Bayesian parameter estimation for dynamical models in systems biology
Fig 9
Comprehensive parameter estimation and uncertainty quantification reveal failures to predict the correct long-term model behavior.
(A) We estimated marginal posterior distributions of the model parameters from noisy data with an LTP-inducing calcium input. Distributions are visualized by fitting a kernel density estimator to 547,500 (150 walkers with 3,649 steps each) MCMC samples obtained using CIUKF-MCMC with AIES for MCMC after discarding the first 4,351 samples per walker as burn-in. (B) Posterior distribution of the trajectories of the state variables show LTP (normalized EPSP >1) and LTD (normalized EPSP <1) responses for an LTP inducing input. The true trajectory (dashed black line) shows the dynamics with the nominal parameters, the dotted blue line shows the trajectory evaluated at the MAP point, and the points show the noisy data (covariance is 1% of the variance of the true trajectory). The 95% credible interval shows the region between the 2.5th and 97.5th percentiles that contains 95% of 30,000 posterior trajectories. (C) Sample posterior trajectories (100 out of 30,000 total) highlight the LTP (blue lines) and LTD (black lines) in response to the LTP inducing input (top) and the LTD inducing input (bottom). The dashed green lines show the true trajectories for the respective calcium inputs. (D) Histograms reveal the distribution of the long-term responses to the LTP-inducing input (top) and the LTD-inducing input (bottom). The dashed black lines show the true response for the respective calcium inputs. (E) Quantifying the percentage of the 30,000 sample trajectories that produce LTD and LTP responses for each calcium input. The LTP-inducing input yields 76.59% (22,972 samples) of the responses in the LTP state and 23.41% (7,024 samples) in the LTD state. The LTD inducing input yields 68.93% (20,680 samples) of the responses in the LTP state and 31.07% (9,320 samples) in the LTD state.