Mechanistic and microscopic models describe phenomena using our bottom-up understanding of the physical world. However, in experimental scenarios across physics, chemistry, and especially the biosciences, accessible observables under a given experimental design are fundamentally insufficient to constrain the full set of microscopic parameters.

In the best case, we rely on simplified models, either analytically or heuristically derived from mechanistic descriptions, to avoid overinterpreting measurements. In less ideal scenarios, optimization algorithms extract nominal best-fit parameters, despite subsequent analyses revealing that individual parameters may vary over orders of magnitude without significantly altering model predictions.

In this seminar, we explore how to detect parameter non-identifiability and sloppiness, using the Fisher Information Matrix. We then introduce an information geometry approach, the Manifold Boundary Approximation Method (MBAM), which follows geodesics along sloppy directions to uncover simplified models at manifold boundaries, demonstrating its application to a mechanistic model of the large-conductance potassium (BK) ion channel.

We end with a discussion of how this framework extends to biological adaptation and evolution, drawing a direct parallel between experimental designs and environmental pressures. Just as assay observables leave sloppy parameter directions unconstrained, environmental demands select for performance along a few stiff phenotypic directions. The remaining unconstrained directions in parameter space form vast neutral spaces where hidden variation can freely accumulate. Environmental shifts reorient the metric tensor, exposing latent parameter variation as an immediate driver of adaptation or a substrate for evolutionary selection.