The simulations used in Lab Books are all based on a simple core program that stores spatial information for each displayed particle and updates its location for each unit of time (called a time slice).
To move each particle, two random numbers are drawn: one is used
to update the x-axis position, the other to update the y-axis position. The random
numbers themselves are produced from an algorithm that calculates its output according to
a bell-shaped (Gaussian) curve. The peak probability of this Gaussian distribution
is set at zero, with decreasing probability of obtaining either a positive or negative
value further and further from zero. For the simulations used here, the Gaussian
distribution for single particles, lipids and water molecules has a standard deviation
(SD) of 5 units, while the Gaussian distribution for the movement of larger ion/water
assemblies and proteins is much more tightly clustered around the mean, having an SD of 2
units. As with all Gaussian distributions, +/- 1 SD accounts for about two-thirds of all
the values; +/- 3 SD includes 99% of all possible values.
This random walk scheme approximates Brownian (diffusion) movement actually observed in a solution or other fluid medium. Each molecule in a real fluid, however, is vibrating and continuously colliding and interacting with its neighbors, but these events occur on a time scale faster than we can observe and simulate. During a period equivalent to our time slice, the "net" movement simulated is the average of a large number of such collisions and interactions. The average of many such random events is well described by the bell-shaped Gaussian curve used for our calculations. Also, solute molecules in solution are transiently associated with water molecules, but these associations change more rapidly than we can simulate. Thus, we illustrate solvated solute assemblies in our osmosis simulations as if they contained the same water molecules all the time. Clearly, they don't but our approximation is not unreasonable. Moreover, in our FRAP simulations we depict lipids diffusing in the plane of a membrane about 2.5 more rapidly than integral proteins, which clearly underestimates their relative difference in velocity. Also, because we havedrawn the protein images much larger than their virtual locations and have shaded them appropriately, they seem to overlap and to cluster in the third dimension; their clustered appearance is a simulation artifact.
Before the position of each particle is updated, a few checks are done. If the new position would lie beyond the borders of the compartment, then the particle "bounces". The compartment in the FRAP experiments, however, is considered a "window", and any particle leaving the window is replaced by another entering at a random location around the frame; all bleached particles diffusing out of the window are replaced by unbleached ones. (In this manner, the FRAP experiments have been simulated within a square "microscope field-of-view.") If the new position is on the other side of a membrane, then a new random number is drawn to see if the particle can cross the membrane. In the various electrochemical simulations the only effect of voltage is in determining the membrane-crossing probability (as governed by the Constant Field Equation); voltage exerts no influence on the movement of individual particles in the free solution. Likewise, in the osmosis simulations the membrane is freely permeable to water molecules but not to the larger complexes of water and solute. An ion or other solute that fails to permeate "bounces" off the membrane just as it did off the wall. Otherwise, the only force "driving" the various movements are the Gaussian random numbers in the x and y directions. Using this approach, our membrane transport simulations reproduce well the actual movement of ions and other molecules across a real membrane.
The programs themselves are written in the language Java. They make use of the concept of "object-oriented" programming by making each element in the simulation responsible for its own properties. Thus, each particle knows how to draw itself, stores its position and charge, and updates its position based on the constraints placed on its motion.