Stochastic simulations of minimal cells: the Ribocell model

BMC Bioinformatics

Table 2 Deterministic rates against propensity density probability for reacting and transport events.

Event	Deterministic Rate (Ms)^-1	Propensity Density Probability s ^-1
Internal Chemical reactions ^(a) $a_{1, ρ} X_{1} + \dots a_{N, ρ} X_{N} \to_{r_{ρ}}^{} b_{1, ρ} X_{1} + \dots b_{N, ρ} X_{N}$	$k_{ρ} \prod_{j}^{N} {(\frac{n_{j}^{C}}{V_{C} N_{A}})}^{a_{j}, ρ}$	$\frac{k_{ρ}}{{(V_{C} N_{A})}^{M_{ρ} - 1}} \prod_{j}^{N} (\begin{matrix} n_{j}^{C} \\ a_{j, p} \end{matrix})$
Solute X_n membrane transport ^(b)	$P_{n} \frac{S_{μ}}{V_{C}} (C_{n}^{E} - C_{n}^{C})$	$D_{n} S_{μ} {\frac{\|(C_{n}^{E} - C_{n}^{C})\|}{λ_{μ}}}^{(c)}$
Membrane Lipid Release	$\frac{k_{o u t} n_{L}^{μ}}{N_{A} V_{C}}$	$k_{o u t} n_{L}^{μ}$
Membrane Lipid Uptake	$(\frac{k_{i n} S_{μ} [X_{L}^{C}]}{N_{A} V_{C}})$	$k_{i n} S_{μ} [X_{L}^{C}]$
Water Flux ^(d)	$v_{a q} P_{a q} S_{μ} (C_{T}^{E} - C_{T}^{C})$	$V_{C} = \sum_{i = 1}^{N} n_{i}^{C} / (N_{A} C_{T}^{E})$

^a)a and b stoichiometric matrixes, N_A Avogadro's number, k_ρ kinetic constant, M_ρmolecularity [22]
^(b) The relationship between the macroscopic permeability P_n and the molecular diffusion coefficient D_n is: D_n = P_nλ_μN_A, λ_μ being the membrane thickness.
^(c) The absolute value guarantees that the propensity density probability is positive and the molecules move in the opposite direction from the concentration gradient.
^(d)v_aq is the water molar volume, while C_T^E and C_T^C are the total osmotic concentration in the external and internal aqueous solutions, respectively.

ISSN: 1471-2105