Bayesian parameter estimation for dynamical models in systems biology
Fig 8
Parameter estimation for a coupled kinase-phosphatase switch for long-term potentiation and long-term depression in neurons as a function of calcium input.
(A) Network diagram of the simplified coupled kinase-phosphatase signaling model where calcium Ca2+(t) acts as the input. (B) Trajectories of the three state variables in response to long-term potentiation (LTP; pulse of Ca2+(t) ≡ 4.0 [μM] from 2 ≤ t ≤ 3 (sec)) and long-term depression (LTD; pulse of Ca2+(t) ≡ 2.2 [μM] from 2 ≤ t ≤ 3 (sec)) inducing calcium inputs. The calcium level is set to a baseline of Ca2+(t) ≡ 0.1 [μM] before and after stimulus. We compute normalized EPSP by normalizing A(t) to its initial condition as described in [57]. The synthetic noisy data for the LTP and LTD cases are indicated by the black square and green circle marks, respectively, with the noise covariance equal to 1% of the variance of the data. (C and D) Sobol sensitivity indices for all free model parameters in response to LTP-inducing and LTD-inducing inputs, respectively. The quantities of interest are the steady state values of each state variable. We show both the first-order sensitivity indices Si and the total-order indices . We select a reduced set of free parameters by choosing the parameters whose first-order sensitivity index is greater than 0.05, e.g., Si > 0.05. This gives us the same set of free parameters,
, k6, K0, P0, Ktot, Ptot, Atot]⊤, for both the LTP and LTD cases. Remaining model parameters are fixed to the nominal values in S4 Table.