Adaptive nonequilibrium design of actin-based metamaterials: Fundamental and practical limits of control.

The adaptive and surprising emergent properties of biological materials self-assembled in far-from-equilibrium environments serve as an inspiration for efforts to design nanomaterials. In particular, controlling the conditions of self-assembly can modulate material properties, but there is no systematic understanding of either how to parameterize external control or how controllable a given material can be. Here, we demonstrate that branched actin networks can be encoded with metamaterial properties by dynamically controlling the applied force under which they grow and that the protocols can be selected using multi-task reinforcement learning. These actin networks have tunable responses over a large dynamic range depending on the chosen external protocol, providing a pathway to encoding "memory" within these structures. Interestingly, we obtain a bound that relates the dissipation rate and the rate of "encoding" that gives insight into the constraints on control-both physical and information theoretical. Taken together, these results emphasize the utility and necessity of nonequilibrium control for designing self-assembled nanostructures.

Data-Efficient Generation of Protein Conformational Ensembles with Backbone-to-Side-Chain Transformers.

Excitement at the prospect of using data-driven generative models to sample configurational ensembles of biomolecular systems stems from the extraordinary success of these models on a diverse set of high-dimensional sampling tasks. Unlike image generation or even the closely related problem of protein structure prediction, there are currently no data sources with sufficient breadth to parametrize generative models for conformational ensembles. To enable discovery, a fundamentally different approach to building generative models is required: models should be able to propose rare, albeit physical, conformations that may not arise in even the largest data sets. Here we introduce a modular strategy to generate conformations based on "backmapping" from a fixed protein backbone that (1) maintains conformational diversity of the side chains and (2) couples the side-chain fluctuations using global information about the protein conformation. Our model combines simple statistical models of side-chain conformations based on rotamer libraries with the now ubiquitous transformer architecture to sample with atomistic accuracy. Together, these ingredients provide a strategy for rapid data acquisition and hence a crucial ingredient for scalable physical simulation with generative neural networks.

Ensuring thermodynamic consistency with invertible coarse-graining.

Coarse-grained models are a core computational tool in theoretical chemistry and biophysics. A judicious choice of a coarse-grained model can yield physical insights by isolating the essential degrees of freedom that dictate the thermodynamic properties of a complex, condensed-phase system. The reduced complexity of the model typically leads to lower computational costs and more efficient sampling compared with atomistic models. Designing "good" coarse-grained models is an art. Generally, the mapping from fine-grained configurations to coarse-grained configurations itself is not optimized in any way; instead, the energy function associated with the mapped configurations is. In this work, we explore the consequences of optimizing the coarse-grained representation alongside its potential energy function. We use a graph machine learning framework to embed atomic configurations into a low-dimensional space to produce efficient representations of the original molecular system. Because the representation we obtain is no longer directly interpretable as a real-space representation of the atomic coordinates, we also introduce an inversion process and an associated thermodynamic consistency relation that allows us to rigorously sample fine-grained configurations conditioned on the coarse-grained sampling. We show that this technique is robust, recovering the first two moments of the distribution of several observables in proteins such as chignolin and alanine dipeptide.

Unified, Geometric Framework for Nonequilibrium Protocol Optimization.

Controlling thermodynamic cycles to minimize the dissipated heat is a long-standing goal in thermodynamics, and more recently, a central challenge in stochastic thermodynamics for nanoscale systems. Here, we introduce a theoretical and computational framework for optimizing nonequilibrium control protocols that can transform a system between two distributions in a minimally dissipative fashion. These protocols optimally transport a system along paths through the space of probability distributions that minimize the dissipative cost of a transformation. Furthermore, we show that the thermodynamic metric-determined via a linear response approach-can be directly derived from the same objective function that is optimized in the optimal transport problem, thus providing a unified perspective on thermodynamic geometries. We investigate this unified geometric framework in two model systems and observe that our procedure for optimizing control protocols is robust beyond linear response.

Probing the theoretical and computational limits of dissipative design.

Self-assembly, the process by which interacting components form well-defined and often intricate structures, is typically thought of as a spontaneous process arising from equilibrium dynamics. When a system is driven by external nonequilibrium forces, states statistically inaccessible to the equilibrium dynamics can arise, a process sometimes termed direct self-assembly. However, if we fix a given target state and a set of external control variables, it is not well-understood (i) how to design a protocol to drive the system toward the desired state nor (ii) the cost of persistently perturbing the stationary distribution. In this work, we derive a bound that relates the proximity to the chosen target with the dissipation associated with the external drive, showing that high-dimensional external control can guide systems toward target distribution but with an inevitable cost. Remarkably, the bound holds arbitrarily far from equilibrium. Second, we investigate the performance of deep reinforcement learning algorithms and provide evidence for the realizability of complex protocols that stabilize otherwise inaccessible states of matter.

Kinetic modeling reveals additional regulation at co-transcriptional level by post-transcriptional sRNA regulators.

Small RNAs (sRNAs) are important gene regulators in bacteria. Many sRNAs act post-transcriptionally by affecting translation and degradation of the target mRNAs upon base-pairing interactions. Here we present a general approach combining imaging and mathematical modeling to determine kinetic parameters at different levels of sRNA-mediated gene regulation that contribute to overall regulation efficacy. Our data reveal that certain sRNAs previously characterized as post-transcriptional regulators can regulate some targets co-transcriptionally, leading to a revised model that sRNA-mediated regulation can occur early in an mRNA's lifetime, as soon as the sRNA binding site is transcribed. This co-transcriptional regulation is likely mediated by Rho-dependent termination when transcription-coupled translation is reduced upon sRNA binding. Our data also reveal several important kinetic steps that contribute to the differential regulation of mRNA targets by an sRNA. Particularly, binding of sRNA to the target mRNA may dictate the regulation hierarchy observed within an sRNA regulon.

An Automated Image Analysis Method for Segmenting Fluorescent Bacteria in Three Dimensions.

Single-cell fluorescence imaging is a powerful technique for studying inherently heterogeneous biological processes. To correlate a genotype or phenotype to a specific cell, images containing a population of cells must first be properly segmented. However, a proper segmentation with minimal user input becomes challenging when cells are clustered or overlapping in three dimensions. We introduce a new analysis package, Seg-3D, for the segmentation of bacterial cells in three-dimensional (3D) images, based on local thresholding, shape analysis, concavity-based cluster splitting, and morphology-based 3D reconstruction. The reconstructed cell volumes allow us to directly quantify the fluorescent signals from biomolecules of interest within individual cells. We demonstrate the application of this analysis package in 3D segmentation of individual bacterial pathogens invading host cells. We believe Seg-3D can be an efficient and simple program that can be used to analyze a wide variety of single-cell images, especially for biological systems involving random 3D orientation and clustering behavior, such as bacterial infection or colonization.