It is important to note that while there is no net flow of $K^{+}$ at the $K^{+}$ equilibrium potential, $K^{+}$ is still flowing out of the cell and continues to generate the negative membrane (equilibrium) potential. $K^{+}$ also continues to be pumped into the cell by the $N{a}^{+}$/$K^{+}$ ATPase pumps. The term ”equilibrium” for equilibrium potential means equilibrium in flows (no net flow, no net gain in or outside the cell).

Note from Figure 4.9 that the equilibrium potential of $C{l}^{-}$ is close to $K^{+}$. The implication is that $C{l}^{-}$, despite its concentration gradient encouraging inward flow, does not at RMP, have net inward flow. $C{l}^{-}$ has a higher permeability than $N{a}^{+}$ at rest, but a much lower permeability than $K^{+}$. An important attribute about $C{l}^{-}$ for the sarcolemma and axon membranes is that the permeability of the membrane does not change much, even during an AP. This contributes to the stability of the RMP and helps prevent recurrent self excitation in these membranes.

The equilibrium potential of $N{a}^{+}$ is positive (opposite of $K^{+}$ and $C{l}^{-}$). At RMP the permeability for $N{a}^{+}$ is very low. Therefore $N{a}^{+}$ has very little impact on the RMP. The importance of $N{a}^{+}$ starts when ligand and then voltage gated $N{a}^{+}$ channels start to open - that’s when the action begins.

The events leading to an action potential on the sarcolemma are initiated by the opening of ligand gated $N{a}^{+}$ channels by the binding of ACh to these receptors at the motor end plate. The micro potentials created by the opening of the ligand gated $N{a}^{+}$ channels then open voltage gated $N{a}^{+}$ channels due to a change in voltage in the membrane potential (becoming less negative). The number of voltage gated $N{a}^{+}$ channels that open is proportional to the change in the membrane potential. This cycle of opening in response to a voltage change is self perpetuating since once a $N{a}^{+}$ channel opens $N{a}^{+}$ flows into the cell due to the $N{a}^{+}$ concentration gradient. Due to the movement (not a change in the actual gradient) the membrane potential voltage changes (becomes less negative) as the potential moves toward the $N{a}^{+}$ equilibrium potential. The point that approximately half of the voltage gated $N{a}^{+}$ channels open is considered a threshold potential. At the threshold potential the voltage gated $N{a}^{+}$ channels continue to rapidly open until the equilibrium potential approaches that of $N{a}^{+}$ (as opposed to $K^{+}$). At this point the membrane is more permeable to $N{a}^{+}$. The equilibrium potential for $N{a}^{+}$ is approximately 66 mV. Once a membrane reaches the threshold potential an action potential is inevitable. It is at this point that the action potential is said to be “all or none.” Prior to the threshold potential membranes can undergo micro potential changes. These micro potentials can be depolarizing (excitatory potentials that move the membrane potential toward the threshold), or hyperpolarizing (inhibitory potentials that move the membrane potential further away from the threshold potential). The use of micro potentials to regulate muscle tension is an important part of Chapter 5 on Regulation since it is a process that occurs at the $\alpha$-motor neuron dendrites in the spinal cord. It is not a process that occurs at the NMJ.

Background: A peak ahead to an important concept

An $\alpha$-motor neuron, once excited, will release only one neurotransmitter, ACh at its axon terminal. ACh will only have one effect at the NMJ, creating excitatory micro-potentials on the motor end plate. However, in the Central Nervous System (such as the Spinal Cord) competing neurotransmitters can be released at synapses of the $\alpha$-motor neuron dendrites. The impact of these neurotransmitters can be excitatory or inhibitory. Since they occur after the synaspse they are called excitatory post synaptic potentiations (EPSPs) or inhibitory post synaptic potentiations (IPSPs). Whether, and how frequently, an $\alpha$-motor neuron sends an excitation to the muscle fibers it innervates is balanced by competition between the EPSPs and the IPSPs.

