# 3D animation of listeria moving in Xenopus extract in 2D
# Version 1.0  9-27-09
# Based on Shenoy et al (in Julie Theriot's group)PNAS May 15, 2007 vol. 104
#
# Plots the trajectory of a listeria bacterium and then its distance and speed vs. time
# Listeria is a pathogenic bacterium responsible for much food-borne illness
# It moves along its substrate by polymerizing the protein actin, pushing off against
# the substrate by leaving a "comet tail" easily visualized under light microscopy
# Theriot's group has shown that listeria rotates as it travels.  

# Movies of all this can be viewed at Julie Theriot's group website at:  http://cmgm.stanford.edu/theriot/
 
from visual import *
from visual.graph import *  # import graphing features

# STUDENT PARAMETERS

# ratio between w, the rate at which the listeria rotates around its long axis
# and Omega, the rate of change of the angle the long axis makes with the x axis.
wOmega = 0.1


# timestep in dimensionless units wt
dt = 0.1                                      

Ntimesteps = 3000                               # total number of timesteps for the simulation


#########################
#
# Small amplitude sine: wOmega=0.1, dt = 0.1, Ntimesteps = 3000
# S curve or Large amplitude sine: wOmega=0.5-1.0, dt = 0.1, Ntimesteps = 3000
# Serpentine: wOmega=1.5-1.0, dt = 0.1, Ntimesteps = 3000
# Translating figure 8 wOmega=2.5, dt = 0.1, Ntimesteps = 3000
# Spirals wOmega=20.2, dt =0.01, Ntimesteps = 3000
#
#
#
##############################

oxa = 1
oya = 1
oza = 0.1
                       
x_o = 0                 # initial value of x, y and z--starts at the origin
y_o = 0
z_o = 0



# Initialize graphics scene - put the 3D box at x=50, y=0, make it 800 wide and 200 high
scene=display(width=1200,height=600,x=50, y=0)

scene.ambient=0.24
scene.background=color.white
scene.title="Listeria trajectory, parameter value ="+str(wOmega)
scene.range=(oxa,oya,oza)
#this sets the viewing angle
scene.forward=(0,0,1)

# create wireframe with dimensions of the pixel sizes along x,y,z for now
# create the 8 points. then join em up
p1 = (oxa,oya,oza)
p2 = (-oxa,oya,oza)
p3 = (-oxa,-oya,oza)
p4 = (oxa,-oya,oza)
p5 = (oxa,oya,-oza)
p6 = (-oxa,oya,-oza)
p7 = (-oxa,-oya,-oza)
p8 = (oxa,-oya,-oza)
square1 = curve(pos=[p1,p2,p3,p4,p1],color=color.black)
square2 = curve(pos=[p5,p6,p7,p8,p5],color=color.black)
square3 = curve(pos=[p1,p5,p8,p4,p1],color=color.black)
square4 = curve(pos=[p2,p6,p7,p3,p2],color=color.black)
# end of wireframe

 # initialize listeria's position at (xo,yo,zo), pointing along +y
listeria = cone(pos=(x_o,y_o,z_o), radius=0.01, axis=(0,0.01,0), color=color.white)    

listeria_position=[]
listeria_speed=[]

# create curve to plot the listeria's trajectory
c = curve(pos=(x_o,y_o,z_o),color=color.red)            

n=0

while n <= Ntimesteps:
    rate (30)                                           # screen refresh rate           

    t = n*dt                                            # current time

    #   first update velocity, then update position second!
    #   If switched in order, it looses energy and orbits don't close!

    listeria.velocity = vector([-sin(wOmega*sin(t)),cos(wOmega*sin(t)),0.0])

    listeria.pos = listeria.pos + listeria.velocity*dt        
    listeria.axis = 0.1*vector([-sin(wOmega*sin(t)),cos(wOmega*sin(t)),0.0])
    listeria_position.append(mag(listeria.pos))
    listeria_speed.append(mag(listeria.velocity))
    c.append(pos=listeria.pos)
    n=n+1