Rohan Abeyaratne

Abstract Starting from the Langevin-type dynamics proposed in Loy & Preziosi (2023 Bull. Math. Bio.85, 60. (doi:10.1007/s11538-023-01161-4)) to describe fluctuations in cell reorientation under cyclic stretch, we apply the framework of ‘stochastic thermodynamics with internal variables’ (STIV) introduced in Leadbetter et al. (2023 PNAS Nexus2, pgad417. (doi:10.1093/pnasnexus/pgad417)) to obtain a two-dimensional dynamical system that is analytically more tractable than the original stochastic dynamics and effectively captures the evolution of the orientation distribution as well as its spreading. The insight provided by the phase-portrait analysis of our reduced model reveals a novel and interesting phenomenon, which we call two-stage reorientation: When cells begin aligned with an energy maximum, their orientations spread before concentrating at the energy minimum. Our theoretical prediction suggests a new experiment to test the stochastic model.

Starting from the Langevin-type dynamics proposed in Loy &amp; Preziosi (2023 <i>Bull. Math. Bio.</i> <b>85</b>, 60. (doi:10.1007/s11538-023-01161-4)) to describe fluctuations in cell reorientation under cyclic stretch, we apply the framework of ‘stochastic thermodynamics with internal variables’ (STIV) introduced in Leadbetter <i>et al.</i> (2023 <i>PNAS Nexus</i> <b>2</b>, pgad417. (doi:10.1093/pnasnexus/pgad417)) to obtain a two-dimensional dynamical system that is analytically more tractable than the original stochastic dynamics and effectively captures the evolution of the orientation distribution as well as its spreading. The insight provided by the phase-portrait analysis of our reduced model reveals a novel and interesting phenomenon, which we call two-stage reorientation: When cells begin aligned with an energy maximum, their orientations spread before concentrating at the energy minimum. Our theoretical prediction suggests a new experiment to test the stochastic model.

Starting from the Langevin-type dynamics proposed in Loy &amp; Preziosi (2023 <i>Bull. Math. Bio.</i> <b>85</b>, 60. (doi:10.1007/s11538-023-01161-4)) to describe fluctuations in cell reorientation under cyclic stretch, we apply the framework of ‘stochastic thermodynamics with internal variables’ (STIV) introduced in Leadbetter <i>et al.</i> (2023 <i>PNAS Nexus</i> <b>2</b>, pgad417. (doi:10.1093/pnasnexus/pgad417)) to obtain a two-dimensional dynamical system that is analytically more tractable than the original stochastic dynamics and effectively captures the evolution of the orientation distribution as well as its spreading. The insight provided by the phase-portrait analysis of our reduced model reveals a novel and interesting phenomenon, which we call two-stage reorientation: When cells begin aligned with an energy maximum, their orientations spread before concentrating at the energy minimum. Our theoretical prediction suggests a new experiment to test the stochastic model.

Starting from the Langevin-type dynamics proposed in Loy &amp; Preziosi (2023 <i>Bull. Math. Bio.</i> <b>85</b>, 60. (doi:10.1007/s11538-023-01161-4)) to describe fluctuations in cell reorientation under cyclic stretch, we apply the framework of ‘stochastic thermodynamics with internal variables’ (STIV) introduced in Leadbetter <i>et al.</i> (2023 <i>PNAS Nexus</i> <b>2</b>, pgad417. (doi:10.1093/pnasnexus/pgad417)) to obtain a two-dimensional dynamical system that is analytically more tractable than the original stochastic dynamics and effectively captures the evolution of the orientation distribution as well as its spreading. The insight provided by the phase-portrait analysis of our reduced model reveals a novel and interesting phenomenon, which we call two-stage reorientation: When cells begin aligned with an energy maximum, their orientations spread before concentrating at the energy minimum. Our theoretical prediction suggests a new experiment to test the stochastic model.

Starting from the Langevin-type dynamics proposed in Loy &amp; Preziosi (2023 <i>Bull. Math. Bio.</i> <b>85</b>, 60. (doi:10.1007/s11538-023-01161-4)) to describe fluctuations in cell reorientation under cyclic stretch, we apply the framework of ‘stochastic thermodynamics with internal variables’ (STIV) introduced in Leadbetter <i>et al.</i> (2023 <i>PNAS Nexus</i> <b>2</b>, pgad417. (doi:10.1093/pnasnexus/pgad417)) to obtain a two-dimensional dynamical system that is analytically more tractable than the original stochastic dynamics and effectively captures the evolution of the orientation distribution as well as its spreading. The insight provided by the phase-portrait analysis of our reduced model reveals a novel and interesting phenomenon, which we call two-stage reorientation: When cells begin aligned with an energy maximum, their orientations spread before concentrating at the energy minimum. Our theoretical prediction suggests a new experiment to test the stochastic model.

Generative AI, and specifically GPT, can produce a remarkable solution to a mechanical engineering analysis problem - but also, on occasion, a flawed solution. For example, an elementary mechanics problem is solved flawlessly in one GPT instance and incorrectly in a subsequent GPT instance, with a success probability of only 85%. This unreliability renders "out-of-the-box" GPT unsuitable for deployment in education or engineering practice. We introduce an "N-Plus-1" GPT Agency for Initial (Low-Cost) Analysis of mechanical engineering Problem Statements. Agency first launches N instantiations of Agent Solve to yield N independent Proposed Problem Solution Realizations; Agency then invokes Agent Compare to summarize and compare the N Proposed Problem Solution Realizations and to provide a Recommended Problem Solution. We argue from Condorcet's Jury Theorem that, for a Problem Statement characterized by per-Solve success probability greater than 1/2 (and N sufficiently large), the Predominant (Agent Compare) Proposed Problem Solution will, with high probability, correspond to a Correct Proposed Problem Solution. Furthermore, Agent Compare can also incorporate aspects of Secondary (Agent Compare) Proposed Problem Solutions, in particular when the latter represent alternative Problem Statement interpretations - different Mathematical Models - or alternative Mathematical Solution Procedures. Comparisons to Grok Heavy, a commercial multi-agent model, show similarities in design and performance, but also important differences in emphasis: our Agency focuses on transparency and pedagogical value.

The aim of this paper is to place the cell locomotion problem within the general framework of classical continuum mechanics, and while doing so, to account for the deformation of the actin network in the cytoskeleton; the myosin activity on the lamellum including its effect on depolymerization at the trailing edge; model the stress-dependent driving forces and kinetic laws controlling polymerization at the leading edge, depolymerization at the trailing edge and ATP hydrolysis consistently with the dissipation inequality; and, based on the observations in Gardel et al. (Gardel et al. 2008 J. Cell Biol. 183 , 999–1005 ( doi:10.1083/jcb.200810060 )), include a biphasic velocity-dependent traction stress acting on the actin network. While we chose certain specific models for each of these, in part to allow for an analytical solution, the generality of the framework allows one to readily introduce different constitutive laws to describe these phenomena as might be needed, for example, to study some different type of cells. As described in §5, the predictions of the model compare well with observations such as the magnitude of the very different actin retrograde speeds in the lamellum and lamellipodium including their jump at the interface, the magnitude of the cell speed, and the relative lengths of the lamellipodium and lamellum.