Stochastically modeling multiscale stationary biological processes.

Large scale biological responses are inherently uncertain, in part as a consequence of noisy systems that do not respond deterministically to perturbations and measurement errors inherent to technological limitations. As a result, they are computationally difficult to model and current approaches are notoriously slow and computationally intensive (multiscale stochastic models), fail to capture the effects of noise across a system (chemical kinetic models), or fail to provide sufficient biological fidelity because of broad simplifying assumptions (stochastic differential equations). We use a new approach to modeling multiscale stationary biological processes that embraces the noise found in experimental data to provide estimates of the parameter uncertainties and the potential mis-specification of models. Our approach models the mean stationary response at each biological level given a particular expected response relationship, capturing variation around this mean using conditional Monte Carlo sampling that is statistically consistent with training data. A conditional probability distribution associated with a biological response can be reconstructed using this method for a subset of input values, which overcomes the parameter identification problem. Our approach could be applied in addition to dynamical modeling methods (see above) to predict uncertain biological responses over experimental time scales. To illustrate this point, we apply the approach to a test case in which we model the variation associated with measurements at multiple scales of organization across a reproduction-related Adverse Outcome Pathway described for teleosts