Publications

The extracellular signal–regulated kinase (ERK) controls multiple critical processes in the cell and is deregulated in human cancers, congenital abnormalities, immune diseases, and neurodevelopmental syndromes. Catalytic activity of ERK requires dual phosphorylation by an upstream kinase, in a mechanism that can be described by two sequential Michaelis-Menten steps. The estimation of individual reaction rate constants from kinetic data in the full mechanism has proved challenging. Here, we present an analytically tractable approach to parameter estimation that is based on the phase plane representation of ERK activation and yields two combinations of six reaction rate constants in the detailed mechanism. These combinations correspond to the ratio of the specificities of two consecutive phosphorylations and the probability that monophosphorylated substrate does not dissociate from the enzyme before the second phosphorylation. The presented approach offers a language for comparing the effects of mutations that disrupt ERK activation and function in vivo. As an illustration, we use phase plane representation to analyze dual phosphorylation under heterozygous conditions, when two enzyme variants compete for the same substrate.

Computers, as well as most neuromorphic hardware systems, use central processing and top-down algorithmic control to train for machine learning tasks. In contrast, brains are ensembles of 100 billion neurons working in tandem, giving them tremendous advantages in power efficiency and speed. Many physical systems `learn' through history dependence, but training a physical system to perform arbitrary nonlinear tasks without a processor has not been possible. Here we demonstrate the successful implementation of such a system - a learning meta-material. This nonlinear analog circuit is comprised of identical copies of a single simple element, each following the same local update rule. By applying voltages to our system (inputs), inference is performed by physics in microseconds. When labels are properly enforced (also via voltages), the system's internal state evolves in time, approximating gradient descent. Our system; it requires no processor. Once trained, it performs inference passively, requiring approximately 100~W of total power dissipation across its edges. We demonstrate the flexibility and power efficiency of our system by solving nonlinear 2D classification tasks. Learning meta-materials have immense potential as fast, efficient, robust learning systems for edge computing, from smart sensors to medical devices to robotic control.

The prospect of substantial reductions in the power consumption of AI is a major motivation for the development of neuromorphic hardware. Less attention has been given to the complementary research of power-efficient learning rules for such systems. Here we study self-learning physical systems trained by local learning rules based on contrastive learning. We show how the physical learning rule can be biased toward finding power-efficient solutions to learning problems, and demonstrate in simulations and laboratory experiments the emergence of a trade-off between power-efficiency and task performance.

Nearly, all dense suspensions undergo dramatic and abrupt thickening transitions in their flow behavior when sheared at high stresses. Such transitions occur when the dominant interactions between the suspended particles shift from hydrodynamic to frictional. Here, we interpret abrupt shear thickening as a precursor to a rigidity transition and give a complete theory of the viscosity in terms of a universal crossover scaling function from the frictionless jamming point to a rigidity transition associated with friction, anisotropy, and shear. Strikingly, we find experimentally that for two different systems—cornstarch in glycerol and silica spheres in glycerol—the viscosity can be collapsed onto a single universal curve over a wide range of stresses and volume fractions. The collapse reveals two separate scaling regimes due to a crossover between frictionless isotropic jamming and frictional shear jamming, with different critical exponents. The material-specific behavior due to the microscale particle interactions is incorporated into a scaling variable governing the proximity to shear jamming, that depends on both stress and volume fraction. This reformulation opens the door to importing the vast theoretical machinery developed to understand equilibrium critical phenomena to elucidate fundamental physical aspects of the shear thickening transition.

Inferring dynamical models from low-resolution temporal data continues to be a significant challenge in biophysics, especially within transcriptomics, where separating molecular programs from noise remains an important open problem. We explore a common scenario in which we have access to an adequate amount of cross-sectional samples at a few time-points, and assume that our samples are generated from a latent diffusion process. We propose an approach that relies on the probability flow associated with an underlying diffusion process to infer an autonomous, nonlinear force field interpolating between the distributions. Given a prior on the noise model, we employ score-matching to differentiate the force field from the intrinsic noise. Using relevant biophysical examples, we demonstrate that our approach can extract non-conservative forces from non-stationary data, that it learns equilibrium dynamics when applied to steady-state data, and that it can do so with both additive and multiplicative noise models.

Recent studies have highlighted the significance of the spindle midzone – the region positioned between chromosomes – in ensuring proper chromosome segregation. By combining advanced 3D electron tomography and cutting-edge light microscopy we have discovered a previously unknown role of the regulation of microtubule dynamics within the spindle midzone of C. elegans. Using Fluorescence recovery after photobleaching and a combination of second harmonic generation and two-photon fluorescence microscopy, we found that the length of the antiparallel microtubule overlap zone in the spindle midzone is constant throughout anaphase, and independent of cortical pulling forces as well as the presence of the microtubule bundling protein SPD-1. Further investigations of SPD-1 and the chromokinesin KLP-19 in C. elegans suggest that KLP-19 regulates the overlap length and functions independently of SPD-1. Our data shows that KLP-19 plays an active role in regulating the length and turn-over of microtubules within the midzone as well as the size of the antiparallel overlap region throughout mitosis. Depletion of KLP-19 in mitosis leads to an increase in microtubule length in the spindle midzone, which also leads to increased microtubule – microtubule interaction, thus building up a more robust microtubule network. The spindle is globally stiffer and more stable, which has implications for the transmission of forces within the spindle affecting chromosome segregation dynamics. Our data shows that by localizing KLP-19 to the spindle midzone in anaphase microtubule dynamics can be locally controlled allowing the formation of a functional midzone.

