Discrete-State Stochastic Models of Calcium-Regulated Calcium Influx and Subspace Dynamics Are Not Well-Approximated by ODEs That Neglect Concentration Fluctuations

Figure 8

Subspace volume-dependence of concentration fluctuation and channel open probability for multiple calcium-activated channels. (A) Steady-state probability distribution for 𝑣 = 𝑣₀ (a), 2𝑣₀ (b), and 4𝑣₀ (c) (𝜅=0.45 μM, 𝑘⁺=5×10⁻⁴ μM⁻² ms⁻¹). For each panel, the dashed black line denotes the conditional expected concentration (E^𝑚[C]). The steady-state probability distribution is shown for each possible number of closed (𝑁_𝐶) and open (𝑁_𝑂) channels. (B) (a) Steady-state E[C] and 𝑝_open for the monostable system as a function of 𝑣 for rate constants of calcium binding (𝑘⁺=5×10⁻⁵ to 5×10⁻³ μM⁻² ms⁻¹). The fast/large and slow system limits are shown in red and blue, respectively. (b) Steady-state E[C] and 𝑝_open for the bistable system (𝜅=2 μM) as a function of 𝑣 using 𝑘⁺= 0.005 to 0.015 μM⁻² ms⁻¹. In the bistable system, the larger of the two stable equilibrium (large system limit) is shown in red. The smaller equilibrium is approximately equal to the slow system limit (shown in blue).