PHYC452Biophysics:Assignments/HW3 4

MATLAB code

%452: Biophysics, HW#3
% (4) Numerical warmup: Compute numerically a 30 second trajectory of a
% membrane protein diffusing with D=0.05 micron^2/s. Use 1000 time steps to
% generate the trajectory. Use the computer program of your choice
% (but MATLAB is recommended). Give the code, and the trajectory with
% properly labeled axes.

dt=30/1000; %time interval between each point
D=0.05; %units are micron^2/s

x=zeros(1000,1);
y=zeros(1000,1);
t=(0:999)*dt;

%<r^2>=4*D*dt so then
r=sqrt(4*D*dt);

for ii=2:1000
%chose a random direction:
phi=rand*2*pi;
x(ii)=x(ii-1)+r*cos(phi);
y(ii)=y(ii-1)+r*sin(phi);
end

figure
plot(x,y)
xlabel(' X Position (microns)')
ylabel(' Y Position (microns)')
title('A 30 second trajectory of a particle diffusing in 2D with D=0.05 micron^2/s')
axis equal

Results