ptransmodelODE {magi}

Protein transduction model

Description

The protein transduction equations model a biochemical reaction involving a signaling protein that degrades over time. The system components X = (S, S_d, R, S_R, R_{pp}) represent the levels of signaling protein, its degraded form, inactive state of R, S-R complex, and activated state of R.

S, S_d, R, S_R and R_{pp} are governed by the following differential equations:

\frac{dS}{dt} = -k_1 \cdot S -k_2 \cdot S \cdot R + k_3 \cdot S_R

\frac{dS_d}{dt} = k_1 \cdot S

\frac{dR}{dt} = -k_2 \cdot S \cdot R + k_3 \cdot S_R + \frac{V \cdot R_{pp}}{K_m + R_{pp}}

\frac{dS_R}{dt} = k_2 \cdot S \cdot R - k_3 \cdot S_R - k_4 \cdot S_R

\frac{dR_{pp}}{dt} = k_4 \cdot S_R - \frac{V \cdot R_{pp}}{K_m + R_{pp}}

where \theta = (k_1, k_2, k_3,k_4, V, K_m) are system parameters.

Usage

ptransmodelODE(theta, x, tvec)

ptransmodelDx(theta, x, tvec)

ptransmodelDtheta(theta, x, tvec)

Arguments

theta

vector of parameters.

x

matrix of system states (one per column) at the time points in tvec.

tvec

vector of time points

Value

ptransmodelODE returns an array with the values of the derivatives \dot{X}.

ptransmodelDx returns a 3-D array with the values of the gradients with respect to X.

ptransmodelDtheta returns a 3-D array with the values of the gradients with respect to \theta.

References

Vyshemirsky, V., & Girolami, M. A. (2008). Bayesian Ranking of Biochemical System Models. Bioinformatics, 24(6), 833-839.

Examples

theta <- c(0.07, 0.6, 0.05, 0.3, 0.017, 0.3)
x <- matrix(1:25, nrow = 5, ncol = 5)
tvec <- 1:5

ptransmodelODE(theta, x, tvec)