Publications

Although optimal control (OC) has been studied in stochastic thermodynamics for systems with continuous state variables, less is known in systems with discrete state variables, such as chemical reaction networks (CRNs). Here, we develop a general theoretical framework to study OC of CRNs for changing the system from an initial distribution of states to a final distribution with minimum dissipation. We derive a “Kirchhoff’s law” for the probability current in the adiabatic limit, from which the optimal kinetic rates are determined analytically for any given probability trajectory allowed by local rate constraints. By using the optimal rates, we show that the total dissipation is determined by a 𝐿2-distance measure in the probability space and derive an analytical expression for the metric tensor that depends on the probability distribution, network topology, and capacity of each link. Minimizing the total dissipation leads to the geodesic trajectory in the probability space and the corresponding OC protocol is determined by the Kirchhoff’s law. To demonstrate our general approach, we use it to find a lower bound for the minimum dissipation that is tighter than existing bounds obtained with only global constraints in the adiabatic limit. We also apply it to simple networks, e.g., fully connected three-state CRNs with different local constraints and show that indirect pathway and nonfunctional transient state can play a crucial role in switching between different probability distributions efficiently. Future directions in studying OC in CRNs by using our general framework are discussed.

The centrosomal aster is a mobile and adaptable cellular organelle that exerts and transmits forces necessary for tasks such as nuclear migration and spindle positioning. Recent experimental and theoretical studies of nematode and human cells demonstrate that pulling forces on asters by cortically anchored force generators are dominant during such processes. Here, we present a comprehensive investigation of the S-model (S for stoichiometry) of aster dynamics based solely on such forces. The model evolves the astral centrosome position, a probability field of cell-surface motor occupancy by centrosomal microtubules (under an assumption of stoichiometric binding), and free boundaries of unattached, growing microtubules. We show how cell shape affects the stability of centering of the aster, and its transition to oscillations with increasing motor number. Seeking to understand observations in single-cell nematode embryos, we use highly accurate simulations to examine the nonlinear structures of the bifurcations, and demonstrate the importance of binding domain overlap to interpreting genetic perturbation experiments. We find a generally rich dynamical landscape, dependent upon cell shape, such as internal constant-velocity equatorial orbits of asters that can be seen as traveling wave solutions. Finally, we study the interactions of multiple asters which we demonstrate an effective mutual repulsion due to their competition for surface force generators. We find, amazingly, that centrosomes can relax onto the vertices of platonic and nonplatonic solids, very closely mirroring the results of the classical Thomson problem for energy-minimizing configurations of electrons constrained to a sphere and interacting via repulsive Coulomb potentials. Our findings both explain experimental observations, providing insights into the mechanisms governing spindle positioning and cell division dynamics, and show the possibility of new nonlinear phenomena in cell biology.

The 2024 New York City Integrative Structural Biology Symposium focused on understanding the challenges and opportunities of applying integrative structural biology techniques to biomedical research. To foster connections across different fields and disciplines, this symposium offered hands-on workshops. These workshops provided attendees an opportunity to use state-of-the-art instrumentation and software programs in the structural biology sciences that they may not have access to in their own laboratories. Moreover, the symposium provided a vibrant environment for scientific discourse where cutting-edge research talks presented the trends in integrative structural biology in the New York City area. In this TrendsTalk, the symposium organizers bring to you the highlights of the workshops and scientific sections from this event.

Extracting conformational heterogeneity from cryo-electron microscopy (cryo-EM) images is particularly challenging for flexible biomolecules, where traditional 3D classification approaches often fail. Over the past few decades, advancements in experimental and computational techniques have been made to tackle this challenge, especially Bayesian-based approaches that provide physically interpretable insights into cryo-EM heterogeneity. To reduce the computational cost for Bayesian approaches, and building upon previously developed Fourier–Bessel image-representation methods, we created CryoLike, computationally efficient software for evaluating image-to-structure (or image-to-volume) likelihoods across large image data sets, packaged in a user-friendly Python workflow.

