<simulation>
<header>
<title lang="french">Cinétique de croissance de Graef-Andrews</title>
<title lang="english">Graef-Andrews's growth kinetics</title>
<title lang="spanish">Cinética de crecimiento de Graef-Andrews</title>
<author>Pauss André, Mottelet Stéphane, Sarrazin Catherine, Guillaume Barbaud</author>
<date>August 24th, 2005</date>
<keywords>simulation,scilab,xml</keywords>
<keywords lang="spanish">Simulación, Scilab, XML</keywords>
<image href="graef-andrews.gif" />
</header>
<parameters><section>
<title lang="french">Paramètres cinétiques et de rendement</title>
<title lang="english">Kinetics and yield parameters</title>
<title lang="spanish">Parámetros cinéticos y de rendimiento</title>
<scalar increment="0.05" label="muMax" max="1" min="0.001" scale="1" state="normal" unit="h-1"><name lang="french">Mumax (h-1)</name><name lang="english">Mumax (h-1)</name><name lang="spanish">Mumax (h-l)</name><notes lang="french">
<p>Taux de croissance maximale</p>
</notes><notes lang="english">
<p>Maximal growth rate</p>
</notes><notes lang="spanish">
<p>Tasa de crecimiento máximo</p>
</notes><value>0.3</value></scalar>
<scalar increment="0.1" label="Ks" max="10" min="0.1" scale="1" state="normal" unit="g / L"><name lang="french">Ks (g / L)</name><name lang="english">Ks (g / L)</name><name lang="spanish">Ks (g / L)</name><notes lang="french">
<p>Constante de saturation</p>
</notes><notes lang="english">
<p>Saturation constant</p>
</notes><notes lang="spanish">
<p>Constante de saturación</p>
</notes><value>2</value></scalar>
<scalar increment="0.5" label="Ki" max="100" min="0.1" scale="1" state="normal" unit="g / L"><name lang="french">Ki (g / L)</name><name lang="english">Ki (g / L)</name><name lang="spanish">Ki (g / L)</name><notes lang="french">
<p>Constante de saturation</p>
</notes><notes lang="english">
<p>Saturation constant</p>
</notes><notes lang="spanish">
<p>Constante de saturación</p>
</notes><value>20</value></scalar>
<scalar increment="0.02" label="kd" max="0.5" min="0"><name lang="french">kd (h-1)</name><name lang="english">kd (h-1)</name><name lang="spanish">kd (h-l)</name><notes lang="french">
<p>Constante de mortalité</p>
</notes><notes lang="english">
<p>Decay constant</p>
</notes><notes lang="spanish">
<p>Constante de mortalidad</p>
</notes><value>0</value></scalar>
<scalar increment="0.05" label="YF" max="1" min="0.001" scale="1" state="normal"><name lang="french">Y X/S</name><name lang="english">Y X/S</name><name lang="spanish">Y X/S</name><notes lang="french">
<p>Rendement de croissance, masse de cellule par masse de
substrat</p>
</notes><notes lang="english">
<p>Yield factor, gram of produced cell per gram of consumed
substrate</p>
</notes><notes lang="spanish">
<p>Rendimiento de crecimiento, masa de célula por masa de sustrato</p>
</notes><value>0.45</value></scalar>
</section><section>
<title lang="french">Concentrations initiales</title>
<title lang="english">Initial concentrations</title>
<title lang="spanish">Concentraciones iníciales</title>
<scalar increment="0.1" label="x0" max="5" min="0.001" scale="1" state="normal" unit="g / L"><name lang="french">Xo (g / L)</name><name lang="english">Xo (g / L)</name><name lang="spanish">Xo (g / L)</name><notes lang="french">
<p>Concentration initiale de microorganisme</p>
</notes><notes lang="english">
<p>Initial concentration of cells</p>
</notes><notes lang="spanish">
<p>Concentración inicial de microorganismo</p>
</notes><value>0.15</value></scalar>
<scalar increment="1" label="s0" max="100" min="0.001" scale="1" state="normal" unit="g / L"><name lang="french">So (g / L)</name><name lang="english">So (g / L)</name><name lang="spanish">So (g / L)</name><notes lang="french">
<p>Concentration initiale de substrat</p>
</notes><notes lang="english">
<p>Initial concentration of substrate</p>
</notes><notes lang="spanish">
<p>Concentración inicial de sustrato</p>
</notes><value>25</value></scalar>
</section><section>
