Fit_Fig1B.m

function main()

D=xlsread('Data chemotaxis benefit.xlsx',1,'D2:G10')
lam=D(:,1);
SDlam=D(:,2);
Ptar=D(:,3);
SDPtar=D(:,4);

%        A   Lam0
guess=[10000, 1];
fit=fminsearch(@(par) chi2(par,lam,Ptar),guess)

1000*fit(2)

Lam=0.1:0.1:1;
Phic=fit(1)*(1-Lam/fit(2));


plot(lam,Ptar,'s',Lam,Phic,'k-')
xlim([0.3 1])
xlabel ('Growth rate \lambda');
ylabel ('P_{tar} activity');
    
filename = 'fit_Fig1b.xlsx';
A = [Lam' Phic']
xlswrite(filename,A)

function error=chi2(par,lam,data)
   error=sum((data-par(1)*(1-lam/par(2))).^2);
end

Fit_Fig1E_WTvsCheY_beads_Nvalue.m

function fit1F()

   % data     
   D=xlsread('Data chemotaxis benefit mod.xlsx',1,'D35:L43');
   Lam=D(:,1); % exp growth rate
   WTpc=0.5*(D(:,3)+D(:,5)); % exp WT percentages
   Nval=D(:,9); % corresponding model N values

          %s2,  betab
   guess=[0.2,100*4.6e-3];
   fit=fminsearch(@(par) chi2(par,Nval,WTpc),guess,optimset('MaxFunEvals',50))

   % run again with best fit parameters
   ratio=[];
   Nvalue=[];
   L1=[];
   
   i=1;
   
   for nval=0.1:0.01:0.6
   
        %                          N1 N2  n1 n2  s2   betab  Nvalue
        [t,y]=ode45(@model,[0 15],[1e3;0;1e3;0;fit(1);fit(2);nval]);
 
        % culture only
        WT=y(numel(t),1)+y(numel(t),2);
        cheY=y(numel(t),3)+y(numel(t),4);
        
        ratio(i)=100*WT/(cheY+WT);
        Nvalue(i)=nval;
        
        rho=0.76;
        w=0.9;
        phiRmax=0.55; 
        phi0=0.76*0.087;
        kt=4.5;
        calphaEkEmaxS=nval*5.8;
        Kn1=calphaEkEmaxS*rho; % N value [h^{-1}]
        l1=kt*Kn1*w/(kt+Kn1*w)*(phiRmax-phi0)/rho; %
        
        L1(i)=l1;
        i=i+1;
   
   end
   
   % plot best fit parameters
   plot(Lam,WTpc,'s',L1,ratio,'r--');
   xlabel('N value');
   ylabel('Percentage WT');
   title('WT vs \Delta{cheY} with bead secretion (fit for Fig. 1f)')
   
   filename = 'fit_Fig1f.xlsx';
   A = [L1' ratio'];
   xlswrite(filename,A)
   
end

function error=chi2(par,Nval,data)

   ratio=[];

   for i=1:numel(Nval) % Nvalue=sugar concentrationhere
        
        %                           N1 N2 n1 n2  s2   betab  Nvalue  
        [t,y]=ode45(@model,[0 15],[1e3;0;1e3;0;par(1);par(2);Nval(i)]); 
 
        % culture only
        WT=y(numel(t),1)+y(numel(t),2);
        cheY=y(numel(t),3)+y(numel(t),4);
        
        ratio(i)=100*WT/(cheY+WT);
        
        i=i+1;
   
   end
   
   error=sum((data-ratio').^2)
end

function dydt=model(t,y)

   N1=y(1);
   N2=y(2);
   n1=y(3);
   n2=y(4);
   s2=y(5);
   betab=abs(y(6));
   NvalueS=y(7);
    
   % nutrient
   S1=20000; % mM and not uM
   S2=20000;
   s1=0;
   
   % primary crabon source
   calphaEkEmaxS=NvalueS*5.8;
   
   % secondary carbon source
   Nvalues=1;% N value for CA is growth rate [h^{-1}]
   calphaEkEmaxs=Nvalues*5.8;
   beta=2.5e-10;%10; % uM
   Ks=0.5; % threshold
   
   % other parameters
   phiRmax=0.55;
   phi0=0.76*0.087;
   rho=0.76;
   kt=4.5;
   KE=1; %Michaelis constant uM
   KM=0;
   D=300; %um^2/s
   kd=D/10^8*3600; % motility hopping rate, converted to [h^-1]  
   w=0.9;
   e=8; % chemotactic efficiency (should really be 0.5)
   
   % use all carbon sources
   Kn1=calphaEkEmaxS*rho*S1/(KE+S1); % N value [h^{-1}]
   Kn2=calphaEkEmaxS*rho*S2/(KE+S2); % N value
   kn1=calphaEkEmaxs*rho*s1/(KE+s1); % N value [h^{-1}]
   kn2=calphaEkEmaxs*rho*s2/(KE+s2); % N value
       
   % individual growth rates
   L1=kt*Kn1*w/(kt+Kn1*w)*(phiRmax-phi0)/rho; % [h^(-1)]
   L2=kt*Kn2*w/(kt+Kn2*w)*(phiRmax-phi0)/rho;
   l1=kt*kn1*w/(kt+kn1*w)*(phiRmax-phi0)/rho; % [h^(-1)]
   l2=kt*kn2*w/(kt+kn2*w)*(phiRmax-phi0)/rho;
   
   % combined growth rate Eq. 7 in above paper
   lc=1.2; %/h fit
   lam1=(L1+l1-2*L1*l1/lc)/(1-L1*l1/lc^2);
   lam2=(L2+l2-2*L2*l2/lc)/(1-L2*l2/lc^2);
   
   % gradients for chemotaxis
   dS12=e*(S1-S2);
   Sbar=(S1+S2)/2;
   ds12=e*(s1-s2);
   sbar=(s1+s2+Ks)/2;
   
   % fraction of protein involved in chemotaxis or motility
   phip1=phiRmax-phi0; 
   phip2=phiRmax-phi0;
   
   lam0=1.03; %/h fit
   
   phic1=(1-w)*phip1;%*(1-lam1/lam0); % growth rate dependent chemotactic fraction
   phic2=(1-w)*phip2;%*(1-lam2/lam0);
   
   % WT
   dN1dt=lam1*N1+2*(phic2*N2-phic1*N1)*kd*(Sbar/(KM+Sbar)+sbar/(KM+sbar))+(phic2*N2+phic1*N1)*kd*(dS12/(KM+Sbar)+ds12/(KM+sbar));
   dN2dt=lam2*N2-2*(phic2*N2-phic1*N1)*kd*(Sbar/(KM+Sbar)+sbar/(KM+sbar))-(phic2*N2+phic1*N1)*kd*(dS12/(KM+Sbar)+ds12/(KM+sbar));
 
   % cheY
   dn1dt=lam1*n1+2*(phic2*n2-phic1*n1)*kd*(Sbar/(KM+Sbar)+sbar/(KM+sbar));
   dn2dt=lam2*n2-2*(phic2*n2-phic1*n1)*kd*(Sbar/(KM+Sbar)+sbar/(KM+sbar));

   % secondary nutrient
   ds2dt=betab-beta*L2*(N2+n2)*heaviside(s2)*sign(s2);
   
dydt=[dN1dt;dN2dt;dn1dt;dn2dt;ds2dt;0;0];
end

Fit_Fig2A_WTvsCheY_secretion_Nvalue

function fit2a()

   % data     
   D=xlsread('Data chemotaxis benefit mod.xlsx',1,'D46:L54');
   Lam=D(:,1); % exp growth rate
   WTpc=0.5*(D(:,3)+D(:,5)); % exp WT percentages
   Nval=D(:,9); % corresponding model N values

          %s2,  betac
   guess=[1, 2.5e-10];
   fit=fminsearch(@(par) chi2(par,Nval,WTpc),guess,optimset('MaxFunEvals',30))

   fit(2)*1e0 % to get full precision
   
   % run again with best fit parameters
   ratio=[];
   Nvalue=[];
   L1=[];
   
   i=1;
   
   for nval=0.1:0.01:0.6
   
        %                          N1 N2  n1 n2  s2   betac  Nvalue
        [t,y]=ode45(@model,[0 15],[1e3;0;1e3;0;fit(1);fit(2);nval]);
 
        % culture only
        WT=y(numel(t),1)+y(numel(t),2);
        cheY=y(numel(t),3)+y(numel(t),4);
        
        ratio(i)=100*WT/(cheY+WT);
        Nvalue(i)=nval;
        
        rho=0.76;
        w=0.9;
        phiRmax=0.55; 
        phi0=0.76*0.087;
        kt=4.5;
        calphaEkEmaxS=nval*5.8;
        Kn1=calphaEkEmaxS*rho; % N value [h^{-1}]
        l1=kt*Kn1*w/(kt+Kn1*w)*(phiRmax-phi0)/rho; %
        
        L1(i)=l1;
        i=i+1;
   
   end
   
   % plot best fit parameters
   plot(Lam,WTpc,'s',L1,ratio,'r--');
   xlabel('N value');
   ylabel('Percentage WT');
   title('WT vs \Delta{cheY} with metabolite secretion (fit for Fig. 2a)')
   
   filename = 'fit_Fig2a.xlsx';
   A = [L1' ratio'];
   xlswrite(filename,A)
   
end

function error=chi2(par,Nval,data)

   ratio=[];

   for i=1:numel(Nval) % Nvalue=sugar concentrationhere
        
        %                           N1 N2 n1 n2  s2   betac  Nvalue  
        [t,y]=ode45(@model,[0 15],[1e3;0;1e3;0;par(1);par(2);Nval(i)]); 
 
        % culture only
        WT=y(numel(t),1)+y(numel(t),2);
        cheY=y(numel(t),3)+y(numel(t),4);
        
        ratio(i)=100*WT/(cheY+WT);
        
        i=i+1;
   
   end
   
   error=sum((data-ratio').^2)
end

function dydt=model(t,y)

   N1=y(1);
   N2=y(2);
   n1=y(3);
   n2=y(4);
   s2=y(5);
   betac=y(6);
   NvalueS=y(7);
    
   % nutrient
   S1=20000; % mM and not uM
   S2=20000;
   s1=0;
   
   % primary crabon source
   calphaEkEmaxS=NvalueS*5.8;
   
   % secondary carbon source
   Nvalues=1;% N value for CA is growth rate [h^{-1}]
   calphaEkEmaxs=Nvalues*5.8;
   beta=2.5e-10; % uM
   Ks=0.5; % threshold
   
   % other parameters
   phiRmax=0.55;
   phi0=0.76*0.087;
   rho=0.76;
   kt=4.5;
   KE=1; %Michaelis constant uM
   KM=0;
   D=300; %um^2/s
   kd=D/10^8*3600; % motility hopping rate, converted to [h^-1]  
   w=0.9;
   e=8; % chemotactic efficiency (should really be 0.5)
   
   % use all carbon sources
   Kn1=calphaEkEmaxS*rho*S1/(KE+S1); % N value [h^{-1}]
   Kn2=calphaEkEmaxS*rho*S2/(KE+S2); % N value
   kn1=calphaEkEmaxs*rho*s1/(KE+s1); % N value [h^{-1}]
   kn2=calphaEkEmaxs*rho*s2/(KE+s2); % N value
       
   % individual growth rates
   L1=kt*Kn1*w/(kt+Kn1*w)*(phiRmax-phi0)/rho; % [h^(-1)]
   L2=kt*Kn2*w/(kt+Kn2*w)*(phiRmax-phi0)/rho;
   l1=kt*kn1*w/(kt+kn1*w)*(phiRmax-phi0)/rho; % [h^(-1)]
   l2=kt*kn2*w/(kt+kn2*w)*(phiRmax-phi0)/rho;
   
   % combined growth rate Eq. 7 in above paper
   lc=1.2; %/h fit
   lam1=(L1+l1-2*L1*l1/lc)/(1-L1*l1/lc^2);
   lam2=(L2+l2-2*L2*l2/lc)/(1-L2*l2/lc^2);
   
   % gradients for chemotaxis
   dS12=e*(S1-S2);
   Sbar=(S1+S2)/2;
   ds12=e*(s1-s2);
   sbar=(s1+s2+Ks)/2;
   
   % fraction of protein involved in chemotaxis or motility
   phip1=phiRmax-phi0; 
   phip2=phiRmax-phi0;
   
   lam0=1.03; %/h fit
   
   phic1=(1-w)*phip1;%*(1-lam1/lam0); % growth rate dependent chemotactic fraction
   phic2=(1-w)*phip2;%*(1-lam2/lam0);
   
   % WT
   dN1dt=lam1*N1+2*(phic2*N2-phic1*N1)*kd*(Sbar/(KM+Sbar)+sbar/(KM+sbar))+(phic2*N2+phic1*N1)*kd*(dS12/(KM+Sbar)+ds12/(KM+sbar));
   dN2dt=lam2*N2-2*(phic2*N2-phic1*N1)*kd*(Sbar/(KM+Sbar)+sbar/(KM+sbar))-(phic2*N2+phic1*N1)*kd*(dS12/(KM+Sbar)+ds12/(KM+sbar));
 
   % cheY
   dn1dt=lam1*n1+2*(phic2*n2-phic1*n1)*kd*(Sbar/(KM+Sbar)+sbar/(KM+sbar));
   dn2dt=lam2*n2-2*(phic2*n2-phic1*n1)*kd*(Sbar/(KM+Sbar)+sbar/(KM+sbar));

   % secondary nutrient
   ds2dt=betac*lc*(N1+N2+n1+n2)-beta*L2*(N2+n2)*heaviside(s2)*sign(s2);

dydt=[dN1dt;dN2dt;dn1dt;dn2dt;ds2dt;0;0];
end

Fit_FigS4d

function main()

D=xlsread('Data chemotaxis benefit.xlsx',1,'D89:G97')
lam1=D(:,1);
SDlam=D(:,2);
Dlam=D(:,3);
SDDlam=D(:,4);

%     lamC  lam2
guess=[1.16 1];
fit=fminsearch(@(par) chi2(par,lam1,Dlam),guess)

Lam1=0.2:0.1:1;
DLam=(Lam1+fit(2)-2*Lam1*fit(2)/fit(1))./(1-Lam1*fit(2)/fit(1)^2)-Lam1;

plot(lam1,Dlam,'s',Lam1,DLam,'k-')
xlim([0.3 1])
xlabel ('Growth rate \lambda');
ylabel ('Difference \Delta\lambda');

filename = 'fit_FigS5c.xlsx';
A = [Lam1' DLam']
xlswrite(filename,A)


function error=chi2(par,lam1,data)
   %lam2=1;
   model=(lam1+par(2)-2*lam1*par(2)/par(1))./(1-lam1*par(2)/par(1)^2)-lam1;
   error=sum((data-model).^2);
end