*Bull Math Biol ; 83(3): 21, 2021 Jan 16.*

##### RESUMO

In developmental biology as well as in other biological systems, emerging structure and organization can be captured using time-series data of protein locations. In analyzing this time-dependent data, it is a common challenge not only to determine whether topological features emerge, but also to identify the timing of their formation. For instance, in most cells, actin filaments interact with myosin motor proteins and organize into polymer networks and higher-order structures. Ring channels are examples of such structures that maintain constant diameters over time and play key roles in processes such as cell division, development, and wound healing. Given the limitations in studying interactions of actin with myosin in vivo, we generate time-series data of protein polymer interactions in cells using complex agent-based models. Since the data has a filamentous structure, we propose sampling along the actin filaments and analyzing the topological structure of the resulting point cloud at each time. Building on existing tools from persistent homology, we develop a topological data analysis (TDA) method that assesses effective ring generation in this dynamic data. This method connects topological features through time in a path that corresponds to emergence of organization in the data. In this work, we also propose methods for assessing whether the topological features of interest are significant and thus whether they contribute to the formation of an emerging hole (ring channel) in the simulated protein interactions. In particular, we use the MEDYAN simulation platform to show that this technique can distinguish between the actin cytoskeleton organization resulting from distinct motor protein binding parameters.

*PLoS One ; 15(10): e0241381, 2020.*

##### RESUMO

In the United States, the public has a constitutional right to access criminal trial proceedings. In practice, it can be difficult or impossible for the public to exercise this right. We present JUSTFAIR: Judicial System Transparency through Federal Archive Inferred Records, a database of criminal sentencing decisions made in federal district courts. We have compiled this data set from public sources including the United States Sentencing Commission, the Federal Judicial Center, the Public Access to Court Electronic Records system, and Wikipedia. With nearly 600,000 records from the years 2001-2018, JUSTFAIR is the first large scale, free, public database that links information about defendants and their demographic characteristics with information about their federal crimes, their sentences, and, crucially, the identity of the sentencing judge.

*Bull Math Biol ; 82(10): 126, 2020 Sep 16.*

##### RESUMO

In many biological systems, the movement of individual agents is characterized having multiple qualitatively distinct behaviors that arise from a variety of biophysical states. For example, in cells the movement of vesicles, organelles, and other intracellular cargo is affected by their binding to and unbinding from cytoskeletal filaments such as microtubules through molecular motor proteins. A typical goal of theoretical or numerical analysis of models of such systems is to investigate effective transport properties and their dependence on model parameters. While the effective velocity of particles undergoing switching diffusion dynamics is often easily characterized in terms of the long-time fraction of time that particles spend in each state, the calculation of the effective diffusivity is more complicated because it cannot be expressed simply in terms of a statistical average of the particle transport state at one moment of time. However, it is common that these systems are regenerative, in the sense that they can be decomposed into independent cycles marked by returns to a base state. Using decompositions of this kind, we calculate effective transport properties by computing the moments of the dynamics within each cycle and then applying renewal reward theory. This method provides a useful alternative large-time analysis to direct homogenization for linear advection-reaction-diffusion partial differential equation models. Moreover, it applies to a general class of semi-Markov processes and certain stochastic differential equations that arise in models of intracellular transport. Applications of the proposed renewal reward framework are illustrated for several case studies such as mRNA transport in developing oocytes and processive cargo movement by teams of molecular motor proteins.

*Mol Biol Cell ; 31(7): 640-654, 2020 03 19.*

##### RESUMO

Neurofilaments are abundant space-filling cytoskeletal polymers in axons that are transported along microtubule tracks. Neurofilament transport is accelerated at nodes of Ranvier, where axons are locally constricted. Strikingly, these constrictions are accompanied by sharp decreases in neurofilament number, no decreases in microtubule number, and increases in the packing density of these polymers, which collectively bring nodal neurofilaments closer to their microtubule tracks. We hypothesize that this leads to an increase in the proportion of time that the filaments spend moving and that this can explain the local acceleration. To test this, we developed a stochastic model of neurofilament transport that tracks their number, kinetic state, and proximity to nearby microtubules in space and time. The model assumes that the probability of a neurofilament moving is dependent on its distance from the nearest available microtubule track. Taking into account experimentally reported numbers and densities for neurofilaments and microtubules in nodes and internodes, we show that the model is sufficient to explain the local acceleration of neurofilaments within nodes of Ranvier. This suggests that proximity to microtubule tracks may be a key regulator of neurofilament transport in axons, which has implications for the mechanism of neurofilament accumulation in development and disease.

