A Model for the Interaction Between Cells in the Nervous System

Summation of Synaptic Electrical Potentials

Mark C. Cattrell and Mike A. Bloom

Intro

Neuroscience can be considered an almost unexplored region of today's scientific frontier. Because of its vast complexity, the human brain and the functions of its individual cells continue to mystify scientists. It is our intention to spend this semester creating a model of behavior of the human brain as a function of several variables that affect its behavior. Our model will account for the effects of spatial and temporal variance as well as the permeability and capacitance of a neuron's membrane. After we create a robust program that accommodates for different values of these parameters, we will work with Professor James A. Murray of Colby's biology department to determine which other behaviors and variables we can approach.

Variables

When multiple electrical stimuli are influencing a neuron, the sum of their effects is called a summation. Summations occur differently when the distance that a potential must travel and the time between stimuli is not at a constant.

1.

Spatial variance is the intrinsic variability of distance that separates synaptic interfaces from the position in the neuron at which summation takes place (the spike initiation zone, or SIE). When a message is sent to a specific cell in the nervous system, it travels in the form of a positive current of electricity entering the cell. Because a cell is not a perfect conductor, the potential entering a cell will naturally dissipate as it extends around the cell body. As the distance separating the input potential from the position in the cell that requires a threshold potential increases, the potential remaining in the cell becomes weaker.

2.

Temporal summation occurs in a similar way: When a pulse reaches a cell, its strength dissipates over time inside the cell. But if the cell is stimulated again before the potential is allowed to return to its resting level, the net potential will be the sum of the two pulses.

3.

The permeability of the cell membrane wall is another parameter which can affect the rate at which an electrical potential diminishes. This will inevitably be a difficult (though manageable) characteristic for us to model because the permeability of the cell membrane is affected by various factors. For instance, there are several kinds of "pumps" on the surface of the cell that actively move Na+ and K+ ions into and out of the cell. These pumps will almost all be completely closed when a stimulus occurs, but there are many other channels through which these ions and electrical charge can escape. Each neuron is unique regarding these characteristics, which requires that we create a dynamic program to accurately account for each intricacy.

The appearance of our program

As far as the aesthetics of the program go, we are planning on using a fairly extensive GUI. When the program is run, a picture of the neurons will appear on the screen. In the upper right hand corner of the screen, we will have an "EKG" type meter that displays the excitement and dissipation of the pulse.

We will also have arrow buttons (or something of that nature) that the user can manipulate in order to determine how close he wants to move one neuron toward the other (remember: the time it takes the second neuron to fire is a function of the distance between the stimulus and the SIE) There will also be similar arrow buttons to click to determine the resistance of the cytoplasm within the cell and the ease with which the pulse can escape.

Of course we will use the technical terms for these variables. All of these functions will be brought up on the screen when the user touches a button that brings down a drop-down window containing the choices. We will also use a GUI to cause the neuron to fire every time the user pushes the space bar. Each time the space bar is pushed, the user will be able to see the pulse moving toward the second neuron, and one will be able to see how close the potential in the cell is coming to the threshold on the EKG meter in the upper right hand corner.

When the pulse crosses the threshold, the target neuron will fire, causing the potential to rise much farther on the meter. The user will also be able to see the second neuron fire in the diagram.

Implementation

We will be writing our code in Java so that our finished product can be freely available via the world wide web. We will need to write several applets, learn the details of and create a graphical user interface, and write code that can be readily understood, but which will nevertheless dynamically model many aspects one of the most complicated processes known to man.

Schedule

Because of our previous experience with the Java programming environment, we feel that we can progress in this project fairly quickly and consistently. Over the next few weeks we will be focusing on the basic applet that will comprise our "EKG" component. We are confident that we will be able to have a graphic of a synapse fairly soon as well, depending on the complexity of the code that this would involve. By spring break we intend to have our GUI in working order, and we will have begun to implement the code for the actual physiological behaviors.

It is hard to extrapolate beyond Spring Break, but we are confident that our project will be proceeding smoothly and that we will be able to begin adding more involved features so that our software can be used as an educational tool.

This calendar is a rough estimate that we intend to follow, but we realize that there will likely be hurdles and setbacks along the way.