example.html

Cellerator Examples

This page provides an examples of how a Cellerator Notebook looks, translated into html format, so that Mathematica is not required. It demonstrates several reaction to differential equation translations, a time course prediction, and an input-output relation

Creation, Annihilation, and Conversion Reactions

${{A^′[t] k1 - k2 A[t], B^′[t] k2 A[t] - k3 B[t], P^′[t] &# ... 004 Q[t] - k003 R[t] S[t], S^′[t] k004 Q[t] - k003 R[t] S[t]}, {A, B, P, Q, R, S}}$

Rate constants are automatically generated when they are omitted:

Unidirectional Catalytic Reaction with intermediate complex formation

e+S→$S$e$

$S$e$→e+S

$S$e$→e+P

e+P→$S$e$

The following arrow is slightly different:

e+S→$S$e$

$S$e$→e+S

$S$e$→$P$e$

$P$e$→$S$e$

$P$e$→e+P

e+P→$P$e$

${{e^′[t]  -a e[t] S[t] + d $S$e$[t] + k $S$e$[t], P^′[t] k $S$e$ ... + d $S$e$[t], $S$e$^′[t] a e[t] S[t] - d $S$e$[t] - k $S$e$[t]}, {e, P, S, $S$e$}}$

${{e^′[t]  -a e[t] S[t] + d $S$e$[t], P^′[t] 0, S^′[t] > ... e$[t], $S$e$^′[t] a e[t] S[t] - d $S$e$[t] - k $S$e$[t]}, {e, P, S, $P$e$, $S$e$}}$

Bidirectional Catalytic Reaction with intermediate complex formation

Ef+S→SEf

SEf→Ef+S

SEf→Ef+P

Ef+P→SEf

Er+P→PEr

PEr→Er+P

PEr→Er+S

Er+S→PEr

interpret[{{Underoverscript[S⇄P, Er, arg3], af, df, kf, ar, dr, kr}}]

${{Ef^′[t]  -af Ef[t] S[t] + df SEf[t] + kf SEf[t], Er^′[t]  -ar ... SEf[t], SEf^′[t] af Ef[t] S[t] - df SEf[t] - kf SEf[t]}, {Ef, Er, P, PEr, S, SEf}}$

Catalytic Reaction without intermediate complex formation

A+C→B+C

${{A^′[t]  -k A[t] C[t], B^′[t] k A[t] C[t], C^′[t] 0}, {A, B, C}}$

Catalytic Reaction - Michaelis Menten

${{A^′[t]  -(Kd A[t] e[t])/(v + A[t]), B^′[t]  (Kd A[t] e[t])/(v + A[t]), e^′[t] 0}, {A, B, e}}$

${{A^′[t]  -(Kd A[t])/(v + A[t]), B^′[t]  (Kd A[t])/(v + A[t])}, {A, B}}$

${{A^′[t]  -(k A[t] e[t])/((d + k)/a + A[t]), B^′[t]  (k A[t] e[t])/((d + k)/a + A[t]), e^′[t] 0}, {A, B, e}}$

interpret[{{Underoverscript[A⟺B, Er, arg3], MM[{vf, Kf}, {vr, Kr}]}}]

${{A^′[t]  -(Kf A[t] Ef[t])/(vf + A[t]) + (Kr B[t] Er[t])/(vr + B[t]), B^′ ... (Kr B[t] Er[t])/(vr + B[t]), Ef^′[t] 0, Er^′[t] 0}, {A, B, Ef, Er}}$

Catalytic Reaction - Hill function

interpret[{{Overscript[A↦B, C], vmax V, nhill n, khalf K}}]

${{A^′[t]  -(V A[t]^n C[t])/(K^n + A[t]^n), B^′[t]  (V A[t]^n C[t])/(K^n + A[t]^n), C^′[t] 0}, {A, B, C}}$

interpret[{{Overscript[A↦∅, C], vmax V, nhill n, khalf K}}]

${{A^′[t]  -(V A[t]^n C[t])/(K^n + A[t]^n), C^′[t] 0}, {A, C}}$

Annihilation by Hill Function

interpret[{{Overscript[A↦∅, ∅], vmax V, nhill n, khalf K}}]

${{A^′[t]  -(V A[t]^n)/(K^n + A[t]^n)}, {A}}$

S-System

interpret[{ {va↦v1, SSystem[taua1, kp, km, ca1p, ca1m]}, {vb↦v1, SSystem ... b1, kp3, km3, cp3, cm3]},  {vb↦v2, SSystem[tau2, kp2, km2, cb2p, cb2m]} }]

${{v1^′[t]  (-km va[t]^ca1m vb[t]^cb1m vc[t]^cm3 + kp va[t]^ca1p vb[t]^cb1p vc[ ... a^′[t] 0, vb^′[t] 0, vc^′[t] 0}, {v1, v2, va, vb, vc}}$

Diffusion

interpret[{{AB + C, k}, {A▽, dA}, {B▽, dB * DiagonalMatrix[{dB1, dB2, dB3}]}, {C▽, Array[dC, {3, 3}]} }]

${{A^(1, 0, 0, 0)[t, x, y, z]  -k A[t, x, y, z] + dA A^(0, 0, 0, 2)[t, x, y, z] + dA ... , y, z] + dC[2, 1] C^(0, 1, 1, 0)[t, x, y, z] + dC[1, 1] C^(0, 2, 0, 0)[t, x, y, z]}, {A, B, C}}$