Quantifying collective motion patterns in mesenchymal cell populations using topological data analysis and agent-based modeling.

Fibroblasts in a confluent monolayer are known to adopt elongated morphologies in which cells are oriented parallel to their neighbors. We collected and analyzed new microscopy movies to show that confluent fibroblasts are motile and that neighboring cells often move in anti-parallel directions in a collective motion phenomenon we refer to as "fluidization" of the cell population. We used machine learning to perform cell tracking for each movie and then leveraged topological data analysis (TDA) to show that time-varying point-clouds generated by the tracks contain significant topological information content that is driven by fluidization, i.e., the anti-parallel movement of individual neighboring cells and neighboring groups of cells over long distances. We then utilized the TDA summaries extracted from each movie to perform Bayesian parameter estimation for the D'Orsgona model, an agent-based model (ABM) known to produce a wide array of different patterns, including patterns that are qualitatively similar to fluidization. Although the D'Orsgona ABM is a phenomenological model that only describes inter-cellular attraction and repulsion, the estimated region of D'Orsogna model parameter space was consistent across all movies, suggesting that a specific level of inter-cellular repulsion force at close range may be a mechanism that helps drive fluidization patterns in confluent mesenchymal cell populations.

Local Identifiability Analysis, Parameter Subset Selection and Verification for a Minimal Brain PBPK Model.

Physiologically-based pharmacokinetic (PBPK) modeling is important for studying drug delivery in the central nervous system, including determining antibody exposure, predicting chemical concentrations at target locations, and ensuring accurate dosages. The complexity of PBPK models, involving many variables and parameters, requires a consideration of parameter identifiability; i.e., which parameters can be uniquely determined from data for a specified set of concentrations. We introduce the use of a local sensitivity-based parameter subset selection algorithm in the context of a minimal PBPK (mPBPK) model of the brain for antibody therapeutics. This algorithm is augmented by verification techniques, based on response distributions and energy statistics, to provide a systematic and robust technique to determine identifiable parameter subsets in a PBPK model across a specified time domain of interest. The accuracy of our approach is evaluated for three key concentrations in the mPBPK model for plasma, brain interstitial fluid and brain cerebrospinal fluid. The determination of accurate identifiable parameter subsets is important for model reduction and uncertainty quantification for PBPK models.

Modeling and Parameter Subset Selection for Fibrin Polymerization Kinetics with Applications to Wound Healing.

During the hemostatic phase of wound healing, vascular injury leads to endothelial cell damage, initiation of a coagulation cascade involving platelets, and formation of a fibrin-rich clot. As this cascade culminates, activation of the protease thrombin occurs and soluble fibrinogen is converted into an insoluble polymerized fibrin network. Fibrin polymerization is critical for bleeding cessation and subsequent stages of wound healing. We develop a cooperative enzyme kinetics model for in vitro fibrin matrix polymerization capturing dynamic interactions among fibrinogen, thrombin, fibrin, and intermediate complexes. A tailored parameter subset selection technique is also developed to evaluate parameter identifiability for a representative data curve for fibrin accumulation in a short-duration in vitro polymerization experiment. Our approach is based on systematic analysis of eigenvalues and eigenvectors of the classical information matrix for simulations of accumulating fibrin matrix via optimization based on a least squares objective function. Results demonstrate robustness of our approach in that a significant reduction in objective function cost is achieved relative to a more ad hoc curve-fitting procedure. Capabilities of this approach to integrate non-overlapping subsets of the data to enhance the evaluation of parameter identifiability are also demonstrated. Unidentifiable reaction rate parameters are screened to determine whether individual reactions can be eliminated from the overall system while preserving the low objective cost. These findings demonstrate the high degree of information within a single fibrin accumulation curve, and a tailored model and parameter subset selection approach for improving optimization and reducing model complexity in the context of polymerization experiments.

Uncertainty Quantification and Sensitivity Analysis of Partial Charges on Macroscopic Solvent Properties in Molecular Dynamics Simulations with a Machine Learning Model.

