In[ ]:= params = {μ mGlucose → 0.662, μ mXylose → 0.190, ν mGlucose → 2.005, ν mXylose → 0.250, KsGlucose → 0.565, KsXylose → 3.400, KiGlucose → 283.7, KiXylose → 18.1, PmGlucose → 129.9, PmXylose → 59.04, β → 1.29, γ → 1.42 } ; μ Glucose [ S _] : = μ mGlucose ***** S   KsGlucose + S + S ^ 2  KiGlucose  /. params μ Xylose [ S _] : = μ mXylose ***** S   KsXylose + S + S ^ 2  KiXylose  /. params ν Glucose [ S _] : = ν mGlucose ***** S   KsGlucose + S + S ^ 2  KiGlucose  /. params ν Xylose [ S _] : = ν mXylose ***** S   KsXylose + S + S ^ 2  KiXylose  /. params μ Inhibition [ Ethanol _ , μ 0 _ , Pm _ , β_] : = μ 0 *** ** 1 -  Ethanol  Pm  ^ β ν Inhibition [ Ethanol _ , ν 0 _ , Pm _ , γ_] : = ν 0 *** ** 1 -  Ethanol  Pm  ^ γ fermentationEquations = { glucose ' [ t ] ⩵ - μ Glucose [ glucose [ t **]] *** cells [ t ] , xylose ' [ t ] ⩵ - μ Xylose [ xylose [ t **]] *** cells [ t ] , ethanol ' [ t ] ⩵ ν Glucose [ glucose [ t **]] *** cells [ t ] + ν Xylose [ xylose [ t **]] *** cells [ t ] , cells ' [ t ] ⩵ μ Glucose [ glucose [ t **]] *** cells [ t ] + μ Xylose [ xylose [ t **]] *** cells [ t ]} ; initialConditions = { glucose [ 0 ] ⩵ 50, xylose [ 0 ] ⩵ 50, ethanol [ 0 ] ⩵ 0, cells [ 0 ] ⩵ 0.1 } ; solution = resolve numéricamente equação diferencial

NDSolve [{ fermentationEquations, initialConditions } ,

{ glucose, xylose, ethanol, cells } , { t, 0, 48 }] ;

gráf⋯

Plot [ calcula

Evaluate [{ glucose [ t ] , xylose [ t ] , ethanol [ t ] , cells [ t ]} /. solution ] , { t, 0, 48 } ,

etiquetas de representação

PlotLabels → { "Glucose ( g / L ) ", "Xylose ( g / L ) ", "Ethanol ( g / L ) ", " lista de células

Cells ( g / L ) " } ,

legenda do gráfico

PlotLegends → "Expressions", legenda dos eixos

AxesLabel → { "Time ( hours ) ", "Concentration ( g / L ) " }]

Out[ ]=

Glucose (g/L)

Xylose (g/L)

Ethanol (g/L)

Cells (g/L)

10 20 30 40 Time^ (hours)

50

100

150

200

Concentration (g/L)

InterpolatingFunction Domain Output

In[ ]:= (* Parameters for the kinetic model ) params = ( Maximum specific growth rate and Monod constants )μ max → 0.313, ( 1  h ) Ks → 47.51, ( g / L )( Substrate and product inhibition constants ) KIS → 308.13, ( g / L ) KIP → 299.67, ( g / L ) KSP → 28.39, ( g / L ) ( Maximum ethanol concentrations for growth and production ) PXmax → 83.35, ( g / L ) PPmax → 107.79, ( g / L )( Maximum specific ethanol production rate ) qmax → 3.69, ( g / g  h )( Yields and maintenance coefficients ) YXS → 0.48, ( g / g ) YPS → 0.50, ( g / g ) m → 0.001 ( 1  h *) ;

(* Define the specific growth rate function  modified Monod ) μ[* S _ , PE _] : = μ max S    Ks + S + S ^ 2  KIS   1 - ( PE / PXmax ) ^ 1.53  /. params;

(* Define the ethanol production rate function  Andrew - Levenspiel )* qP [ S _ , PE _] : =  qmax S    KSP + S + S ^ 2  KIP   1 - ( PE / PPmax ) ^ 1.53  /. params;

(* Define the system of differential equations ) eqs = ( Substrate  S  consumption ) S ' [ t ] ⩵ -  1  YXS  X [ t ] μ[ S [ t ] , PE [ t ]] +  1  YPS  X [ t ] qP [ S [ t ] , PE [ t ]] + m X [ t ] /. params, ( célula

Cell growth ( X ))* X ' [ t ] ⩵ X [ t ] μ[ S [ t ] , PE [ t ]] ,

(* Ethanol production ( PE ))* PE ' [ t ] ⩵ X [ t ] qP [ S [ t ] , PE [ t ]] ;

(* Initial conditions for substrate  S  ,cell mass ( X ) ,and ethanol ( PE ))* initConditions = { S [ 0 ] ⩵ 225, (* g / L initial sugar concentration ) X [ 0 ] ⩵ 0.01, ( g / L initial cell concentration ) PE [ 0 ] ⩵ 0 ( g / L initial ethanol concentration *)} ;

resolve

Solve the system of differential equations over time  0 to 100 hours )*

solution = resolve numéricamente equação diferencial

NDSolve [{ eqs, initConditions } , { S, X, PE } , { t, 0, 100 }] ;

gráfico

Plot the results:Substrate, lista de células

Cells,and Ethanol over time *)

gráf⋯

Plot [ calcula

Evaluate [{ S [ t ] , X [ t ] , PE [ t ]} /. solution ] , { t, 0, 100 } ,

etiquetas de representação

PlotLabels → { "Substrate ( g / L ) ", " lista de células

Cells ( g / L ) ", "Ethanol ( g / L ) " } ,

legenda do gráfico

PlotLegends → "Expressions", legenda dos eixos

AxesLabel → { "Time ( hours ) ", "Concentration ( g / L ) " } ,

estilo do gráfico

PlotStyle → { azul

Blue, ve⋯

Red, verde

Green }]

2 Cinetica Bioquimica ART 1-2.nb