Notwithstanding the evidence against them, classical variational phase-field models continue to be used and pursued in an attempt to describe fracture nucleation in elastic brittle materials. In this context, the main objective of this paper is to provide a comprehensive review of the existing evidence against such a class of models as descriptors of fracture nucleation. To that end, a review is first given of the plethora of experimental observations of fracture nucleation in nominally elastic brittle materials under quasi-static loading conditions, as well as of classical variational phase-field models, without and with energy splits. These models are then confronted with the experimental observations. The conclusion is that they cannot possibly describe fracture nucleation in general. This because classical variational phase-field models cannot account for material strength as an independent macroscopic material property. The last part of the paper includes a brief summary of a class of phase-field models that can describe fracture nucleation. It also provides a discussion of how pervasively material strength has been overlooked in the analysis of fracture at large, as well as an outlook into the modeling of fracture nucleation beyond the basic setting of elastic brittle materials.

This work addresses the question of uniqueness and regularity of the minimizers of a convex but not strictly convex integral functional with linear growth in a two-dimensional setting. The integrand -- whose precise form derives directly from the theory of perfect plasticity -- behaves quadratically close to the origin and grows linearly once a specific threshold is reached. Thus, in contrast with the only existing literature on uniqueness for functionals with linear growth, that is that which pertains to the generalized least gradient, the integrand is not a norm. We make use of hyperbolic conservation laws hidden in the structure of the problem to tackle uniqueness. Our argument strongly relies on the regularity of a vector field -- the Cauchy stress in the terminology of perfect plasticity -- which allows us to define characteristic lines, and then to employ the method of characteristics. Using the detailed structure of the characteristic landscape evidenced in our preliminary study BF, we show that this vector field is actually continuous, save for possibly two points. The different behaviors of the energy density at zero and at infinity imply an inequality constraint on the Cauchy stress. Under a barrier type convexity assumption on the set where the inequality constraint is saturated, we show that uniqueness holds for pure Dirichlet boundary data devoid of any regularity properties, a stronger result than that of uniqueness for a given trace on the whole boundary since our minimizers can fail to attain the boundary data. We also show a partial regularity result for the minimizer.

Surface tension at cavity walls can play havoc with the mechanical properties of perforated soft solids when the cavities are filled with a fluid. This study is an investigation of the macroscopic elastic properties of elastomers embedding spherical cavities filled with a pressurized liquid in the presence of surface tension, starting with the linearization of the fully nonlinear model and ending with the enhancement properties of the linearized model when many such liquid filled cavities are present.

We use a combination of unsupervised clustering and sparsity-promoting inference algorithms to learn locally dominant force balances that explain macroscopic pattern formation in self-organized active particle systems. The self-organized emergence of macroscopic patterns from microscopic interactions between self-propelled particles can be widely observed in nature. Although hydrodynamic theories help us better understand the physical basis of this phenomenon, identifying a sufficient set of local interactions that shape, regulate and sustain self-organized structures in active particle systems remains challenging. We investigate a classic hydrodynamic model of self-propelled particles that produces a wide variety of patterns, such as asters and moving density bands. Our data-driven analysis shows that propagating bands are formed by local alignment interactions driven by density gradients, while steady-state asters are shaped by a mechanism of splay-induced negative compressibility arising from strong particle interactions. Our method also reveals analogous physical principles of pattern formation in a system where the speed of the particle is influenced by the local density. This demonstrates the ability of our method to reveal physical commonalities across models. The physical mechanisms inferred from the data are in excellent agreement with analytical scaling arguments and experimental observations.

Learning in living organisms is typically associated with networks of neurons. The use of large numbers of adjustable units has also been a crucial factor in the continued success of artificial neural networks. In light of the complexity of both living and artificial neural networks, it is surprising to see that very simple organisms -- even unicellular organisms that do not possess a nervous system -- are capable of certain forms of learning. Since in these cases learning may be implemented with much simpler structures than neural networks, it is natural to ask how simple the building blocks required for basic forms of learning may be. The purpose of this study is to discuss the simplest dynamical systems that model a fundamental form of non-associative learning, habituation, and to elucidate technical implementations of such systems, which may be used to implement non-associative learning in neuromorphic computing and related applications.