Introduction 

MetaNeuron is a computer program that models the basic electrical properties of neurons and axons. Different aspects of neuronal behavior are highlighted in the six lessons presented in MetaNeuron. With the exception of lesson 3, which models a dendrite of infinite length, each MetaNeuron lesson represents 1 cm² of neuronal membrane, having a capacitance of 1 μF. The graph in the lower portion of the screen displays the membrane potential, the Na⁺ and K⁺ equilibrium potentials, and the stimulus. 

Lesson 1, Resting Membrane Potential 

Lesson 1 illustrates how K⁺ and Na⁺ channels contribute to the generation of the resting membrane potential.  The neuron in this lesson is modeled by passive conductances to K⁺ and Na⁺. These conductances are voltage-independent and the neuron does not generate action potentials. 

The concentrations of K⁺ and Na⁺, both outside and inside the cell, can be varied. The program calculates the electrochemical equilibrium potential for each ion, based on the ion concentration gradient across the membrane, using the Nernst equation. 

The resting membrane potential of the neuron is determined by the concentrations of K⁺ and Na⁺ outside and inside the cell and by the permeability of the membrane to K⁺ and Na⁺. The relative membrane permeabilities to K⁺ and Na⁺ can be varied.  The membrane potential is calculated using the Goldman-Hodgkin-Katz equation. 

Lesson 2, Membrane Time Constant 

Lesson 2 illustrates the effect of the membrane time constant, τ, on the time course of electrical responses in neurons. The neuron in this lesson is modeled by a passive membrane resistance, R_m, a membrane capacitance, C_m, and a current source.  The membrane capacitance equals 1 μF/cm², or simply 1 μF, since MetaNeuron represents 1 cm² of membrane.  The value of the membrane resistance as well as the time course and amplitude of the current source can be varied. The neuron in this lesson does not generate action potentials. 

The membrane resistance and capacitance together determine the time constant of the membrane, as described by the equation, 

            τ = R_m ∙ C_m 

When the "Synaptic Potential" box in the "Stimulus" window is selected, a potential is generated by turning on a conductance with rising and falling time constants of 0.39 and 3.9 times the width of the stimulus.  This is a good approximation of the current generated by a fast excitatory synapse. MetaNeuron can be used to assess the effect of the membrane time constant on temporal summation of synaptic potentials by choosing multiple stimuli in the "Stimulus Train" window. The "Threshold" potential shown in the graph indicates the approximate voltage at which action potentials will be initiated in a neuron. 

Lesson 3, Membrane Length Constant 

Lesson 3 illustrates the effect of the length constant on the passive spread of voltage down the length of a dendrite or axon. (For simplicity, this will be called a dendrite hereafter.) The lesson models the dendrite as a cylindrical process of uniform diameter and infinite length having a passive leak conductance. The dendrite has a membrane capacitance of 1 μF/cm². Values of the membrane resistance (R_m), the internal (cytoplasmic) resistivity (R_i), and the diameter (d) of the dendrite can be varied. Stimuli are applied to the process at X = 0. Responses are calculated from the cable equations, first developed by Lord Kelvin in the 1850's. When the "Normalize Stimulus to Resistance and Diameter" box in the "Dendrite/Axon Properties" window is selected, the stimulus is scaled to R_m, R_i, and d, such that the steady-state depolarization at X = 0 produced by a stimulus does not change when these parameters are varied. When the "Synaptic Potential" box in the "Stimulus" window is selected, a synaptic potential is generated at X = 0. The potential is generated by turning on a conductance with rising and falling time constants of 0.39 and 3.9 times the width of the stimulus. 

Responses can be displayed in two modes: "Potential vs. Distance" and "Potential vs. Time". The familiar steady-state exponential decay of voltage with distance can be viewed in the "Potential vs. Distance" mode when both the stimulus "Width" in the "Stimulus" window and the "Time" in the "Potential vs. Distance" window are set to a time much longer than the membrane time constant (try 50 ms). The attenuation and slowing of a synaptic potential as it passively spreads from the dendrite to the soma can be viewed in the "Potential vs, Time" mode. Set "Stimulus" to "Synaptic Potential", stimulus "Width" to 1 ms, and select the range option for "Position" in the "Potential vs. Time" window.  

