Neurons and Action Potentials

Neurons and Action Potentials

• Zafer İşcan (PhD) specializes in Engineering in Neuroscience.
• Ramón y Cajal's work in 1896 contributed significantly to understanding neurons.
• Cajal received the Nobel Prize in Physiology or Medicine in 1906.

Single Neuron Structure and Function

• Dendrites are input devices that gather data from other neurons, transmitting it to the soma.
• The soma serves as the CPU, performing nonlinear processing; an output signal is generated if the total input surpasses a threshold.
• Axons function as output devices, delivering signals to other neurons.

Action Potential

• Voltage-gated sodium channels, voltage-gated potassium channels, and mechanically-gated ion channels are involved in action potentials.
• Researchers have mapped the behavior of all voltage-gated potassium channels.

Spike Trains

• A sequence of action potentials emitted by a single neuron forms a spike train.
• It's the quantity and timing of spikes that matter, as individual spike forms do not carry information.
• Action potential is the basic unit of signal transmission.

Refractory Periods

• The absolute refractory period is the minimal distance between two spikes.
• Following the absolute refractory period is the relative refractoriness phase, where exciting an action potential is difficult, but possible.

Synapses

• Synapses are sites where a presynaptic neuron's axon connects with a postsynaptic cell's dendrite or soma.
• The most common synapse in the vertebrate brain is the chemical synapse.
• The synaptic cleft is the small space between pre- and postsynaptic cell membranes.
• Action potentials at the synapse trigger a complex biochemical process, resulting in neurotransmitter release from the presynaptic terminal into the synaptic cleft.
• Transmitter molecules bind to receptors on the postsynaptic cell membrane resulting in ion channel opening and flow of ions from the extracellular fluid into the cell.
• Resulting ion influx leads to a change in membrane potential at the postsynaptic site; thus, the chemical signal is translated into an electrical response.
• Postsynaptic potential is the voltage response of the postsynaptic neuron to a presynaptic action potential.
• Neurons can be coupled by electrical synapses in addition to chemical synapses.

Postsynaptic Potentials (PSPs)

• A postsynaptic neuron receives input from two presynaptic neurons.
• Each presynaptic spike induces an excitatory postsynaptic potential (EPSP).
• An electrode can measure EPSP as a potential difference, which is expressed as ϵij(t)=ui(t) − urest.

Firing Threshold and Action Potential Dynamics

• When a second presynaptic neuron fires a spike shortly after the first one, it causes a second postsynaptic potential that adds to the first.
• The total change of the potential is approximately the sum of the individual PSPs.
• When ui(t) reaches the threshold θ, an action potential is triggered, the membrane potential starts a significant positive pulse-like shift.
• After the pulse, voltage shifts to an amount below the resting potential, or hyperpolarization.

Spike Response Model (SRM)

• Membrane potential of neuron i is expressed as: ui(t) = η(t - î) + ΣΣ ϵij(t-tf) + urest
• In the equation above î denotes the last firing time of neuron i.
• Firing occurs whenever ui reaches the threshold θ, at which point the derivate is > 0.

Formal Models of Spiking Neurons

• The action potential shape is usually replaced by a δ pulse.
• Negative overshoot (spike-afterpotential) after the pulse is contained in the kernel, taking care of 'reset' and 'refractoriness'.
• The pulse is triggered by the threshold crossing at t₁(1), the resting state being set to zero.

Spike Train Representation

• Spike train of a neuron i is expressed as: S¡(t) = Σ δ(t - t¡(f)).
• Spikes are reduced to points in time.

Limitations of Models

• Adaptation (of ISI), No adaptation, Bursting neuron, and Inhibitory rebound spike are types of model limitations.
• The shape of postsynaptic potentials relies on the neuron's internal state, and particularly on the timing relative to previous action potentials.

The Problem of Neuronal Coding

• The mammalian brain has a highly intricate network containing > 1010 densely packed neurons.
• Each millisecond, thousands of spikes are emitted in every small cortical region.
• The UvaNlf neuron increases its firing rate during playback, while the HVCI neuron produces only few bursts.
• Questions of neuronal coding include: 1) what information is contained within spatio-temporal patterns of pulses, 2) how neurons transmit that information, 3) how other neurons decode the signal, and 4) how external observers interpret neuronal activity patterns.

Mean Firing Rate

• Relevant information was thought to be mostly in the neuron's mean firing rate.
• Definition of the mean firing happens via averaging over time.
• Gain function (schematic) shows output rate relative total input.
• Peri-Stimulus-Time Histogram (PSTH) is an average over several runs.
• Population activity is defined as a fraction of active neurons [t, t+∆t] divided by Δt.

Spike Codes

• "Time to First Spike" highlights the timing of initial neuronal responses.
• Neurons fire at different phases with respect to the background oscillation that could code relevant information
• The upper four neurons from the plots are synchronous.
• Stimulus reconstruction involves averaging stimulus around spikes to identify relevant typical time courses.

Summary

• Neuronal signals are short voltage pulses called action potentials (or spikes).
• These pulses move along the axon, reaching postsynaptic neurons and inducing postsynaptic potentials.
• The membrane electric potential will reach a critical value when a postsynaptic neuron gets many spikes, in a short time window. This triggers the action potential.
• Action potential is the output signal, sequence of action potentials contains the information that is conveyed from one neuron to the next.
• The problem of neuronal coding is not fully resolved yet.

Detailed Neuron Models

• Action potentials arise from currents passing through ion channels in the cell membrane.
• Hodgkin and Huxley measured these currents and described their dynamics mathematically.
• Hodgkin-Huxley equations serve as a model for detailed neuron models to account for: 1) Numerous ion channels, 2) different types of synapses, and 3) the specific spatial geometry of an individual neuron.

Equilibrium Potential

• Neurons are enclosed by a membrane, separating the cell’s interior from the extracellular space.
• Ion concentration differs between the inside and outside of cells.
• The difference in concentration generates an electrical potential that is an important component role in neuronal dynamics.
• The probability of a molecule having an energy state is proportional to the Boltzmann factor expressed as p(E) ∝ exp(−E/kT).
• In relation to the equation above, k is the Boltzmann constant.

Nernst Potential and Ion Distribution

• Thermal equilibrium results and voltage difference generates a gradient in concentration of positive ions
• Thermal equilibrium results and a difference in ion concentration generates an electrical potential called the Nernst-potential.
• Specific proteins act as ion gates, and ion pumps transport ions from one side to another.
• Na+ concentration is lower inside cells (+50mV) than outside.
• K+ concentration is higher inside cells (-77mV) than outside.

Hodgkin-Huxley Model

• Semipermeable cell membrane separates interior of cell from the extracellular liquid and functions as a capacitor.
• Input current (I(t)) can add further charge on the capacitor, or leak through channels in the cell membrane.
• The Nernst potential is represented by a battery.

Formal Spiking Models

• Spikes are generated when the membrane potential (u) goes beyond a threshold (ϑ) from below.
• The moment of threshold crossing establishes the firing time.

Integrate-and-Fire Model

• A current charges the RC circuit.
• The voltage is compared to a threshold.
• If the voltage reaches the threshold, an output pulse is generated.
• Presynaptic spike is low-filtered generates generates the input current pulse.