Team:Stanford/Research/Modeling

From 2010.igem.org

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{{Template:Stanford_2010_Main_Menu}}
{{Template:Stanford_2010_Main_Menu}}
<div class="contents">
<div class="contents">
 +
==Goals==
==Goals==
Our intuition for what makes a good ratio sensor could only take us so far.  From the very first stages of design, we wanted to back up and test our ideas with mathematical tools.  Luckily, we found that solving the equations of mass action kinetics at steady-state was enough gave us clear design criteria.  We present the mathematical basis for sensors that are capable of sensing a single ratio digitally, or many ratios in an analog fashion.
Our intuition for what makes a good ratio sensor could only take us so far.  From the very first stages of design, we wanted to back up and test our ideas with mathematical tools.  Luckily, we found that solving the equations of mass action kinetics at steady-state was enough gave us clear design criteria.  We present the mathematical basis for sensors that are capable of sensing a single ratio digitally, or many ratios in an analog fashion.
Line 13: Line 14:
Boolean model for the sRNA system. This is mean to provide a significantly simplified mathematical understanding of the dynamics involved.
Boolean model for the sRNA system. This is mean to provide a significantly simplified mathematical understanding of the dynamics involved.
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      --><title>iGEM_boolean_sRNA_model</title><meta name="generator" content="MATLAB 7.10"><meta name="date" content="2010-10-27"><meta name="m-file" content="iGEM_boolean_sRNA_model"><style type="text/css">
 
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-
  </style></head><body><div class="content"><pre class="codeinput">clear <span class="string">all</span>
 
-
clc
 
-
 
-
<span class="comment">%Constants and Values</span>
 
-
trackingNum = 6;    <span class="comment">%mRNA_pA, mRNA_pB, sRNA_A, sRNA_B, protein_A, protein_B;</span>
 
-
inputNum = 2;      <span class="comment">%A, B;</span>
 
-
processNum = 6;    <span class="comment">%Trx_pA, Trx_sRNA_A, Trx_pB, Trx_sRNA_B, Trl_A, Trl_B;</span>
 
-
 
-
<span class="comment">%Cell/Matrix Dimensions</span>
 
-
m = 2^trackingNum;
 
-
n = 2^inputNum;
 
-
c = cell(m+1, n+1);
 
-
 
-
trackingMatrix = de2bi(0:m-1);
 
-
inputMatrix = de2bi(0:n-1);
 
-
processMatrix = zeros(1,processNum);
 
-
 
-
<span class="comment">%Populating the Cell (Tracking x Input)</span>
 
-
c{1,1} = [0];
 
-
<span class="keyword">for</span> j = 1
 
-
    <span class="keyword">for</span> i = 2:m+1
 
-
        c{i,j} = trackingMatrix(i-1,:);
 
-
    <span class="keyword">end</span>
 
-
<span class="keyword">end</span>
 
-
<span class="keyword">for</span> i = 1
 
-
    <span class="keyword">for</span> j = 2:n+1
 
-
        c{i,j} = inputMatrix(j-1,:);
 
-
    <span class="keyword">end</span>
 
-
<span class="keyword">end</span>
 
-
<span class="keyword">for</span> i = 2:m+1
 
-
    <span class="keyword">for</span> j = 2:n+1
 
-
        c{i,j} = processMatrix;
 
-
    <span class="keyword">end</span>
 
-
<span class="keyword">end</span>
 
-
 
-
<span class="comment">%Rules, Acessing, and Changing</span>
 
-
<span class="keyword">for</span> j = 2:n+1
 
-
    A = c{1,j}(1);
 
-
    B = c{1,j}(2);
 
-
 
-
    <span class="keyword">for</span> i = 2:m+1
 
-
        mRNA_pA = c{i,1}(1);
 
-
        mRNA_pB = c{i,1}(2);
 
-
        sRNA_A = c{i,1}(3);
 
-
        sRNA_B = c{i,1}(4);
 
-
        protein_A = c{i,1}(5);
 
-
        protein_B = c{i,1}(6);
 
-
 
-
        <span class="comment">%Trx_pA</span>
 
-
        <span class="keyword">if</span> A == 1
 
-
            c{i,j}(1) = 1;
 
-
        <span class="keyword">end</span>
 
-
 
-
        <span class="comment">%Trx_pB</span>
 
-
        <span class="keyword">if</span> B == 1
 
-
            c{i,j}(2) = 1;
 
-
        <span class="keyword">end</span>
 
-
 
-
        <span class="comment">%Trx_sRNA_A</span>
 
-
        <span class="keyword">if</span> A == 1
 
-
            c{i,j}(3) = 1;
 
-
        <span class="keyword">end</span>
 
-
 
-
        <span class="comment">%Trx_sRNA_B</span>
 
-
        <span class="keyword">if</span> B == 1
 
-
            c{i,j}(4) = 1;
 
-
        <span class="keyword">end</span>
 
-
 
-
        <span class="comment">%Trl_A</span>
 
-
        <span class="keyword">if</span> mRNA_pA == 1 &amp;&amp; mRNA_pB == 0
 
-
            c{i,j}(5) = 1;
 
-
        <span class="keyword">end</span>
 
-
 
-
        <span class="comment">%Trl_B</span>
 
-
        <span class="keyword">if</span> mRNA_pB == 1 &amp;&amp; mRNA_pA == 0
 
-
            c{i,j}(6) = 1;
 
-
        <span class="keyword">end</span>
 
-
 
-
    <span class="keyword">end</span>
 
-
<span class="keyword">end</span>
 
-
 
-
<span class="comment">%Display Results (Column by Column)</span>
 
-
[nrows,ncols]= size(c);
 
-
<span class="comment">%Condense Cell and Display</span>
 
-
<span class="keyword">for</span> i = 1:nrows
 
-
    <span class="keyword">for</span> j = 1:ncols
 
-
        string = num2str(c{i,j});
 
-
        l = length(string);
 
-
        r = 1;
 
-
        s = 1;
 
-
        t = 0;
 
-
 
-
        <span class="keyword">while</span> t ~= 1
 
-
            <span class="keyword">if</span> r == l
 
-
            t = 1;
 
-
            <span class="keyword">end</span>
 
-
 
-
            noSpacesString(s) = string(r);
 
-
            r = r+3;
 
-
            s = s+1;
 
-
        <span class="keyword">end</span>
 
-
        c{i,j} = noSpacesString;
 
-
    <span class="keyword">end</span>
 
-
<span class="keyword">end</span>
 
-
c(:,:)
 
-
 
-
<span class="comment">%Find Steady States and Corresponding Inputs</span>
 
-
counter = 1;
 
-
<span class="keyword">for</span> i = 2:m+1
 
-
    <span class="keyword">for</span> j = 2:n+1
 
-
        <span class="keyword">if</span> c{i,j} == c{i,1}
 
-
            completeMatrix{counter,1} = c{i,j};            <span class="comment">%Steady state values</span>
 
-
            completeMatrix{counter,2} = num2str([i-1,j-1]); <span class="comment">%Location (n x m) within results area</span>
 
-
            completeMatrix{counter,3} = c{1,j};            <span class="comment">%Corresponding input values</span>
 
-
            counter = counter+1;
 
-
        <span class="keyword">end</span>
 
-
    <span class="keyword">end</span>
 
-
<span class="keyword">end</span>
 
-
SS_mXn_Input = completeMatrix
 
-
 
-
time = 0:processNum;
 
-
<span class="comment">%plot(time,,time,,time,,time,,time,,time,)</span>
 
-
 
-
<span class="comment">%New Cell for Specific Cases</span>
 
-
<span class="comment">% d(:,1) = c(:,1);</span>
 
-
<span class="comment">% for j = 2:n+1</span>
 
-
<span class="comment">%    C1 = '0000';</span>
 
-
<span class="comment">%    C2 = '0011';</span>
 
-
<span class="comment">%    C3 = '0100';</span>
 
-
<span class="comment">%    C4 = '0111';</span>
 
-
<span class="comment">%    C5 = '1000';</span>
 
-
<span class="comment">%    C6 = '1011';</span>
 
-
<span class="comment">%    C7 = '1100';</span>
 
-
<span class="comment">%</span>
 
-
<span class="comment">%    a = {C1, C2, C3, C4, C5, C6, C7};</span>
 
-
<span class="comment">%    for b = 1:1:length(a)</span>
 
-
<span class="comment">%        if strcmp(c(1,j),a(b)) == 1</span>
 
-
<span class="comment">%            d(:,b+1) = c(:,j);</span>
 
-
<span class="comment">%        end</span>
 
-
<span class="comment">%    end</span>
 
-
<span class="comment">% end</span>
 
-
<span class="comment">% d</span>
 
-
</pre><pre class="codeoutput">
 
-
ans =
 
-
 
-
  Columns 1 through 4
 
-
 
-
    '0'        '00'        '01'        '10'   
 
-
    '000000'    '000000'    '010100'    '101000'
 
-
    '000001'    '000000'    '010100'    '101000'
 
-
    '000010'    '000000'    '010100'    '101000'
 
-
    '000011'    '000000'    '010100'    '101000'
 
-
    '000100'    '000000'    '010100'    '101000'
 
-
    '000101'    '000000'    '010100'    '101000'
 
-
    '000110'    '000000'    '010100'    '101000'
 
-
    '000111'    '000000'    '010100'    '101000'
 
-
    '001000'    '000000'    '010100'    '101000'
 
-
    '001001'    '000000'    '010100'    '101000'
 
-
    '001010'    '000000'    '010100'    '101000'
 
-
    '001011'    '000000'    '010100'    '101000'
 
-
    '001100'    '000000'    '010100'    '101000'
 
-
    '001101'    '000000'    '010100'    '101000'
 
-
    '001110'    '000000'    '010100'    '101000'
 
-
    '001111'    '000000'    '010100'    '101000'
 
-
    '010000'    '000001'    '010101'    '101001'
 
-
    '010001'    '000001'    '010101'    '101001'
 
-
    '010010'    '000001'    '010101'    '101001'
 
-
    '010011'    '000001'    '010101'    '101001'
 
-
    '010100'    '000001'    '010101'    '101001'
 
-
    '010101'    '000001'    '010101'    '101001'
 
-
    '010110'    '000001'    '010101'    '101001'
 
-
    '010111'    '000001'    '010101'    '101001'
 
-
    '011000'    '000001'    '010101'    '101001'
 
-
    '011001'    '000001'    '010101'    '101001'
 
-
    '011010'    '000001'    '010101'    '101001'
 
-
    '011011'    '000001'    '010101'    '101001'
 
-
    '011100'    '000001'    '010101'    '101001'
 
-
    '011101'    '000001'    '010101'    '101001'
 
-
    '011110'    '000001'    '010101'    '101001'
 
-
    '011111'    '000001'    '010101'    '101001'
 
-
    '100000'    '000010'    '010110'    '101010'
 
-
    '100001'    '000010'    '010110'    '101010'
 
-
    '100010'    '000010'    '010110'    '101010'
 
-
    '100011'    '000010'    '010110'    '101010'
 
-
    '100100'    '000010'    '010110'    '101010'
 
-
    '100101'    '000010'    '010110'    '101010'
 
-
    '100110'    '000010'    '010110'    '101010'
 
-
    '100111'    '000010'    '010110'    '101010'
 
-
    '101000'    '000010'    '010110'    '101010'
 
-
    '101001'    '000010'    '010110'    '101010'
 
-
    '101010'    '000010'    '010110'    '101010'
 
-
    '101011'    '000010'    '010110'    '101010'
 
-
    '101100'    '000010'    '010110'    '101010'
 
-
    '101101'    '000010'    '010110'    '101010'
 
-
    '101110'    '000010'    '010110'    '101010'
 
-
    '101111'    '000010'    '010110'    '101010'
 
-
    '110000'    '000000'    '010100'    '101000'
 
-
    '110001'    '000000'    '010100'    '101000'
 
-
    '110010'    '000000'    '010100'    '101000'
 
-
    '110011'    '000000'    '010100'    '101000'
 
-
    '110100'    '000000'    '010100'    '101000'
 
-
    '110101'    '000000'    '010100'    '101000'
 
-
    '110110'    '000000'    '010100'    '101000'
 
-
    '110111'    '000000'    '010100'    '101000'
 
-
    '111000'    '000000'    '010100'    '101000'
 
-
    '111001'    '000000'    '010100'    '101000'
 
-
    '111010'    '000000'    '010100'    '101000'
 
-
    '111011'    '000000'    '010100'    '101000'
 
-
    '111100'    '000000'    '010100'    '101000'
 
-
    '111101'    '000000'    '010100'    '101000'
 
-
    '111110'    '000000'    '010100'    '101000'
 
-
    '111111'    '000000'    '010100'    '101000'
 
-
 
-
  Column 5
 
-
 
-
    '11'   
 
-
    '111100'
 
-
    '111100'
 
-
    '111100'
 
-
    '111100'
 
-
    '111100'
 
-
    '111100'
 
-
    '111100'
 
-
    '111100'
 
-
    '111100'
 
-
    '111100'
 
-
    '111100'
 
-
    '111100'
 
-
    '111100'
 
-
    '111100'
 
-
    '111100'
 
-
    '111100'
 
-
    '111101'
 
-
    '111101'
 
-
    '111101'
 
-
    '111101'
 
-
    '111101'
 
-
    '111101'
 
-
    '111101'
 
-
    '111101'
 
-
    '111101'
 
-
    '111101'
 
-
    '111101'
 
-
    '111101'
 
-
    '111101'
 
-
    '111101'
 
-
    '111101'
 
-
    '111101'
 
-
    '111110'
 
-
    '111110'
 
-
    '111110'
 
-
    '111110'
 
-
    '111110'
 
-
    '111110'
 
-
    '111110'
 
-
    '111110'
 
-
    '111110'
 
-
    '111110'
 
-
    '111110'
 
-
    '111110'
 
-
    '111110'
 
-
    '111110'
 
-
    '111110'
 
-
    '111110'
 
-
    '111100'
 
-
    '111100'
 
-
    '111100'
 
-
    '111100'
 
-
    '111100'
 
-
    '111100'
 
-
    '111100'
 
-
    '111100'
 
-
    '111100'
 
-
    '111100'
 
-
    '111100'
 
-
    '111100'
 
-
    '111100'
 
-
    '111100'
 
-
    '111100'
 
-
    '111100'
 
-
 
-
 
-
SS_mXn_Input =
 
-
 
-
    '000000'    '1  1'      '00'
 
-
    '010101'    '22  2'    '01'
 
-
    '101010'    '43  3'    '10'
 
-
    '111100'    '61  4'    '11'
 
-
 
-
</pre><p class="footer"><br>
 
-
      Published with MATLAB&reg; 7.10<br></p></div><!--
 
-
##### SOURCE BEGIN #####
 
-
clear all
 
-
clc
 
-
 
-
%Constants and Values
 
-
trackingNum = 6;    %mRNA_pA, mRNA_pB, sRNA_A, sRNA_B, protein_A, protein_B;
 
-
inputNum = 2;      %A, B;
 
-
processNum = 6;    %Trx_pA, Trx_sRNA_A, Trx_pB, Trx_sRNA_B, Trl_A, Trl_B;
 
-
 
-
%Cell/Matrix Dimensions
 
-
m = 2^trackingNum;
 
-
n = 2^inputNum;
 
-
c = cell(m+1, n+1);
 
-
 
-
trackingMatrix = de2bi(0:m-1);
 
-
inputMatrix = de2bi(0:n-1);
 
-
processMatrix = zeros(1,processNum);
 
-
 
-
%Populating the Cell (Tracking x Input)
 
-
c{1,1} = [0];
 
-
for j = 1
 
-
    for i = 2:m+1
 
-
        c{i,j} = trackingMatrix(i-1,:);
 
-
    end
 
-
end
 
-
for i = 1
 
-
    for j = 2:n+1
 
-
        c{i,j} = inputMatrix(j-1,:);
 
-
    end
 
-
end
 
-
for i = 2:m+1
 
-
    for j = 2:n+1
 
-
        c{i,j} = processMatrix;
 
-
    end
 
-
end
 
-
 
-
%Rules, Acessing, and Changing
 
-
for j = 2:n+1
 
-
    A = c{1,j}(1);
 
-
    B = c{1,j}(2);
 
-
   
 
-
    for i = 2:m+1
 
-
        mRNA_pA = c{i,1}(1);
 
-
        mRNA_pB = c{i,1}(2);
 
-
        sRNA_A = c{i,1}(3);
 
-
        sRNA_B = c{i,1}(4);
 
-
        protein_A = c{i,1}(5);
 
-
        protein_B = c{i,1}(6);
 
-
       
 
-
        %Trx_pA
 
-
        if A == 1
 
-
            c{i,j}(1) = 1;
 
-
        end
 
-
       
 
-
        %Trx_pB
 
-
        if B == 1
 
-
            c{i,j}(2) = 1;
 
-
        end
 
-
       
 
-
        %Trx_sRNA_A
 
-
        if A == 1
 
-
            c{i,j}(3) = 1;
 
-
        end
 
-
       
 
-
        %Trx_sRNA_B
 
-
        if B == 1
 
-
            c{i,j}(4) = 1;
 
-
        end
 
-
       
 
-
        %Trl_A
 
-
        if mRNA_pA == 1 && mRNA_pB == 0
 
-
            c{i,j}(5) = 1;
 
-
        end
 
-
       
 
-
        %Trl_B
 
-
        if mRNA_pB == 1 && mRNA_pA == 0
 
-
            c{i,j}(6) = 1;
 
-
        end
 
-
       
 
-
    end
 
-
end
 
-
 
-
%Display Results (Column by Column)
 
-
[nrows,ncols]= size(c);
 
-
%Condense Cell and Display
 
-
for i = 1:nrows
 
-
    for j = 1:ncols       
 
-
        string = num2str(c{i,j});
 
-
        l = length(string);
 
-
        r = 1;
 
-
        s = 1;
 
-
        t = 0;
 
-
       
 
-
        while t ~= 1
 
-
            if r == l
 
-
            t = 1;
 
-
            end
 
-
           
 
-
            noSpacesString(s) = string(r);
 
-
            r = r+3;
 
-
            s = s+1;
 
-
        end
 
-
        c{i,j} = noSpacesString;
 
-
    end
 
-
end
 
-
c(:,:)
 
-
 
-
%Find Steady States and Corresponding Inputs
 
-
counter = 1;
 
-
for i = 2:m+1
 
-
    for j = 2:n+1
 
-
        if c{i,j} == c{i,1}
 
-
            completeMatrix{counter,1} = c{i,j};            %Steady state values
 
-
            completeMatrix{counter,2} = num2str([i-1,j-1]); %Location (n x m) within results area
 
-
            completeMatrix{counter,3} = c{1,j};            %Corresponding input values           
 
-
            counter = counter+1;
 
-
        end
 
-
    end
 
-
end
 
-
SS_mXn_Input = completeMatrix
 
-
 
-
time = 0:processNum;
 
-
%plot(time,,time,,time,,time,,time,,time,)
 
-
 
-
%New Cell for Specific Cases
 
-
% d(:,1) = c(:,1);
 
-
% for j = 2:n+1
 
-
%    C1 = '0000';
 
-
%    C2 = '0011';
 
-
%    C3 = '0100';
 
-
%    C4 = '0111';
 
-
%    C5 = '1000';
 
-
%    C6 = '1011';
 
-
%    C7 = '1100';
 
-
%   
 
-
%    a = {C1, C2, C3, C4, C5, C6, C7};
 
-
%    for b = 1:1:length(a)
 
-
%        if strcmp(c(1,j),a(b)) == 1
 
-
%            d(:,b+1) = c(:,j);
 
-
%        end
 
-
%    end
 
-
% end
 
-
% d
 
-
##### SOURCE END #####
 
-
--></body>
 
-
</html>
 
</div>
</div>

Revision as of 23:55, 27 October 2010

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Contents

Goals

Our intuition for what makes a good ratio sensor could only take us so far. From the very first stages of design, we wanted to back up and test our ideas with mathematical tools. Luckily, we found that solving the equations of mass action kinetics at steady-state was enough gave us clear design criteria. We present the mathematical basis for sensors that are capable of sensing a single ratio digitally, or many ratios in an analog fashion.

The System

Analog

Digital

Boolean model for the sRNA system. This is mean to provide a significantly simplified mathematical understanding of the dynamics involved.


Retrieved from "http://2010.igem.org/Team:Stanford/Research/Modeling"