The design of protein interaction inhibitors is a promising approach to address aberrant protein interactions that cause disease. One strategy in designing inhibitors is to use peptidomimetic scaffolds that mimic the natural interaction interface. A central challenge in using peptidomimetics as protein interaction inhibitors, however, is determining how best the molecular scaffold aligns to the residues of the interface it is attempting to mimic. Here we present the Scaffold Matcher algorithm that aligns a given molecular scaffold onto hotspot residues from a protein interaction interface. To optimize the degrees of freedom of the molecular scaffold we implement the covariance matrix adaptation evolution strategy (CMA-ES), a state-of-the-art derivative-free optimization algorithm in Rosetta. To evaluate the performance of the CMA-ES, we used 26 peptides from the FlexPepDock Benchmark and compared with three other algorithms in Rosetta, specifically, Rosetta's default minimizer, a Monte Carlo protocol of small backbone perturbations, and a Genetic algorithm. We test the algorithms' performance on their ability to align a molecular scaffold to a series of hotspot residues (i.e., constraints) along native peptides. Of the 4 methods, CMA-ES was able to find the lowest energy conformation for all 26 benchmark peptides. Additionally, as a proof of concept, we apply the Scaffold Match algorithm with CMA-ES to align a peptidomimetic oligooxopiperazine scaffold to the hotspot residues of the substrate of the main protease of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Our implementation of CMA-ES into Rosetta allows for an alternative optimization method to be used on macromolecular modeling problems with rough energy landscapes. Finally, our Scaffold Matcher algorithm allows for the identification of initial conformations of interaction inhibitors that can be further designed and optimized as high-affinity reagents.

Vertebrate groups have evolved strikingly diverse color patterns. However, it remains unknown to what extent the diversification of such patterns has been shaped by the proximate, developmental mechanisms that regulate their formation. While these developmental mechanisms have long been inaccessible empirically, here we take advantage of recent insights into rodent pattern formation to investigate the role of development in shaping pattern diversification across rodents. Based on a broad survey of museum specimens, we first establish that various rodents have independently evolved diverse patterns consisting of longitudinal stripes, varying across species in number, color, and relative positioning. We then interrogate this diversity using a simple model that incorporates recent molecular and developmental insights into stripe formation in African striped mice. Our results suggest that, on the one hand, development has facilitated pattern diversification: The diversity of patterns seen across species can be generated by a single developmental process, and small changes in this process suffice to recapitulate observed evolutionary changes in pattern organization. On the other hand, development has constrained diversification: Constraints on stripe positioning limit the scope of evolvable patterns, and although pattern organization appears at first glance phylogenetically unconstrained, development turns out to impose a cryptic constraint. Altogether, this work reveals that pattern diversification in rodents can in part be explained by the underlying development and illustrates how pattern formation models can be leveraged to interpret pattern evolution.

During morphogenesis, epithelial monolayers actively alter their shape to create future body parts of the animal; this makes the epithelium one of the most active and critical structures in early animal development. While epithelia are often modeled as two-dimensional systems, real epithelia are not necessarily thin relative to cell cross section, and advances in 3D imaging have shown the possibility of substantial cell deformations in the third dimension, as well as differences in dynamics of the apical and basal surfaces indicative of three-dimensional coupling. With the importance of the third dimension in mind, we have developed a self-sculpting, three-dimensional model of epithelia whose dynamics are driven by active forces on its surface. We present a first, fundamental study for a reduced version of epithelia that investigates how surface forces affect its internal dynamics. Our model captures the 3D slab-like geometry of epithelia, viscoelasticity of tissue response, fluid surroundings, and driving from active surface forces. We represent epithelial tissue as a thick slab, a 3D continuum comprised of a Stokes fluid with an extra viscoelastic stress. Employing this model, we present both analytical and numerical solutions of the system and make quantitative predictions about cell shapes, cell dynamics, and the tissue's response to surface force in a three-dimensional setting. In particular, we investigate the implications of our model on the initiation of ventral furrow invagination and T1 transitions in Drosophila embryogenesis. In the former, we demonstrate the importance of fluid and geometric surroundings to drive invagination. In the latter, we show the limitations of surface forces alone to drive T1 transitions.

In this paper, we present a novel methodology for automatic adaptive weighting of Bayesian Physics-Informed Neural Networks (BPINNs), and we demonstrate that this makes it possible to robustly address multi-objective and multiscale problems. BPINNs are a popular framework for data assimilation, combining the constraints of Uncertainty Quantification (UQ) and Partial Differential Equation (PDE). The relative weights of the BPINN target distribution terms are directly related to the inherent uncertainty in the respective learning tasks. Yet, they are usually manually set a-priori, that can lead to pathological behavior, stability concerns, and to conflicts between tasks which are obstacles that have deterred the use of BPINNs for inverse problems with multiscale dynamics.

The present weighting strategy automatically tunes the weights by considering the multitask nature of target posterior distribution. We show that this remedies the failure modes of BPINNs and provides efficient exploration of the optimal Pareto front. This leads to better convergence and stability of BPINN training while reducing sampling bias. The determined weights moreover carry information about task uncertainties, reflecting noise levels in the data and adequacy of the PDE model.

We demonstrate this in numerical experiments in Sobolev training, and compare them to analytically ε-optimal baseline, and in a multiscale Lotka-Volterra inverse problem. We eventually apply this framework to an inpainting task and an inverse problem, involving latent field recovery for incompressible flow in complex geometries.