<title lang="french">Paramètres de simulation</title>
<title lang="english">Simulation parameters</title>
<title lang="spanish">Parámetros de simulación</title>
<scalar increment="1" label="tf" max="200" min="0.001" scale="1" state="normal" unit="h"><name lang="french">Temps final (h)</name><name lang="english">Final time (h)</name><name lang="spanish">Tiempo final (h)</name><value>50</value></scalar>
<scalar increment="50" label="simulation_step" max="1000" min="100"><name lang="french">Nombre de pas de simulation</name><name lang="english">Number of steps for simulation</name><name lang="spanish">Numero de pasos de simulación</name><value>200</value></scalar>
</section><section>
<title lang="french">Points expérimentaux</title>
<title lang="english">Experimental data</title>
<title lang="spanish">Puntos experimentales</title>
<matrix clear="yes" cols="2" label="user_curve_mat" load="yes" rows="64" save="yes" stripcol="no" striprow="yes" widget="normal">
<name />
<name lang="spanish" />
<col>
<name lang="french">Temps (h)</name>
<name lang="english">Time (h)</name>
<name lang="spanish">Tiempo (h)</name>
<value>0</value>
</col>
<col>
<name lang="french">Concentration (g/L)</name>
<name lang="english">Concentration (g/L)</name>
<name lang="spanish">Concentración (g/L)</name>
<value>0</value>
</col>
</matrix>
</section></parameters>
<compute>
<defdomain1d label="t" unit="h">
<name lang="french">Temps</name>
<name lang="english">Time</name>
<name lang="spanish">Tiempo</name>
<interval discretization="linear" steps="simulation_step">
<initialvalue>0</initialvalue>
<finalvalue>tf</finalvalue>
</interval>
</defdomain1d>
<ode label="monod">
<refdomain1d ref="t" />
<states>
<state label="x" size="1" unit="g / L">
<name lang="french">Concentration en microorganisme</name>
<name lang="english">Cell concentration</name>
<name lang="spanish">Concentración en microorganismo</name>
<derivative>(muMax * s *x / (s+Ks+(s*s/(Ki+%eps)))) - kd *
x</derivative>
<initialcondition>x0</initialcondition>
</state>
<state label="s" size="1">
<name lang="french">Concentration en substrat</name>
<name lang="english">Substrate concentration</name>
<name lang="spanish">Concentración en sustrato</name>
<derivative>- ((muMax * s *x / (s+Ks+(s*s/(Ki+%eps)))) - kd * x) /
(YF+%eps)</derivative>
<initialcondition>s0</initialcondition>
</state>
</states>
<outputs>
<output label="mu">
<name lang="french">mu</name>
<name lang="english">mu</name>
<name lang="spanish">mu</name>
<value>muMax*s./(s+Ks+(s.*s./(Ki+%eps)))</value>
</output>
</outputs>
</ode>
</compute>
<graphs>
<parametriccurve2d label="mu_function_of_s">
<name lang="french">mu en fonction de S</name>
<name lang="english">mu as a function of S</name>
<name lang="spanish">mu en función de S</name>
<x1>
<name lang="french">S (g/L)</name>
<name lang="english">S (g/L)</name>
<name lang="spanish">S (g/L)</name>
<value>s</value>
</x1>
<x2>
<name lang="french">mu (h-1)</name>
<name lang="english">mu (h-1)</name>
<name lang="spanish">mu (h-l)</name>
<value>mu</value>
</x2>
</parametriccurve2d>
<parametriccurve2d label="user_curve">
<name lang="french">Points expérimentaux</name>
<name lang="english">Experimental data</name>
<name lang="spanish">Puntos experimentales</name>
<x1>
<value>user_curve_mat(:,1)</value>
</x1>
<x2>
<value>user_curve_mat(:,2)</value>
</x2>
</parametriccurve2d>
</graphs>
<display>
<window splitx="2">
<title lang="french">Résultats</title>
<title lang="english">Results</title>
<title lang="spanish">Resultados</title>
<axis2d xmax="tf" xmin="0" ymax="1.1*s0" ymin="0">
<drawcurve2d color="red" ref="x" thickness="1" />
<drawcurve2d color="green" ref="s" thickness="1" />
<drawcurve2d linetype="solid" marker="plus" ref="user_curve" />
</axis2d>
<axis2d xmax="1.2*s0" xmin="0" ymax="1.2*muMax" ymin="0">
<drawcurve2d ref="mu_function_of_s" />
</axis2d>
</window>
</display>
<save>
<file href="monod_results" labels="muMax Ks Ki YF kd t s x mu" />
</save>
</simulation>