<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>