*Chaos ; 29(10): 103116, 2019 Oct.*

##### RESUMO

In a complex system, the interactions between individual agents often lead to emergent collective behavior such as spontaneous synchronization, swarming, and pattern formation. Beyond the intrinsic properties of the agents, the topology of the network of interactions can have a dramatic influence over the dynamics. In many studies, researchers start with a specific model for both the intrinsic dynamics of each agent and the interaction network and attempt to learn about the dynamics of the model. Here, we consider the inverse problem: given data from a system, can one learn about the model and the underlying network? We investigate arbitrary networks of coupled phase oscillators that can exhibit both synchronous and asynchronous dynamics. We demonstrate that, given sufficient observational data on the transient evolution of each oscillator, machine learning can reconstruct the interaction network and identify the intrinsic dynamics.

*Biol Cybern ; 113(1-2): 105-120, 2019 04.*

##### RESUMO

Mathematical models can provide useful insights explaining behavior observed in experimental data; however, rigorous analysis is needed to select a subset of model parameters that can be informed by available data. Here we present a method to estimate an identifiable set of parameters based on baseline left ventricular pressure and volume time series data. From this identifiable subset, we then select, based on current understanding of cardiovascular control, parameters that vary in time in response to blood withdrawal, and estimate these parameters over a series of blood withdrawals. These time-varying parameters are first estimated using piecewise linear splines minimizing the mean squared error between measured and computed left ventricular pressure and volume data over four consecutive blood withdrawals. As a final step, the trends in these splines are fit with empirical functional expressions selected to describe cardiovascular regulation during blood withdrawal. Our analysis at baseline found parameters representing timing of cardiac contraction, systemic vascular resistance, and cardiac contractility to be identifiable. Of these parameters, vascular resistance and cardiac contractility were varied in time. Data used for this study were measured in a control Sprague-Dawley rat. To our knowledge, this is the first study to analyze the response to multiple blood withdrawals both experimentally and theoretically, as most previous studies focus on analyzing the response to one large blood withdrawal. Results show that during each blood withdrawal both systemic vascular resistance and contractility decrease acutely and partially recover, and they decrease chronically across the series of blood withdrawals.

##### Assuntos

Sistema Cardiovascular/fisiopatologia , Hemorragia/patologia , Modelos Cardiovasculares , Modelos Teóricos , Fluxo Sanguíneo Regional/fisiologia , Animais , Pressão Sanguínea/fisiologia , Volume Sanguíneo/fisiologia , Intervalos de Confiança , Hemorragia/fisiopatologia , Masculino , Dinâmica não Linear , Ratos , Ratos Sprague-Dawley , Função Ventricular Esquerda*Biophys J ; 112(8): 1714-1725, 2017 Apr 25.*

##### RESUMO

Fluorescence recovery after photobleaching (FRAP) is a well-established experimental technique to study binding and diffusion of molecules in cells. Although a large number of analytical and numerical models have been developed to extract binding and diffusion rates from FRAP recovery curves, active transport of molecules is typically not included in the existing models that are used to estimate these rates. Here we present a validated numerical method for estimating diffusion, binding/unbinding rates, and active transport velocities using FRAP data that captures intracellular dynamics through partial differential equation models. We apply these methods to transport and localization of mRNA molecules in Xenopus laevis oocytes, where active transport processes are essential to generate developmental polarity. By providing estimates of the effective velocities and diffusion, as well as expected run times and lengths, this approach can help quantify dynamical properties of localizing and nonlocalizing RNA. Our results confirm the distinct transport dynamics in different regions of the cytoplasm, and suggest that RNA movement in both the animal and vegetal directions may influence the timescale of RNA localization in Xenopus oocytes. We also show that model initial conditions extracted from FRAP postbleach intensities prevent underestimation of diffusion, which can arise from the instantaneous bleaching assumption. The numerical and modeling approach presented here to estimate parameters using FRAP recovery data is a broadly applicable tool for systems where intracellular transport is a key molecular mechanism.