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=Generating Bacteria Trajectory=
= Generating Bacteria Trajectory =


==Synthetic Motility Data==
== Synthetic Motility Data ==
[[Image:Trajectory_real.TIF|left|150px|Real Bacteria Trajectory]] [[Image:Trajectory_synth.TIF |right|150px|Synthetic Bacteria Trajectory]]
[[Image:Trajectory_real.TIF|left|150px|Real Bacteria Trajectory]] [[Image:Trajectory_synth.TIF |right|150px|Synthetic Bacteria Trajectory]]


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*Tumbling Duration: Exponential Distribution with parameter <math>\lambda</math>
*Tumbling Duration: Exponential Distribution with parameter <math>\lambda</math>


==MATLAB Code==
== MATLAB Code ==


     %Generation of Bacteria Trajectory
     %Generation of Bacteria Trajectory

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Generating Bacteria Trajectory

Synthetic Motility Data

Real Bacteria Trajectory
Real Bacteria Trajectory
Synthetic Bacteria Trajectory
Synthetic Bacteria Trajectory

Synthetic distributions for bacteria run velocity, run duration, tumbling angle and tumbling duration were generated in the data gathering process. Alternative models may be assumed for the above motility characteristics, however we assumed that the run velocity had a Maxwell Distribution like the velocity of gas molecules, run and tumbling duration to be exponentially distributed and tumbling angle to be von Mises distributed. Parameters for the distributions are then user defined.

In this instance, we have decided to use the following distributions:

  • Run Velocity: Maxwell Distribution with parameter a
  • Run Duration: Exponential Distribution with parameter [math]\displaystyle{ \lambda }[/math]
  • Tumbling Angle: von Mises Distribution with parameters a and k
  • Tumbling Duration: Exponential Distribution with parameter [math]\displaystyle{ \lambda }[/math]

MATLAB Code

   %Generation of Bacteria Trajectory
   
   function [coord,nframes]=motility(vid_time,frame_rate,data_pts,von_a,von_k,maxw_a,exp_l)
   
   %Initialise Parameters
   frame_count=0;
   coord_pt=zeros(data_pts,2);
   beta=zeros(data_pts,1);
   tumb_frames=1;  %Bacteria Tubmles in First Frame
   coord(1,:)=coord_pt(1,:);
   n=1;
   
   %Generates Bacteria Motility Statistics
   theta=randraw('vonmises',[von_a,von_k],data_pts+1);      %Generates tumbling angle
   v_run=randraw('maxwell',maxw_a,data_pts+1);  %Generates run speed
   t_run=randraw('exp',1,data_pts+1);           %Generates run duration
   t_tumb=randraw('exp',exp_l,data_pts+1);
   
   %Generates Coordinate Points
   for k=1:data_pts
       beta(k+1)=beta(k)+theta(k);  %Generates cummulative turn angle 
       %Displacement=Velocity*Time
       coord_pt(k+1,1)=coord_pt(k,1)+v_run(k+1)*cos(beta(k+1))*t_run(k+1);    
       coord_pt(k+1,2)=coord_pt(k,2)+v_run(k+1)*sin(beta(k+1))*t_run(k+1); 
   end;
   
   if (sum(t_run+t_tumb))>vid_time
       %Generates Total Number of Frames, Points Data and Skeleton
       while frame_count <= (vid_time*frame_rate)
           %Generates Total Number of Frames
           frame_count=frame_count+round(t_run(n+1)*frame_rate)+round(t_tumb(n+1)*frame_rate);
           
           %Generates Bacteria Trajectory
           run_frames=tumb_frames+round(t_run(n+1)*frame_rate);
           coord(run_frames,:)=coord_pt(n+1,:);
           
           for i=(tumb_frames+1):(run_frames-1)
               coord(i,:)=coord(i-1,:)+(coord(run_frames,:)-coord(tumb_frames,:))/(run_frames-tumb_frames);
           end;
           
           tumb_frames=run_frames+round(t_tumb(n)*frame_rate);
       
           %Generates Trajectory
           for i=(run_frames+1):tumb_frames
               coord(i,:)=coord(run_frames,:);
           end;
         
       %Counter
       n=n+1;
       end;
   else
       sprintf('%s','Insufficient Data Points!')
   end;
   
   nframes=length(coord);


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