Bacterial coexistence driven by motility and spatial competition-模型代码

一、说明

本文主要对文献《Bacterial coexistence driven by motility and spatial competition》使用的代码模型进行注释分享。
- [1] Gude S , Pine E , Taute K M , et al. Bacterial coexistence driven by motility and spatial competition[J]. Nature, 2020.
代码来源于向原作者邮件获取。

二、模型简介

文章中的模型采用空间扩散和Mond结合建立描述大肠杆菌在固体平面的竞争关系。
-运行环境 matlab 2020b

三、模型建立过程

待续
∂p1∂t=r−1∂∂r(rnK+n(D1∂p1∂r−χ1p1∂n∂r))+ln2nK+nμ1p1\frac{\partial {p}_{1}}{\partial t}={r}^{-1}\frac{\partial }{\partial r}\left(r\frac{n}{K+n}\left({D}_{1}\frac{\partial {p}_{1}}{\partial r}-{\chi }_{1}{p}_{1}\frac{\partial n}{\partial r}\right)\right)+\,\mathrm{ln}\,2\frac{n}{K+n}{\mu }_{1}{p}_{1} ∂t∂p1=r−1∂r∂(rK+nn(D1∂r∂p1−χ1p1∂r∂n))+ln2K+nnμ1p1
∂p1∂t=r−1∂∂r(rnK+n(D1∂p1∂r−χ1p1∂n∂r))+ln2nK+nμ1p1\frac{\partial {p}_{1}}{\partial t}={r}^{-1}\frac{\partial }{\partial r}\left(r\frac{n}{K+n}\left({D}_{1}\frac{\partial {p}_{1}}{\partial r}-{\chi }_{1}{p}_{1}\frac{\partial n}{\partial r}\right)\right)+\,\mathrm{ln}\,2\frac{n}{K+n}{\mu }_{1}{p}_{1} ∂t∂p1=r−1∂r∂(rK+nn(D1∂r∂p1−χ1p1∂r∂n))+ln2K+nnμ1p1
∂n∂t=r−1∂∂r(rDn∂n∂r)−ln2nK+n(μ1p1+μ2p2)\frac{\partial n}{\partial t}={r}^{-1}\frac{\partial }{\partial r}\left(r{D}_{n}\frac{\partial n}{\partial r}\right)-\,\mathrm{ln}\,2\frac{n}{K+n}({\mu }_{1}{p}_{1}+{\mu }_{2}{p}_{2}) ∂t∂n=r−1∂r∂(rDn∂r∂n)−ln2K+nn(μ1p1+μ2p2)

四、源码

主函数

%% define parameters
growthRates = [0.404; 0.47]; % db/h
kMonods = [1e-3; 1e-3]; % a.u.
diffusionCoefficients = [0.02; 0.02; 1.8]; % mm^2/h
chis = [0.875; 0.0]; % mm^2/(h a.u.)
lambdas = [10; 10]; % 1/mm
plateauWidths = [1.0; 1.0]; % mm
uMaxs = [0.5e-3; 0.5e-3; 1e0]; % a.u.xmesh = 0:0.1:17.5; % mm
tspan = 0:0.01:4*24; % hoursspeciesNames = {'A', 'B', 'Nutrient'};%% numerically solve system
solution = competition(growthRates, kMonods, diffusionCoefficients, chis, lambdas, uMaxs, plateauWidths, xmesh, tspan);%% display final population ratio and change in population ratio
disp(strcat('Final Ratio (B/A)=', num2str((sum(solution(end,:,2).*xmesh) ./ sum(solution(end,:,1).*xmesh)))));
disp(strcat('Change Ratio =', num2str((sum(solution(end,:,2).*xmesh) ./ sum(solution(end,:,1).*xmesh)) ./ (sum(solution(1,:,2).*xmesh) ./ sum(solution(1,:,1).*xmesh)))));%% visualize solution (A, B and nutrient)
for i=1:size(solution,3)% figure dimensionsh_fig = figure;set(h_fig, 'PaperUnits','centimeters');set(h_fig, 'PaperPosition', [0 0 4.5 4.5]);% actual plottingimagesc(solution(:,:,i)');% axis, labels, ...set(gca, 'FontSize', 9);title(speciesNames{i});xlabel('Time [d]');ylabel('Expansion [mm]');set(gca, 'XTick', 0:2400:length(tspan));set(gca, 'XTickLabel', tspan(1):1:tspan(end)/24);set(gca, 'YTick', 1:50:2001);set(gca, 'YTickLabel', 0:5:200);set(gca,'YDir','normal');axis([1 length(tspan) 1 length(xmesh)]);caxis([0 4.25]);colormap(h_fig, 'jet');%print(h_fig, '-depsc2', strcat('TODO', speciesNames{i}, '.eps'));
end% report amount of nutrients left over at the end of the simulation
disp(strcat('Fraction of nutrients present at the end:', num2str(calculateTotalAmount(solution(end,:,3), xmesh) / calculateTotalAmount(solution(1,:,3), xmesh)), 'a.u.'));
clear

模型方程

function solution = competition( growthRates, kMonods, diffusionCoefficients, chis, lambdas, uMaxs, plateauWidths, xmesh, tspan )% symmetry of the systemm = 1;% numerically solve pdessolution = pdepe(m, @(x,t,u,DuDx)pdefun(x,t,u,DuDx,growthRates,kMonods,diffusionCoefficients,chis), @(x)icfun(x,lambdas,uMaxs,plateauWidths), @bcfun, xmesh, tspan);
end%% Keller-Segel model and diffusion + consumption of nutrient
function [c,f,s] = pdefun(x,t,u,DuDx,growthRates,kMonods,diffusionCoefficients,chis)c = [1; 1; 1];f = [(u(3)./(kMonods(1)+u(3))).*(diffusionCoefficients(1) .* DuDx(1) - chis(1) .* u(1) .* DuDx(3)); (u(3)./(kMonods(2)+u(3))).*(diffusionCoefficients(2) .* DuDx(2) - chis(2) .* u(2) .* DuDx(3)); diffusionCoefficients(3) .* DuDx(3)];s = [(u(3)./(kMonods(1)+u(3))).*log(2).*growthRates(1).*u(1); (u(3)./(kMonods(2)+u(3))).*log(2).*growthRates(2).*u(2); -(log(2).*growthRates(1).*u(1).*(u(3)./(kMonods(1)+u(3))) + log(2).*growthRates(2).*u(2).*(u(3)./(kMonods(2)+u(3))))];
end%% exponentially decaying initial profile
function u0 = icfun(x, lambdas, uMaxs, plateauWidths)u0 = [uMaxs(1).*exp(-lambdas(1).*(x-plateauWidths(1))); uMaxs(2).*exp(-lambdas(2).*(x-plateauWidths(2))); uMaxs(3).*ones(size(x))];u0(1, 1:find(x<=plateauWidths(1), 1, 'last')) = uMaxs(1);u0(2, 1:find(x<=plateauWidths(2), 1, 'last')) = uMaxs(2);
end%% no flux boundary contitions on both sides
function [pl,ql,pr,qr] = bcfun(xl,ul,xr,ur,t)pl = [0; 0; 0];ql = [1; 1; 1];pr = [0; 0; 0];qr = [1; 1; 1];
end

其他

function totalAmount = calculateTotalAmount( u , xmesh )totalAmount = u * xmesh';end

五、文献解读

待续

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文献--Bacterial coexistence driven by motility and spatial competition-模型代码

Bacterial coexistence driven by motility and spatial competition-模型代码

一、说明

二、模型简介

三、模型建立过程

四、源码

五、文献解读

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