The Morris–Lecar model is a
biological neuron model developed by Catherine Morris and Harold Lecar to reproduce the variety of
oscillatory behavior in relation to
Ca++ and
K+ conductance in the muscle fiber of the
giant barnacle .
Morris–Lecar neurons exhibit both class I and class II
neuron
A neuron, neurone, or nerve cell is an membrane potential#Cell excitability, electrically excitable cell (biology), cell that communicates with other cells via specialized connections called synapses. The neuron is the main component of nervous ...
excitability.
History
Catherine Morris (b. 24 December 1949) is a Canadian biologist. She won a Commonwealth scholarship to study at
Cambridge University
, mottoeng = Literal: From here, light and sacred draughts.
Non literal: From this place, we gain enlightenment and precious knowledge.
, established =
, other_name = The Chancellor, Masters and Schola ...
, where she earned her PhD in 1977. She became a professor at the
University of Ottawa
The University of Ottawa (french: Université d'Ottawa), often referred to as uOttawa or U of O, is a bilingual public research university in Ottawa, Ontario, Canada. The main campus is located on directly to the northeast of Downtown Ottaw ...
in the early 1980s. As of 2015, she is an
emeritus professor
''Emeritus'' (; female: ''emerita'') is an adjective used to designate a retired chair, professor, pastor, bishop, pope, director, president, prime minister, rabbi, emperor, or other person who has been "permitted to retain as an honorary title ...
at the University of Ottawa. Harold Lecar (18 October 1935 – 4 February 2014) was an American professor of biophysics and neurobiology at the
University of California Berkeley
The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...
. He graduated with his PhD in physics from
Columbia University
Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manha ...
in 1963.
Experimental method
The Morris–Lecar experiments relied on the voltage clamp method established by
Keynes ''et al.'' (1973).
The principal assumptions underlying the Morris–Lecar model
Among the principal assumptions are these:
#Equations apply to a spatially iso-potential patch of membrane. There are two persistent (non-inactivating) voltage-gated currents with oppositively biased reversal potentials. The depolarizing current is carried by Na+ or Ca2+ ions (or both), depending on the system to be modeled, and the hyperpolarizing current is carried by K+.
#Activation gates follow changes in membrane potential sufficiently rapidly that the activating conductance can instantaneously relax to its steady-state value at any voltage.
#The dynamics of the recovery variable can be approximated by a first-order linear differential equation for the probability of channel opening.
[This assumption is never exactly true, since channel proteins are composed of subunits, which must act in concert, to reach the open state. Despite missing delays in the onset of recovery, the model appears to be adequate for phase-plane considerations for many excitable systems.]
Physiological description
The Morris–Lecar model is a two-dimensional system of
nonlinear
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other ...
differential equations
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, a ...
. It is considered a simplified model compared to the four-dimensional
Hodgkin–Huxley model
The Hodgkin–Huxley model, or conductance-based model, is a mathematical model that describes how action potentials in neurons are initiated and propagated. It is a set of nonlinear differential equations that approximates the electrical charac ...
.
Qualitatively, this system of equations describes the complex relationship between membrane potential and the activation of ion channels within the membrane: the potential depends on the activity of the ion channels, and the activity of the ion channels depends on the voltage. As bifurcation parameters are altered, different classes of neuron behavior are exhibited. is associated with the relative time scales of the firing dynamics, which varies broadly from cell to cell and exhibits significant temperature dependency.
Quantitatively:
:
where
: