main

% This document is the main file for simulate the multi-agent interaction % of HIV, HSC and immune system.

% author: Rongpeng Li, Mingmeng Geng, Fan Jiang % Date: September, 7, 2014 %Version 1.0

delete(gcf);

%Initialize variables and their explainations. thymus = 0; % the stem cell generation capability. hiv = 0; % the hiv counting. high = 0; % the high-resistance T cell counting, low = 0; % the low-resistance T cell counting. interveneTime = 16000; % the intervene time of CRISPR mechanism

method = 0; % 1 for using CRISPR mechnism, 0 for not. At the beginning, start without CRISPR mechanism.

%Initialize parameters and their explainations.

t = 0.01; % the simulation time step. T = 350; %the total time that the programs is going to simulate.

% parameter for thymus update. global thymusGrowthRate; % the self-generation rate of stem cell global N_thymus ; % the possible total thymus counting. global thymusSelfPresure ; % the enviroment pressure for thymus growth in M-model. global hiv2thymus ; % the hiv-caused thymus counting decreasing factor. global highlow2thymus ; % the high and low immune cell induced increasing factor.

% parameter for hiv update. global hivGrowthRate; %the self-generation rate of hiv virus. global hivMutation ; % the mutation factor. global N_hiv ; % the possible total hiv counting, can be set to be infinity. global hivSelfPressure  ; % Almost no self-pressure for hiv virus.

% parameter for high update. global thymus2high ; %the generation rate by thymus counting. global highResist ; % the resistance factor, can be invicible if CRISPR is 100% effective. global decayHigh ; % the decay(death) rate from high resistant T cell to low ones. global gainLow ; % the gain rate from low resistant T cell to high ones.

% parameter for low update. global thymus2low; %generation rate from thymus counting. global lowResist; % the resistance factor. global hiv2low; % the death rate caused by hiv. global gain4high % the gain rate by the immune decaying of high resistant T cells.

% choose parameter sets by user. OK = 0; while OK == 0 % set = input('Please choose the initial parameter set. 1, 2 or 3?'); set =1 ; if set ==1

   [thymusGrowthRate, N_thymus,thymusSelfPresure, hiv2thymus, highlow2thymus] =deal(0.8,0.94,0.3,0.22,0.2);
   [hivGrowthRate, hivMutation, N_hiv, hivSelfPressure] = deal(8,0.15,20,0.1);
   [thymus2high, highResist, decayHigh , gainLow] = deal(0.2,0.6,0.4,0.1);
   [thymus2low, lowResist, hiv2low, gain4high] = deal(0.2,0.2,0.8,0);
   
   [thymus, hiv, high, low]= deal(1,0.2,0.0,0.1);
   
   OK = 1;

elseif set ==2

   [thymusGrowthRate, N_thymus, thymusSelfPresure, hiv2thymus, highlow2thymus] =deal();
   [hivGrowthRate, hivMutation, N_hiv, hivSelfPressure] = deal();
   [thymus2high, highResist, decayHigh , gainLow] = deal();
   [thymus2low, lowResist, hiv2low, gain4high] = deal();
   
   [thymus, hiv, high, low]= deal();
   
   OK = 1;

elseif set ==3

   [thymusGrowthRate, N_thymus, thymusSelfPresure, hiv2thymus, highlow2thymus] =deal();
   [hivGrowthRate, hivMutation, N_hiv, hivSelfPressure] = deal();
   [thymus2high, highResist, decayHigh , gainLow] = deal();
   [thymus2low, lowResist, hiv2low, gain4high] = deal();
   
   [thymus, hiv, high, low]= deal();
   
   OK = 1;

else

   OK = 0;

end end

% Initialize zero-filled arrays to store the data generated. Len = floor(T/t);

[Time,Thymus,HIV,High,Low] = deal(zeros(1,Len));

%update the status

for i = 1:Len

   if i < interveneTime
       [Time(i),Thymus(i),HIV(i),High(i),Low(i)] = deal(t*i,thymus,hiv,high,low);
       [thymus, high, low, hiv,hivMutation,highResist,lowResist ] = update(t,thymus, high, low, hiv, method );
   else
       [Time(i),Thymus(i),HIV(i),High(i),Low(i)] = deal(t*i,thymus,hiv,high,low);
       method = 1;
       [thymus, high, low, hiv, hivMutation,highResist,lowResist] = update(t,thymus, high, low, hiv, method );
   end

% hivMutation end

% Draw pictures

subplot(2,2,1) plot(Time,Thymus,'*'); xlabel('Time') ylabel('Thymus counting') title('Thymus counting versus Time'); grid; hold on;

subplot(2,2,2) plot(Time,High,'+'); xlabel('Time') ylabel('High-resistance T cell counting') title('High-resistance T cell counting versus Time'); grid; hold on;

subplot(2,2,3) plot(Time,Low,'<'); xlabel('Time') ylabel('Low-resistance T cell counting') title('Low-resistance T cell counting versus Time'); grid; hold on;

subplot(2,2,4) plot(Time,HIV,'>'); xlabel('Time') ylabel('HIV counting') title('HIV counting versus Time'); grid;

saveas(gcf,'Trend Graph','bmp'); %delete(gcf);

%Draw phase graph.

update

function [thymus, high, low, hiv,hivMutation,highResist,lowResist ] = update(t,thymus, high, low, hiv, method ) % the function update all the status. % Here are the key of the program. The following function handlers decribes % the interaction details of the agents. You can modify them later to make % them more physical and realistic.

global thymusGrowthRate; % the self-generation rate of stem cell global N_thymus ; % the possible total thymus counting. global thymusSelfPresure ; % the enviroment pressure for thymus growth in M-model. global hiv2thymus ; % the hiv-caused thymus counting decreasing factor. global highlow2thymus ; % the high and low immune cell induced increasing factor.

% parameter for hiv update. global hivGrowthRate; %the self-generation rate of hiv virus. global hivMutation ; % the mutation factor. global N_hiv ; % the possible total hiv counting, can be set to be infinity. global hivSelfPressure  ; % Almost no self-pressure for hiv virus.

% parameter for high update. global thymus2high ; %the generation rate by thymus counting. global highResist ; % the resistance factor, can be invicible if CRISPR is 100% effective. global decayHigh ; % the decay(death) rate from high resistant T cell to low ones. global gainLow ; % the gain rate from low resistant T cell to high ones.

% parameter for low update. global thymus2low; %generation rate from thymus counting. global lowResist; % the resistance factor. global hiv2low; % the death rate caused by hiv. global gain4high % the gain rate by the immune decaying of high resistant T cells.

% To avoid duplicity of variables, I ignore the means of symbol.

f1a = @(hiv)(3*hiv); % HIV's existence,thymus counting is decreasing. f1b = @(hiv)(3 * hiv); % HIV's existence,thymus counting is decreasing. CRISPR exsits. following 'b' means the same logic. f2a = @(high,low)(0.01*high+0.01*low); % The high and low can boost the thymus increasing. f2b = @(high,low)(0.01* high + 0.01*low);

f3a = @(low,high,hivMutation)((low + high) * hivMutation); % T cell as hosts can boost the increasing of HIV f3b = @(low,high,hivMutation)(( low+ 0.3 * high)* hivMutation); f4a = @(high,hiv,hivMutation)((1-hivMutation) * hiv * high );% high resistance ones can decrease HIV counting. % f4a = @(high,hiv,hivMut)(0);

f4b = @(high,hiv,hivMutation)( 1.2* (1-hivMutation) * hiv * high);

f5a = @(thymus)(0.001*thymus); %high resistance ones increase due to thymus counting f5b = @(thymus)(0.001*thymus); f6a = @(hiv)((1- 0.4 * hiv));% HIV caused the high ones increasing slower than normal f6b = @(hiv)(1- 0.2 * hiv); f7a = @(high, highResist,hiv)(0.8*high*exp(-1*highResist)*hiv);% Immune decay rate for high ones due to mutation f7b = @(high, highResist,hiv)(0.5*high*exp(-0.5*highResist)*hiv); f8a = @(low,lowResist)(0.2*low*exp(lowResist));% high ones increase due to low ones that gain immune capacity f8b = @(low,lowResist)(0.3*low*exp(lowResist));

f9a = @(thymus)(0.2*thymus);% low ones increase due to thymus counting f9b = @(thymus)(0.2*thymus); f10a = @(hiv)(1- 0.5 * hiv);% HIV caused the high ones increasing slower than normal f10b = @(hiv)(1- 0.5 * hiv); f11a = @(low,lowResist,hiv)(1.5*low*exp(-1*lowResist)*hiv);% death formula for low ones due to HIV counting. f11b = @(low,lowResist,hiv)(1.5*low*exp(-1*lowResist)*hiv); f12a = @(high,decayHigh)(0);% growth rate due to decay from high ones. f12b = @(high,decayHigh)(0);

if method == 1 % implement with CRISPR mechnism.

   thymus = thymus + t* (thymusGrowthRate*thymus*(1-thymusSelfPresure*thymus/N_thymus) - hiv2thymus*f1b(hiv) + highlow2thymus*f2b(high,low));
   if thymus >1
       thymus = 1;
   elseif thymus < 0
       %thymus =0.1; %thymus system should not be broken
   end
  
   hiv = hiv + t*(hivGrowthRate*hiv*(1-hivSelfPressure*hiv/N_hiv)*f3b(low,high,hivMutation) - f4b(high,hiv,hivMutation));    
   if hiv >1
       hiv = 1;
   elseif hiv < 0
       hiv =0.05; % hiv can not be extinguished becasue there are hiv in other tissues.
   end
   
   high = high + t*( thymus2high*f5b(thymus)*f6b(hiv) - decayHigh*f7b(high, highResist, hiv ) + gainLow*f8b(low,lowResist));
   if high >1
       high = 1;
   elseif high < 0
       high =0;
   end
   
   low = low + t* ( thymus2low*f9b(thymus)*f10b(hiv) - hiv2low*f11b(low,lowResist,hiv) + gain4high*f12b(high,decayHigh) );
   if low >1
       low = 1;
   elseif low < 0
       low =0;
   end
   highResist = 0.8 * thymus;
   hivMutation = 0.1*(high/( high + low ) + 0.3*rand(1)); % update add random elements to the mutation level
     

elseif method ==0 %implement without CRISPR mechnism.

   thymus = thymus + t* (thymusGrowthRate*thymus*(1-thymusSelfPresure*thymus/N_thymus) - hiv2thymus*f1a(hiv) + highlow2thymus*f2a(high,low));
   if thymus >1
       thymus = 1;
   elseif thymus < 0
       thymus =0;
   end
   
   hiv = hiv + t*(hivGrowthRate*hiv*(1-hivSelfPressure*hiv/N_hiv)*f3a(low,high,hivMutation) - f4a(high,hiv,hivMutation) );    
   if hiv >1
       hiv = 1;
   elseif hiv < 0
       hiv =0;
   end
   
   % high = high + t*( thymus2high*f5a(thymus)*f6a(hiv) - decayHigh*f7a(high, highResist, hiv ) + gainLow*f8a(low,lowResist));
   high = 0;
   if high >1
       high = 1;
   elseif high < 0
       high =0;
   end
   
   low = low + t* ( thymus2low*f9a(thymus)*f10a(hiv) - hiv2low*f11a(low,lowResist,hiv) + gain4high*f12a(high,decayHigh) );
   if low >1
       low = 1;
   elseif low < 0
       low =0;
   end    

   hivMutation = 0.1*(high/( high + low ) + 0.3*rand(1)); % update add random elements to the mutation level 

end

% update some important global factors. If necessary, many other global % variables can be updated here.

end