Lesson 4, Axon Action Potential 

Lesson 4 illustrates how voltage- and time-dependent Na⁺ and K⁺ conductances generate the action potential. The MetaNeuron model in this lesson is based on equations published by Alan Hodgkin and Andrew Huxley in 1952 to describe the voltage-dependent Na⁺ and K⁺ conductances of the squid giant axon. The Na⁺ conductance in the MetaNeuron model represents fast, tetrodotoxin-sensitive Na⁺ channels. The K⁺ conductance represents delayed rectifier K⁺ channels. A leak conductance is also included. The values of some of the parameters in the equations have been adjusted to simulate action potential generation in a vertebrate axon. 

Several parameters controlling Na⁺, K⁺, and leak conductances in the model can be adjusted: 

• The Na⁺, K⁺, and leak equilibrium potentials.  Modifying these values will change the driving force for ion flux through the Na⁺, K⁺, and leak channels. 
• gNa⁺ max, gK⁺ max, gLeak, the maximum membrane conductances.  These parameters represent the number of Na⁺, K⁺, and leak channels in the membrane. 
• TTX (tetrodotoxin) and TEA (tetraethylammonium).  Selecting TTX blocks the Na⁺ conductance. Selecting TEA blocks the K⁺ conductance, but not the Leak conductance. 
• Temperature. Raising the temperature reduces the time constants controlling Na⁺ conductance activation and inactivation and K⁺ conductance activation, resulting in a faster action potential. The temperature factor has a Q10 of 3.0. 

Activation of the neuron is controlled by several stimuli: 

• Stimulus 1. The delay, width and amplitude of this current pulse can be varied. 
• Stimulus 2. A second current pulse is added when the "Stimulus 2 On" box is selected. 
• Holding Current.  This continuous current source can be used alone or together with the current pulses. 

Na⁺ and K⁺ conductances or currents are displayed along with the membrane potential when the appropriate boxes are checked in the "Conductances and Currents" window. 

Lesson 5, Axon Voltage Clamp 

Lesson 5 uses the voltage clamp technique to illustrate the voltage- and time-dependent properties of the Na⁺ channels and delayed rectifier K⁺ channels that generate the action potential. The voltage clamp technique uses a negative feedback electronic circuit to hold the membrane potential to a value (the command voltage) specified by the experimenter. The circuit then measures the time-dependent currents flowing through Na⁺ and K⁺ channels at that voltage. It is important to remember that action potentials cannot be generated when an axon is voltage clamped. 

Lesson 5 uses the same Hodgkin-Huxley model of the axon that is used to generate action potentials in Lesson 4. The parameters in Lesson 5 are similar to those in Lesson 4 as well.  The only changes in Lesson 5 are that the axon is now voltage-clamped and the stimuli used are command voltages rather than currents. The "Holding Potential" parameter determines the voltage of the axon at the beginning of the experiment. The "Stimulus 1" and "Stimulus 2" Amplitudes determine the voltage to which the membrane is stepped during the two pulses.  Note that these stimulus amplitudes represent absolute voltages, not relative voltages added onto the Holding Potential. 

A family of voltage clamp traces can be displayed using the "Range" feature of MetaNeuron. Use the 3D Graph feature to view the family of traces in 3D. 

Lesson 6, Synaptic Potential and Current 

Lesson 6 illustrates the synaptic voltages and currents generated at fast ionotropic synapses. The neuron in Lesson 6 is modeled by a leak conductance and by the opening of an ionotropic receptor conductance, simulating a synaptic response. A fast excitatory synapse is modeled by a receptor that is permeable to both Na⁺ and K⁺. The relative permeabilities of the two ions determine the reversal potential of the synapse. A fast inhibitory synapse is modeled by a Cl^- permeable receptor. The neuron in lesson 6 does not generate action potentials. 

The equilibrium potentials for Na⁺, K⁺ and Cl^- in this model are +50, -77 and -75 mV, respectively. The resting membrane potential is determined by a leak conductance having a reversal potential of -65 mV. The synaptic conductance is modeled with rising and falling time constants of 0.1 and 1.0 ms. 

The reversal potential of the synapse can be determined by varying the membrane potential of the neuron (yellow trace) and noting the potential at which the synaptic response reverses polarity. The membrane potential is varied by adjusting the "Holding Current".  The currents flowing through the ionotropic receptor are shown to the right: Na⁺ (green) and K⁺ (blue), for the excitatory receptor and Cl^- (orange) for the inhibitory receptor. Note that when the membrane potential is at the equilibrium potential for an ion, the current of that ion deviates from zero because the membrane potential changes during generation of the synaptic potential. In other words, the neuron is not being voltage-clamped.