The wave of excitation of the AP across the sarcolemma and T-tubules occurs due to the self-perpetuating opening of voltage gated $N{a}^{+}$ channels. When a region of the membrane depolarizes it opens the nearby voltage gated $N{a}^{+}$ channels which depolarize that region, which then opens the nearby voltage gated $N{a}^{+}$ channels which depolarize that region, ”And so it goes.”⁵⁵5A quote for other Kurt Vonnegut fans.

Of course, there cannot be an AP if there is no RMP. Therefore, the AP must end. The membrane must repolarize to be ready for another depolarization. Considering muscle tension is, partly, regulated by how frequently it experiences excitation (which can reach upwards of 180 Hz, that is 180 excitations per second). For those excitations to occur there need to be an equal number of repolarizations.

The process of repolarization occurs due to two mechanisms. The first mechanism is based on voltage gated $N{a}^{+}$ channels having two gates. One is an activation gate and it is closed under resting conditions and opens during excitation. The second is an inactivation gate and it is open under resting conditions but closes soon after the activation gate opens. The inactivation gate closure is timed, it is not triggered by events outside of the molecule itself. Closing the inactivation gate is the first step to stopping an action potential. The closure of the inactivation gates reduces the membrane permeability for $N{a}^{+}$. While the activation gate is open and the inactivation gate is closed the membrane is in the absolute refractory period. This means it cannot undergo depolarization regardless of how great an excitation stimulus may be. To be reset and completely ready for another action potential the activation gate must close and the inactivation gate must open. These are also timed events.

The second mechanism to repolarization is opening of voltage gated $K^{+}$ channels. These are delayed (take longer to open than the voltage gated $N{a}^{+}$ channels). Once the voltage gated $K^{+}$ channels open the membrane permeability to $K^{+}$ increases higher than under resting conditions which expedites the repolarization process and results in a hyper polarized state (slightly more negative membrane potential than the normal resting membrane potential). Closing the voltage gated $K^{+}$ channels is also a timed event. While they are open the membrane is in a relative refractory period. It is resistant to excitation, however, with an increased stimulus it can be excited.

The overall process of repolarization and return to the resting membrane potential takes approximately 3-4 milliseconds (ms). Assuming 3 ms is the fastest interval for another AP, the upper limit on excitations would be approximately 333 Hz (which exceeds the maximum capacity for human muscle fiber twitches per second).

Spread of excitation occurs in one direction (meaning it does not result in cyclic repeating action potentials of the entire membrane) because of the refractory periods.

Background: Domino Model of the Unidirectional Spread of Excitation

Visualize the membrane as a set of dominoes. The resting potential is when the dominoes are upright. An action potential is when a domino falls. Then the refractory period is the period when the domino is still fallen. Because of the fallen domino on one side of the next falling domino, the dominoes fall in one direction away from the starting stimulus.

A further safeguard against cyclic repeating action potentials in the sarcolemma is the constant permeability for $C{l}^{-}$ in the sarcolemma. Recall that at RMP $C{l}^{-}$ has no net flow because its equilibrium potential is near the $K^{+}$ potential. When the membrane potential fluctuates away from the the $K^{+}$ (and $C{l}^{-}$) equilibrium potential there is net movement of $C{l}^{-}$. This $C{l}^{-}$ net movement (into the cell) contributes to repolarization but also to stability of the RMP in the moments following an AP. In situations such as myotonia congenita, altered membrane $C{l}^{-}$ permeability leads to a higher occurrence of myotonia (sustained muscle tetany) due to recurrent muscle excitation from cyclic repeating action potentials [adrian_action_1976].