The molecular dynamics (MD) simulation technique is among the most broadly used computational methods to investigate atomistic phenomena in a variety of chemical and biological systems. One of the most common (and most uncertain) parametrization steps in MD simulations of soft materials is the assignment of partial charges to atoms. Here, we apply uncertainty quantification and sensitivity analysis calculations to assess the uncertainty associated with partial charge assignment in the context of MD simulations of an organic solvent. Our results indicate that the effect of partial charge variance on bulk properties, such as solubility parameters, diffusivity, dipole moment, and density, measured from MD simulations is significant; however, measured properties are observed to be less sensitive to partial charges of less accessible (or buried) atoms. Diffusivity, for example, exhibits a global sensitivity of up to 22 × 10-5 cm2/s per electron charge on some acetonitrile atoms. We then demonstrate that machine learning techniques, such as Gaussian process regression (GPR), can be effective and rapid tools for uncertainty quantification of MD simulations. We show that the formulation and application of an efficient GPR surrogate model for the prediction of responses effectively reduces the computational time of additional sample points from hours to milliseconds. This study provides a much-needed context for the effect that partial charge uncertainty has on MD-derived material properties to illustrate the benefit of considering partial charges as distributions rather than point-values. To aid in this treatment, this work then demonstrates methods for rapid characterization of resulting sensitivity in MD simulations.

Parameter subset selection techniques for problems in mathematical biology.

Patient-specific models for diagnostics and treatment planning require reliable parameter estimation and model predictions. Mathematical models of physiological systems are often formulated as systems of nonlinear ordinary differential equations with many parameters and few options for measuring all state variables. Consequently, it can be difficult to determine which parameters can reliably be estimated from available data. This investigation highlights pitfalls associated with practical parameter identifiability and subset selection. The latter refer to the process associated with selecting a subset of parameters that can be identified uniquely by parameter estimation protocols. The methods will be demonstrated using five examples of increasing complexity, as well as with patient-specific model predicting arterial blood pressure. This study demonstrates that methods based on local sensitivities are preferable in terms of computational cost and model fit when good initial parameter values are available, but that global methods should be considered when initial parameter value is not known or poorly understood. For global sensitivity analysis, Morris screening provides results in terms of parameter sensitivity ranking at a much lower computational cost.

Forecasting and Uncertainty Quantification Using a Hybrid of Mechanistic and Non-mechanistic Models for an Age-Structured Population Model.

In this paper, we present a new method for the prediction and uncertainty quantification of data-driven multivariate systems. Traditionally, either mechanistic or non-mechanistic modeling methodologies have been used for prediction; however, it is uncommon for the two to be incorporated together. We compare the forecast accuracy of mechanistic modeling, using Bayesian inference, a non-mechanistic modeling approach based on state space reconstruction, and a novel hybrid methodology composed of the two for an age-structured population data set. The data come from cannibalistic flour beetles, in which it is observed that the adults preying on the eggs and pupae result in non-equilibrium population dynamics. Uncertainty quantification methods for the hybrid models are outlined and illustrated for these data. We perform an analysis of the results from Bayesian inference for the mechanistic model and hybrid models to suggest reasons why hybrid modeling methodology may enable more accurate forecasts of multivariate systems than traditional approaches.

Use of Bayesian Inference in Crystallographic Structure Refinement via Full Diffraction Profile Analysis.

A Bayesian inference method for refining crystallographic structures is presented. The distribution of model parameters is stochastically sampled using Markov chain Monte Carlo. Posterior probability distributions are constructed for all model parameters to properly quantify uncertainty by appropriately modeling the heteroskedasticity and correlation of the error structure. The proposed method is demonstrated by analyzing a National Institute of Standards and Technology silicon standard reference material. The results obtained by Bayesian inference are compared with those determined by Rietveld refinement. Posterior probability distributions of model parameters provide both estimates and uncertainties. The new method better estimates the true uncertainties in the model as compared to the Rietveld method.