Solving Differential Equations in Computational Biology using Maple, Slides of Biology

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Computational Biology, Part 18

Biochemical Kinetics IV

Robert F. Murphy

Solving a single differential

equation using Maple

 (Define the differential equation dy/dx=6x+2 using the diff operator, assigning the equation to the name deq1 )

 (Integrate analytically using dsolve )

 (Integrate using boundary condition y(0)=5 )

 (Integrate using boundary condition y(0)=a )

 (Integrate dy/dx=bx+c analytically)

 (Integrate using boundary condition y(0)=a )

Solving a set of differential

equations numerically using

Maple

 (Define the differential equations for the enzyme catalyzed reaction discussed in Part 15 )

Solving a set of differential

equations numerically using

Maple

 (Plot the solutions using odeplot )

 (Plot the phase planes using odeplot )

Other systems for exploration

 The following slides describe two additional biochemical systems that can be modeled by simple modifications of the model already developed.

Biochemical System 2

 Reversable catalysis.

E  S

k 1   k  1

C

k 2   k  2

E  P

Biochemical System 3

 Catalytic byproduct.

E  S

k 1   k  1

B  C

C

k 2   k  2

E  P

Biochemical System 3

dE dt

  k 1 ES   k  1  k 2  BC

dS dt

  k 1 ES  k  1 BC

dC dt

 k 1 ES  k  2 EP   k  1  k 2  BC

dP dt

 k 2 C  k  2 EP