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Model Mathematics

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Component: environment

Component: T2

\frac{d}{d time} (T2) = k_5 LT2 + k_1 Bp T3 + ky T2p (Y0 - Yp) + kb T2p (B0 - Bp) - (k5 L T2 + k8 T2 + Vmax \frac{T2}{KR + T2})

KR = \frac{k1a + k1c}{k1b}

Vmax = k1c (R + T2R)

Component: T3

\frac{d}{d time} (T3) = k_6 LT3 + k_2 Bp T4 + ky T3p (Y0 - Yp) + kb T3p (B0 - Bp) - (k6 L T3 + k9 T3 + Vmax \frac{T3}{KR + T3})

KR = \frac{k2a + k2c}{k2b}

Vmax = k2c (R + T3R)

Component: T4

\frac{d}{d time} (T4) = k_7 LT4 + ky T4p (Y0 - Yp) + kb T4p (B0 - Bp) - (k7 L T4 + k10 T4)

Component: T2p

\frac{d}{d time} (T2p) = k_5 LT2p + k_1 Bp T3p + ky T2 (Y0 - Yp) + kb T2 (B0 - Bp) - (k5 L T2p + k8 T2p + Vmax \frac{T2p}{KR + T2p})

KR = \frac{k1a + k1c}{k1b}

Vmax = k1c (R + T2pR)

Component: T3p

\frac{d}{d time} (T3p) = k_6 LT3p + k_2 Bp T4p + ky T3 (Y0 - Yp) + kb T3 (B0 - Bp) - (k6 L T3p + k9 T3p + Vmax \frac{T3p}{KR + T3p})

KR = \frac{k2a + k2c}{k2b}

Vmax = k2c (R + T3pR)

Component: T4p

\frac{d}{d time} (T4p) = k_7 LT4p + ky T4 (Y0 - Yp) + kb T4 (B0 - Bp) - (k7 L T4p + k10 T4p)

Component: LT2

\frac{d}{d time} (LT2) = k_5 T2 + k_3 Bp LT3 + ky LT2p (Y0 - Yp) + kb LT2p (B0 - Bp) - (k5 L LT2 + k11 LT2 + Vmax \frac{LT2}{KR + LT2})

KR = \frac{k3a + k3c}{k3b}

Vmax = k3c (R + LT2R)

Component: LT3

\frac{d}{d time} (LT3) = k_6 T3 + k_4 Bp LT4 + ky LT3p (Y0 - Yp) + kb LT3p (B0 - Bp) - (k6 L LT3 + k12 LT3 + Vmax \frac{LT3}{KR + LT3})

KR = \frac{k4a + k4c}{k4b}

Vmax = k4c (R + LT3R)

Component: LT4

\frac{d}{d time} (LT4) = k_7 T4 + ky LT4p (Y0 - Yp) + kb LT4p (B0 - Bp) - (k7 L LT4 + k13 LT4)

Component: LT2p

\frac{d}{d time} (LT2p) = k_5 T2p + k_3 Bp LT3p + ky LT2 (Y0 - Yp) + kb LT2 (B0 - Bp) - (k5 L LT2p + k11 LT2p + Vmax \frac{LT2p}{KR + LT2p})

KR = \frac{k3a + k3c}{k3b}

Vmax = k3c (R + LT2pR)

Component: LT3p

\frac{d}{d time} (LT3p) = k_6 T3p + k_4 Bp LT4p + ky LT3 (Y0 - Yp) + kb LT3 (B0 - Bp) - (k6 L LT3p + k12 LT3p + Vmax \frac{LT3p}{KR + LT3p})

KR = \frac{k4a + k4c}{k4b}

Vmax = k4c (R + LT3pR)

Component: LT4p

\frac{d}{d time} (LT4p) = k_7 T4p + ky LT4p (Y0 - Yp) + kb LT4p (B0 - Bp) - (k7 L LT4p + k13 LT4p)

Component: Yp

\frac{d}{d time} (Yp) = ky P (Y0 - Yp) - (k_y Z Yp)

Component: Bp

\frac{d}{d time} (Bp) = kb P (B0 - Bp) - (k_b Bp)

Component: P

P = T2p + LT2p + T3p + LT3p + T4p + LT4p

Component: T2R

\frac{d}{d time} (T2R) = k1b T2 R - (k1a T2R + k1c T2R)

Component: T3R

\frac{d}{d time} (T3R) = k2b T3 R - (k2a T3R + k2c T3R)

Component: T2pR

\frac{d}{d time} (T2pR) = k1b T2p R - (k1a T2pR + k1c T2pR)

Component: T3pR

\frac{d}{d time} (T3pR) = k2b T3p R - (k2a T3pR + k2c T3pR)

Component: LT2R

\frac{d}{d time} (LT2R) = k3b LT2 R - (k3a LT2R + k3c LT2R)

Component: LT3R

\frac{d}{d time} (LT3R) = k4b LT3 R - (k4a LT3R + k4c LT3R)

Component: LT2pR

\frac{d}{d time} (LT2pR) = k3b LT2p R - (k3a LT2pR + k3c LT2pR)

Component: LT3pR

\frac{d}{d time} (LT3pR) = k4b LT3p R - (k4a LT3pR + k4c LT3pR)

Component: L

Component: R

Component: Z

Component: Y0

Component: B0

Component: model_parameters

Source: Derived from workspace Spiro, Parkinson, Othmer, 1997 at changeset 690303203f54.

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A model of excitation and adaptation in bacterial chemotaxis