Stochastic Signalling of G‑protein Coupled Receptors Model

Available identifiers

MaRDI QIDQ6771923

signalling pathway model from receptor activation over the G-protein cycle to the calcium channel inhibition

List of mathematical expressions with quantities

Receptor–Ligand Complex Creation	$f_1=k_1\cdot x_L\cdot x_R$
$k_1$ symbol represents Reaction Constant for Receptor-Ligand Complex Creation
$x_R$ symbol represents Number of Receptor Molecules
$x_L$ symbol represents Number of Ligand Molecules
$f_1$ symbol represents Propensity of Receptor-Ligand Complex Creation
Dissociation into α- and βγ-subunits	$f_2=k_2\cdot x_{RL}\cdot x_{\alpha \text{GDP}\beta \gamma }$
$k_2$ symbol represents Reaction Constant for Dissociation into α- and βγ-subunits
$x_{RL}$ symbol represents Number of Receptor-Ligand Complex Molecules
$x_{{\alpha }_{GDP}\beta \gamma }$ symbol represents Number of G-protein Molecules
$f_2$ symbol represents Propensity of Dissociation into α- and βγ-subunits
Hydrolysis of GTP	$f_3=k_3\cdot x_{\alpha \text{GTP}}$
$k_3$ symbol represents Reaction Constant for Hydrolysis of GTP
$x_{{\alpha }_{GTP}}$ symbol represents Number of alpha subunits with GTP attached
$f_3$ symbol represents Propensity of Hydrolysis of GTP
Internalisation of Receptor–Ligand Complex	$f_4=k_4\cdot x_{RL}\cdot x_M$
$k_4$ symbol represents Reaction Constant for Internalisation of Receptor–Ligand Complex
$x_{RL}$ symbol represents Number of Receptor-Ligand Complex Molecules
$f_4$ symbol represents Propensity of Internalisation of Receptor–Ligand Complex
$x_M$ symbol represents Number of Reaction Partner Molecules
Inhibition of Membrane Calcium Channel	$f_5=k_5\cdot x_{\beta \gamma }\cdot x_{{\text{Ca}}_{\text{on}}}$
$k_5$ symbol represents Reaction Constant for Inhibition of Membrane Calcium Channel
$x_{\beta \gamma }$ symbol represents Number of βγ Molecules
$x_{C{a}_{on}}$ symbol represents Number of Active Calcium Channels
$f_5$ symbol represents Propensity of Inhibition of Membrane Calcium Channel
Reformation of G-Protein Complex and Opening of Calcium Channel	$f_6=k_6\cdot x_{\alpha \text{GDP}}\cdot x_{{\text{Ca}}_{\text{off}}}$
$k_6$ symbol represents Reaction Constant for Reformation of G-Protein Complex and Opening of Calcium Channel
$x_{{\alpha }_{GDP}}$ symbol represents Number of alpha subunits loaded with GDP
$x_{C{a}_{off}}$ symbol represents Number of Inactive Calcium Channels
$f_6$ symbol represents Propensity of Reformation of G-Protein Complex and Opening of Calcium Channel
Internalised Receptor recycled to the cell membrane	$f_7=k_7\cdot x_{R{L}_w}$
$k_7$ symbol represents Reaction Constant for Internalised Receptor recycled to the cell membrane
$x_{R{L}_w}$ symbol represents Number of Internalised Receptor
$f_7$ symbol represents propensity of Internalised Receptor recycled to the cell membrane
Degradation of Internalised Receptor	$f_8=k_8\cdot x_{R{L}_w}$
$k_8$ symbol represents Reaction Constant for Degradation of Internalised Receptor
$x_{R{L}_w}$ symbol represents Number of Internalised Receptor
$f_8$ symbol represents Propensity for the Degradation of Internalised Receptor
Degradation of the Reaction Partner	$f_9=k_9\cdot x_M$
$k_9$ symbol represents Reaction Constant for the Degradation of the Reaction Partner
$x_M$ symbol represents Number of Reaction Partner Molecules
$f_9$ symbol represents Propensity of Degradation of the Reaction Partner
Vanishing of Ligand	$f_{10}=k_{10}\cdot x_L$
$k_{10}$ symbol represents Reaction Constant for the Vanishing of Ligand
$x_L$ symbol represents Number of Ligand Molecules
$f_{10}$ symbol represents Propensity of the Vanishing of Ligand
G-protein Activation	$f_{11}=k_{11}\cdot x_R\cdot x_{\alpha \text{GDP}\beta \gamma }$
$k_{11}$ symbol represents Reaction Constant for G-protein Activation
$x_R$ symbol represents Number of Receptor Molecules
$x_{{\alpha }_{GDP}\beta \gamma }$ symbol represents Number of G-protein Molecules
$f_{11}$ symbol represents Propensity of G-protein Activation
Jump in the System State	$x\mapsto x+v_j$
$x$ symbol represents State of System Vector
$v_j$ symbol represents Stoichiometric Vectors
Standard Chemical Master Equation	$\frac{d}{dt}p(\mathit{x},t)=\sum _{j=1}^{11}[f_j(\mathit{x}-{\mathit{v}}_j)p(\mathit{x}-{\mathit{v}}_j,t)-f_j(\mathit{x})p(\mathit{x},t)]$
$p(x,t)$ symbol represents Probability of the System being in a State
$X(t)$ symbol represents Markov Jump Process
$v_j$ symbol represents Stoichiometric Vectors
$f_j$ symbol represents Propensity functions for the signalling of G‑protein coupled receptors reactions
$x$ symbol represents State of System Vector