Learning dynamical information from static protein and sequencing data

Many complex processes, from protein folding to neuronal network dynamics, can be described as stochastic exploration of a high-dimensional energy landscape. While efficient algorithms for cluster detection in high-dimensional spaces have been developed over the last two decades, considerably less is known about the reliable inference of state transition dynamics in such settings. Here, we introduce a flexible and robust numerical framework to infer Markovian transition networks directly from time-independent data sampled from stationary equilibrium distributions. We demonstrate the practical potential of the inference scheme by reconstructing the network dynamics for several protein folding transitions, gene-regulatory network motifs and HIV evolution pathways. The predicted network topologies and relative transition time scales agree well with direct estimates from time-dependent molecular dynamics data, stochastic simulations and phylogenetic trees, respectively. Owing to its generic structure, the framework introduced here will be applicable to high-throughput RNA and protein sequencing datasets and future cryo-electronmicroscopy data

Predicting knee osteoarthritis

Treatment options for osteoarthritis (OA) beyond pain relief or total knee replacement are very limited. Because of this, attention has shifted to identifying which factors increase the risk of OA in vulnerable populations in order to be able to give recommendations to delay disease onset or to slow disease progression. The gold standard is then to use principles of risk management, first to provide subject-specific estimates of risk and then to find ways of reducing that risk. Population studies of OA risk based on statistical associations do not provide such individually tailored information. Here we argue that mechanistic models of cartilage tissue maintenance and damage coupled to statistical models incorporating model uncertainty, united within the framework of structural reliability analysis, provide an avenue for bridging the disciplines of epidemiology, cell biology, genetics and biomechanics. Such models promise subject-specific OA risk assessment and personalized strategies for mitigating or even avoiding OA. We illustrate the proposed approach with a simple model of cartilage extracellular matrix synthesis and loss regulated by daily physical activity

Short-term consolidation of articular cartilage in the long-term context of osteoarthritis

Over ten percent of the population are afflicted by osteoarthritis, a chronic disease of diarthrodial joints such as the knees and hips, costing hundreds of billions of dollars every year. In this condition, the thin layers of articular cartilage on the bones degrade and weaken over years, causing pain, stiffness and eventual immobility. The biggest controllable risk factor is long-term mechanical overloading of the cartilage, but the disparity in time scales makes this process a challenge to model: loading events can take place every second, whereas degradation occurs over many months. Therefore, a suitable model must be sufficiently simple to permit evaluation over long periods of variable loading, yet must deliver results sufficiently accurate to be of clinical use, conditions unmet by existing models. To address this gap, we construct a two-component poroelastic model endowed with a new flow restricting boundary condition, which better represents the joint space environment compared to the typical free-flow condition. Under both static and cyclic loading, we explore the rate of gradual consolidation of the medium. In the static case, we analytically characterise the duration of consolidation, which governs the duration of effective fluid-assisted lubrication. In the oscillatory case, we identify a region of persistent strain oscillations in otherwise consolidated tissue, and derive estimates of its depth and magnitude. Finally, we link the two cases through the concept of an equivalent static stress, and discuss how our results help explain the inexorable cartilage degeneration of osteoarthritis

Generalized Navier-Stokes equations for active suspensions

We discuss a minimal generalization of the incompressible Navier-Stokes equations to describe the complex steady-state dynamics of solvent flow in an active suspension. To account phenomenologically for the presence of an active component driving the ambient fluid flow, we postulate a generic nonlocal extension of the stress-tensor, conceptually similar to those recently introduced in granular flows. Stability and spectral properties of the resulting hydrodynamic model are studied both analytically and numerically for the two-dimensional (2D) case with periodic boundary conditions. Future generalizations of this theory could be useful for quantifying the shear properties of active suspensions

Active polar fluid flow in finite droplets.

We present a continuum level analytical model of a droplet of active contractile fluid consisting of filaments and motors. We calculate the steady state flows that result from a splayed polarisation of the filaments. We account for interaction with the external medium by imposing a viscous friction at the fixed droplet boundary. We then show that the droplet has non-zero force dipole and quadrupole moments, the latter of which is essential for self-propelled motion of the droplet at low Reynolds' number. Therefore, this calculation describes a simple mechanism for the motility of a droplet of active contractile fluid embedded in a three-dimensional environment, which is relevant to cell migration in confinement (for example, embedded within a gel or tissue). Our analytical results predict how the system depends on various parameters such as the effective friction coefficient, the phenomenological activity parameter and the splay of the imposed polarisation