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A simplified explanation of capacitance in neuronal membranes is that higher capacitance will tend to will cause a flow of ions towards the membrane on the cytoplasmic side due to the difference in charge across the membrane, called a displacement current; https://en.wikipedia.org/wiki/Cable_theory#/media/File:NeuronCapacitanceRev.jpg

– Cable theory can be derived in part from Ohm’s law, the fundamental theory of electricity that models the current flowing between two points as equal to the voltage distance between the two points divided by the material’s resistance, or in other words, the classic equation V = IR.

– The greater the cross-sectional area of the neurite’s cytosol (the interior part of it, containing biomolecules, electrolytes, and other ions), the easier an ion can flow through it, so the neurite’s longitudinal resistance, r_l, will be lower.

– If the cell membrane is more resistant to ion flow into or out of the cell (due to high membrane resistance, r_m), then charge will tend to accumulate inside the cell, and it will have a higher ionic current flowing down longer distances in the neurite. This is often represented by a paremeter called the length current, λ, equal to the square root of r_m divided by r_l.

– If a cell membrane has a lower membrane capacitance (c_m, which is usually a fairly constant value), then the relative ion flow down the neurite will be greater, due to a lower displacement current. How quickly the membrane voltage changes in response to a current injected at at given point can be predicted by the time constant, τ, equal to the product of c_m times r_m.

– An electrotonic potential results from a local change in ion conductance, e.g. after a synaptic event, that does not propagate. It becomes exponentially smaller as it spreads. This is opposed to an action potential, which reaches the voltage threshold by which it does propagate down the neurite (due to the opening of voltage-gated ion channels), and then spreads like a wave.

– Dendritic trees can perform non-linear integration of signals that can be predicted on the basis of cable theory. The existence of subthreshold membrane potential fluctuations in dendrites, which based on my understanding should dominate neuronal signaling, can allow variations in synaptic weight distributions and input timing to encode a substantial amount of information within a single neuron.

Inspired by CalTech’s Question #20 for cognitive scientists: “Derive the cable equation (for a uniform cylinder, with optimal boundary conditions). What does it mean for neurons?”

]]> Andy Question #19: Ion channel biophysics https://brainslab.wordpress.com/2022/01/16/question-19-ion-channel-biophysics/ Sun, 16 Jan 2022 19:01:23 +0000 https://brainslab.wordpress.com/?p=3236 Continue reading Question #19: Ion channel biophysics ]]> What are the biophysics of voltage-gated sodium channels? 

Sodium channels are a major component of excitable membranes. They are an intrinsic component of excitable tissue that allows them to generate and propagate action potentials. These electrical signals are essential for proper neuronal communication.

The channel looks like a barrel, with 4-fold symmetry, and a diameter of about 10 nm. The channel has an activation gate, through which sodium ions can flow through. If the activation gate is closed, no ions can pass through, but if it is open, ions can pass through the pore. The channel is closed at rest, wherein the membrane voltage potential is polarized. When a sufficient voltage depolarization across the membrane occurs, the membrane will draw the gates open, allowing sodium ions to flow through and leading to further depolarization. When enough sodium has passed, the further voltage change causes the inactivation gate to close, thus stopping the flow of sodium ions and leading to repolarization.

Sodium channels are selective for sodium ions because the inner filter of the pore is highly negatively charged; the Na+ ion has a positive charge and will bind well to the inner filter. K+ ions, while also positively charged, cannot pass through because of a size restriction. The gate is not large enough for them to fit through. For ions to pass, they need to be smaller than the diameter of the filter; for ions with a larger diameter to pass, the filter would need to enlarge; however, the size of the filter cannot increase because the pore has a fixed size. These are the unique properties of the sodium channel that allow it to selectively conduct sodium.

Sodium channels are good targets for many drugs and toxins. For example, tetrodotoxin specifically binds to voltage-gated sodium channels and can stop sodium channels from opening, thereby blocking all neural signaling. 

What are the biophysics of transmitter-gated channels? 

Transmitter-gated channels are opened by transmitters. They are then generally ion-selective. To open the channel, the transmitter needs to bind to the receptor. The transmitter binding causes an allosteric change that allows another part of the channel to open, known as the ion channel gate. When open, the ion channel gate allows specific ions to pass through.

A special example is the NMDA receptor. Under normal circumstances, the NMDA receptor is blocked by Mg2+ and Zn2+ ions. When the post-synaptic neuron is depolarized, however, Mg2+ and Zn2+ ions are repelled. In this case, the receptor can be activated by glutamate. When activated, the NMDA receptor allows positive ions to pass through (K+, Na+, and Ca2+ ions), which can help sustain depolarization and lead to intracellular signaling events such as long-term potentiation.

NMDA receptors are often called “coincidence detectors” because these two events must occur together for the channel to open. First, the NMDA receptor must be activated by the post-synaptic being depolarized, and second, glutamate must be released.

Another example is the nicotinic acetylcholine receptor. When acetylcholine binds to the receptor, the channel opens. This allows sodium and potassium ions to pass through, which leads to depolarization and therefore a neural signal.

Most types of ion channel activity in the brain need regulation. Regulation can occur post-translationally through the addition of a phosphate group to one or more amino acids. The addition of a phosphate group to a particular location of the AMPA receptor, for example, has been shown to increase the probability of AMPA channel opening. The Ca2+/calmodulin kinase II pathway is able to phosphorylate the GluA1 AMPA receptor subunit at Ser831, causing an increase in AMPA channel conductance.

In addition to the post-translational regulation of channel activity, many channels are regulated by endogenous compounds in the brain. Serotonin is a monoamine neurotransmitter that regulates various types of sodium channels and potassium channels. Dopamine is also a monoamine neurotransmitter, and it can be found in extrasynaptic regions. Dopamine has been shown to increase potassium channel activity by activating dopamine D1 receptors in axons.  

Together, the biophysics of ion channels allow for neural signaling by allowing for the passage of ions into and out of the cell. This allows for changes in membrane potential and intracellular signaling. 

Inspired by CalTech’s Question #19 for cognitive scientists: “Describe the main biophysical characteristics of ionic channels. How does its biophysical properties contribute to its physiological function? What is thought to be the basis for the channels ion selectivity?”

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Andy