Sensory receptors are proteins embedded in cell membranes. Therefore, the cell has control over some dynamic and important behavior of these receptors (indeed, all receptors). Up-regulation is a term for sensory receptor dynamics that includes an increase in the number of receptors. Down-regulation is a term for sensory receptor dynamics that includes a decrease in the number of receptors. With up-regulation or down regulation there are changes to the strength of a excitation and therefore signal sent to the respective neurons. For example, with up-regulation of chemoreceptors for carbon dioxide an individual will have a higher respiratory rate and maintain a lower carbon dioxide level since their response to carbon dioxide is increased. The up-regulation then continues to propagate itself. Since it results in lower carbon dioxide levels, the receptors remain up-regulated in an attempt to be able to respond to the lower carbon dioxide levels. A balance point is eventually achieved. But this new balance point may be enough to result in what is considered altered homeostasis. In individuals taking a beta-blocker (beta-adrenergic blocker medication) the lack of cardiac response to neuroendocrine stimulus results in higher adrenaline levels. The adrenergic receptors of the heart down-regulate in response to higher circulating adrenaline which further blunts cardiac responsiveness to adrenergic stimulation. A balance point is eventually achieved as with the previous example, however, the individual has an alteration to homeostasis.

There are several important neuromuscular sensory receptors that sense signals from the muscle, musculotendonous junction and/or the tendon. Signals for tension (such as golgi tendon organs), signals for changes in length (such as the muscle spindle), and signals for the chemical constituents of the extra cellular fluid surrounding muscle fibers (chemoreceptors). These receptors and their role in muscle function is covered in upcoming chapters.

Curare is paralyzing agent. It stops the excitation of the motor end plate. It does so by competitively and reversibly binding to ACh receptors on the motor end plate which blocks those receptors from binding with ACh. When curare binds to an ACh receptor it does not open the ligand gated $N{a}^{+}$ channel and therefore prevents the initiation of depolarization. As a competitive binding, curare blocks the ACh receptor and thus inhibits the ACh binding and response. Another term for competitive binding is that curare is an antagonist (blocks without producing an effect). Some medications are agonists, they bind and create an effect and are thus utilized to facilitate additional cellular activity beyond that of the normal ligand. As a reversible binding medication, curare can be removed from the ACh receptor. Medications can also create irreversible binding. Curare is also selective, it only binds to skeletal muscle motor end plate ACh receptors. Which means it selectively inhibits these receptors and not other ACh receptors throughout the body. This means the systemic response is limited to skeletal muscle paralysis. If used during surgery without other anaesthetics it would produce paralysis but no change in pain sensation, a very unpleasant surgery that would be stopped when the pain and anxiety of the procedure produced a rapid heart rate and rising blood pressure due to the fight or flight response of the neuroendocrine system (which would not be stopped by curare). In addition to surgical or intensive care situations, curare can be used as a poison, causing death by asphyxiation since the muscles of ventilation (breathing) are skeletal muscles.

A consequence of medications is that they can produce changes in receptors. Up-regulation and down-regulation of receptors due to their pharmacodynamics are a common reason for the need to carefully, and only under supervision, withdraw a dose of medications. If the medication led to up or down regulation and depending on whether it is a receptor antagonist or agonist, could have big implications with sudden cessation. For example, if a medication leads to down regulation of receptors, cessation of that medication could result in a large drop in cellular activity (whatever that activity may be). For example, serotonin re-uptake inhibitors are antagonists that block the re-uptake of serotonin in synapses of the central nervous system. This increases the amount of serotonin which can lead to down-regulation of the serotonin receptors. If the medication is suddenly stopped there will be less serotonin and less receptors (due to down-regulation) which magnifies the effect of having less serotonin, potentially worsening of the original reasons for taking the medication.

There are several medications that influence the autonomic nervous system function for a variety of health conditions. Applying what we know about receptors and pharmacodynamics it should be clear that an adrenergic agonist will increase SNS activity in the cell that the medication binds to, whereas an adrenergic antagonist (blocker) will reduce the SNS activity in the cell that the medication binds. A cholinergic agonist will increase the PNS activity in the cell, whereas a cholinergic antagonist will decrease the PNS activity in the cell. Very simple. Two types of receptors that can effect the receptors in two ways and therefore can create four different cellular responses.

Thankfully there is enough cholinergic receptor specificity that a cholinergic agonist with the therapeutic goal of changing gut motility is specific to the cholinergic receptors in the gut. If all cholinergic receptors were the same, then such a cholinergic agonist could cause wide spread muscle spasms.