Presentation on theme: "Synapses and Multi Compartmental Models"— Presentation transcript:
1 Synapses and Multi Compartmental Models Computational Neuroscience 03Lecture 2
2 Synapses:The synapse is remarkably complex and involves many simultaneousprocesses such as the production and degredation of neurotransmitter.The neurotransmitters directly (A) or indirectly (B) binds to a synaptic channel and activates it.
3 Synaptic conductances: Synaptic transmission begins when an action potential invades the presynaptic terminal and activates voltage dependent Ca2+ channels.This causes transmitter molecules to enter the cleft and bind to receptors on the postsynaptic neuron.As a result ion channels open, which modifies the conductance of the postsynaptic neuronP: open channel probabilitySynaptic conductance:Prel: probability of transmitter releasePs: probability that postsyn. channel opensBoth stochastic processes
4 Postsynaptic conductance: closing rate of the channelopening rate dependent on transmitter concignore during theopening processSpike
5 forforif there is no synaptic release immediately before the releaseat t=0using a simple manipulation we can write in the general caseUpdate rule after spikes
6 Fast synapse:For a fast synapse the rise of the conductance following apresynaptic action potential can be approximated asinstantaneous.For a single presynaptic action potential occurring at t=0 wecan writewithA sequence of action potentials at arbitrary times can be modeledwith an exponential decayand by updating the probability after eachaction potential with:
7 Slow synapse (e.g. GABAA and NMDA): For an isolated presynaptic action potential occurring at t=0 wecan use the same model or a difference of two exponentialsB is a normalizationfactor and ensures thatthe peak value is equalto Pmaxor the alpha functionwith a peak value at
8 Examples of time-dependent open probabilities: Instantaneous riseSingle exp. decayDiff of two exp.exponential decay
9 NMDA: Slow (20ms rise) Physiological correlate of the Hebb learning rule since both, the presynapticand postsynaptic cell have to be active.The voltage dependence is mediated bymagnesium ions which normally blockNDMA receptors. The postsynaptic cellMust be sufficiently depolarized to knockout the blocking ions.Dependence of the NMDA conductanceon the membrane potential V and theextracellular Mg2+ concentration.
10 Probability of transmitter release and short-term plasticity: Depression (D) and facilitation (F)of excitory intercortical synapsesThresholdwiththe release probability after a long period of silence
11 Steady-state release probability for a presynaptic Poisson spike-train: average steady state release probabilityThe facilitationafter each spike is cancelled out by the average exponentialdecrement between presynaptic spikes.Consider two action potentials separated by an intervaland the release probability at the time of the first spike isImmediately after the spike the release probabilityis set toBy the time of the second spike it is decayed to
12 Since we are interested in the average release probability, we have to determine the average exponential decay with aninterspike intervalProbability density of aPoisson spike train withinterspike intervall t.
13 Steady-state release probability for a presynaptic Poisson spike-train: Facilitating synapseDepressing synapse: Synaptic transmission
14 Transmission for a depressing synapse: Due to the 1/r release probability at high rates, the synaptic transmission becomesindependent of the firing rate. Thus, depressing synapses do not convey the valueof high presynaptic firing rates. They emphasize changes in the firing rate.Prior to a change:for highrates rAfter a change:
15 Examples of some synapses: Glutamate activates two different kinds of receptors:AMPA and NMDA.Both receptors lead to an excitation of the membrane.AMPA:fast
16 GABA (g-aminobutyric acid) is the principal inhibitory neurotransmitter.There are two main receptors for GABA, GABAA and GABAB.GABAAGABAA is responsible for fast inhibtion and require onlybrief stimuli to produce a response.
17 GABABGABAB is a much more complex receptor. It involves so-calledsecond messengers. GABAB responses occur when the GABAbinds to another compound (G-potein) which in turn binds to aPotassim channel and opens it up. It takes 4 activated G-proteinsto open the channel.
18 Gap junctions are not chemical synapses but electrical in nature. The produce a current proportional to the difference betweenpre-and postsynaptic potential. No transmitter or action potentialis involved. Many non-neural cells, e.g. muscle, glia, are coupledin this manner.
19 Synaptic in integrate and fire Can also add synapses onto an integrate and fire using:Ps is probability of firingand changes whenever the presynaptic neuron fires using one of the schemes mentioned previously. For simplicity, assume Prel is 1
20 Used to look at eg dynamics of large numbers of inputs and effects of inhibitory/excitatory synapses Have excitatory or inhibitory synapses depending on whether ES is above/below membrane potentialinterestingly inhibitory synapse produces more synchronous firing
21 Cable model Simultaneous recordings from different parts of neurons Have been assuming no spatial variation in membrane potential: Not true especially for neurons with long narrow processesAttenuation and degradation of signal is most severe when current passes down the long cable-like dendritic or axonal branches=> Cable theory: assumption is that cables are radially homogeneousLongtitudinal resistance over cable of length Dx:RL = rL Dx/(pa2)Where rL is intracellular reistivity and a is radius
22 From Ohm’s law, we get a pde relating voltage difference to current im (see abbott and Dayan, pp )im generally complex and must be integrated numerically. However for linear current, no synaptic current and infinite cable can solve analytically to getAnd voltage drops by a factor of exp(-n) at a distance of lWhere electrotonic length
23 This model made more realistic by Rall: equivalent cable model
24 Multi Compartment models Dendrites only locally uniformMake different compartments with different propertiesEach compartment reduces to the cable modelNeed some way of them linking at the ends:Where compartments are indexed by m
28 The value of the conductance between compartments can be calculated from Ohm’s law. If compartments have equal length L and radius aIf not:Can solve the equations and so see how APs propagate along axons.
29 AP PropagationAP propagates since point 0 is depolarised to V0 it causes pt 1 to depolarise to V1. Before reaching V1 however it crosses threshold causing spike, which causes pt 2 which had been moving towards V2 to move towrds V1 etc
30 APs can move either way, but don’t go backwards because of refractory period. Speed of propagation can be shown to be proportional to sqrt(radius) for unmyelinated axons. However, for myelinated axons, at the optimal thickness of myelin inner=0.6outer which is actual thickness of axons (thickness effects membrane capacitance etc) with respect to speed, speed is proportional to radius