Week 3.8 - Neuronal Models & Neurodynamics Flashcards
- Grasp the basic terminology of dynamical systems. - Develop an intuition for the time scales of state variables. - Identify strategies to reduce the number of state variables of the HH model. - Employ F x I curves to distinguish different kinds of neuronal spiking behavior. - Tune single cell models to obtain different kinds of spiking behavior. - Explain transitions in spiking types via bifurcations of dynamical systems. - Describe the elements of the basic LIF neuron (and extensions).
What are the two main classes of neuronal excitability?
- Class 1 neural excitability. Action potentials can be generated with arbitrarily low frequency, depending on the strength of the applied current.
- Class 2 neural excitability. Action potentials are generated in a certain frequency band that is relatively insensitive to changes in the strength of the applied current. The onset of spiking tends to be abrupt.
Bifurcations of equilibria divide neurons into two main groups, these are _____ and _____
integrators (type 1) and resonators (type 2)
What are the properties of a resonator type neuron?
A resonator has sub-threshold oscillations and gated transmission.
What are the properties of an integrator type neuron?
An integrator doesn’t have sub-threshold oscillations. These neurons sum incoming PSP’s linearly.
Describe what is a state and a state variable
Neurons are dynamical systems. Where the state variables fully describe the state of a neuron at a point in time, the state of a system is a particular configuration of state values.
For each a dynamical system, the state is typically given by a vector displayed in the state space (also called ‘phase space’).
What is the phase space of a system?
The set of all the possible state configurations of a system. In other words, the values that state variables can take.
The _________ of a dynamical system depends on the __________
trajectory
initial state
Explain the difference between attractor and repellor equilibria.
attractor : a stable equilibrium
repellor : an unstable equilibrium
Neurons are excitable because the equilibrium is near a __________
explain what this term means
Bifurcation
Small changes of parameters in a dynamical system do not lead to a qualitative change of the behavior of orbits. A bifurcation is a type of abrupt transition in the phase portrait.
Explain what you see on each of these 4 diagrams
a) This is the phase space of a 1D system (a line), where the rate of change of x is plotted on the y-axis. The equilibria are where f(x) crosses the 0 line. The equilibrium is stable, determined by the slope of the graph of f’(x).
b) Given an intial state x(t) it displays the trajectory of the system, i.e. where it will tend to over time.
c) Shows the same phase space, adding a constant won’t change anything, just shifts it up or down.
d) This is the bifurcation diagram. It shows how the equilibrium changes as a function of the parameter.
Define the flow of a system
a set of possible trajectories of the system (given different initial conditions).
What is a Leaky Integrate-and-fire model? How many dimensions does it have?
The LIF model is a simplification of the neuron, where the neuronal activity is a function of current, I(t). It is a 1D model.
The LIF model shows to be a reasonable model for an integrator neuron.
Describe an LIF neuron.
- Spikes are binary
- The threshold is well-defined (no ambiguity)
- It has a relative refractory period
- It has a decay rate (due to membrane leak and capacitance)
- Class 1 excitability - The neuron can continuously encode the strength of an input into the frequency of spiking
What is an FxI curve?
An FxI curve measures the frequency of spikes as a function of the applied current.
What strategies are commonly used to reduce the complexity of a model? (i.e. reduce the number of state variables)
- cut an activation variable (when contribution is small, too slow)
- Make the activation instantaneous (when time constant is short)
- Merge activation gates (when their time scales are similar)
