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The concept that proteins are selected to fold into a well-defined native state has been effectively addressed within the framework of energy landscapes, underpinning the recent successes of structure prediction tools like AlphaFold. The amyloid fold, however, does not represent a unique minimum for a given single sequence. While the cross-βhydrogen-bonding pattern is common to all amyloids, other aspects of amyloid fiber structures are sensitive not only to the sequence of the aggregating peptides but also to the experimental conditions. This polymorphic nature of amyloid structures challenges structure predictions. In this paper, we use AI to explore the landscape of possible amyloid protofilament structures composed of a single stack of peptides aligned in a parallel, in-register manner. This perspective enables a practical method for predicting protofilament structures of arbitrary sequences: RibbonFold. RibbonFold is adapted from AlphaFold2, incorporating parallel in-register constraints within AlphaFold2’s template module, along with an appropriate polymorphism loss function to address the structural diversity of folds. RibbonFold outperforms AlphaFold2/3 on independent test sets, achieving a mean TM-score of 0.5. RibbonFold proves well-suited to study the polymorphic landscapes of widely studied sequences with documented polymorphisms. The resulting landscapes capture these observed polymorphisms effectively. We show that while well-known amyloid-forming sequences exhibit a limited number of plausible polymorphs on their “solubility” landscape, randomly shuffled sequences with the same composition appear to be negatively selected in terms of their relative solubility. RibbonFold is a valuable framework for structurally characterizing amyloid polymorphism landscapes. 

Chromatin is partially structured through the effects of biological motors. “Swimming motors” such as RNA polymerases and chromatin remodelers are thought to act differentially on the active parts of the genome and the stored inactive part. By systematically expanding the many-body master equation for chromosomes driven by swimming motors, we show that this nonuniform aspect of motorization leads to heterogeneously folded conformations, thereby contributing to chromosome compartmentalization. 

Electron transfer is at the heart of many fundamental physical, chemical, and biochemical processes essential for life. The exact simulation of these reactions is often hindered by the large number of degrees of freedom and by the essential role of quantum effects. Here, we experimentally simulate a paradigmatic model of molecular electron transfer using a multispecies trapped-ion crystal, where the donor-acceptor gap, the electronic and vibronic couplings, and the bath relaxation dynamics can all be controlled independently. By manipulating both the ground-state and optical qubits, we observe the real-time dynamics of the spin excitation, measuring the transfer rate in several regimes of adiabaticity and relaxation dynamics. Our results provide a testing ground for increasingly rich models of molecular excitation transfer processes that are relevant for molecular electronics and light-harvesting systems. 

An array of motor proteins consumes chemical energy in setting up the architectures of chromosomes. Here, we explore how the structure of ideal polymer chains is influenced by two classes of motors. The first class which we call “swimming motors” acts to propel the chromatin fiber through three-dimensional space. They represent a caricature of motors such as RNA polymerases. Previously, they have often been described by adding a persistent flow onto Brownian diffusion of the chain. The second class of motors, which we call “grappling motors” caricatures the loop extrusion processes in which segments of chromatin fibers some distance apart are brought together. We analyze these models using a self-consistent variational phonon approximation to a many-body Master equation incorporating motor activities. We show that whether the swimming motors lead to contraction or expansion depends on the susceptibility of the motors, that is, how their activity depends on the forces they must exert. Grappling motors in contrast to swimming motors lead to long-ranged correlations that resemble those first suggested for fractal globules and that are consistent with the effective interactions inferred by energy landscape analyses of Hi-C data on the interphase chromosome. 

Abstract While significant advances have been made in predicting static protein structures, the inherent dynamics of proteins, modulated by ligands, are crucial for understanding protein function and facilitating drug discovery. Traditional docking methods, frequently used in studying protein-ligand interactions, typically treat proteins as rigid. While molecular dynamics simulations can propose appropriate protein conformations, they’re computationally demanding due to rare transitions between biologically relevant equilibrium states. In this study, we present DynamicBind, a deep learning method that employs equivariant geometric diffusion networks to construct a smooth energy landscape, promoting efficient transitions between different equilibrium states. DynamicBind accurately recovers ligand-specific conformations from unbound protein structures without the need for holo-structures or extensive sampling. Remarkably, it demonstrates state-of-the-art performance in docking and virtual screening benchmarks. Our experiments reveal that DynamicBind can accommodate a wide range of large protein conformational changes and identify cryptic pockets in unseen protein targets. As a result, DynamicBind shows potential in accelerating the development of small molecules for previously undruggable targets and expanding the horizons of computational drug discovery. 

Proteins perform their biological functions through motion. Although high throughput prediction of the three-dimensional static structures of proteins has proved feasible using deep-learning-based methods, predicting the conformational motions remains a challenge. Purely data-driven machine learning methods encounter difficulty for addressing such motions because available laboratory data on conformational motions are still limited. In this work, we develop a method for generating protein allosteric motions by integrating physical energy landscape information into deep-learning-based methods. We show that local energetic frustration, which represents a quantification of the local features of the energy landscape governing protein allosteric dynamics, can be utilized to empower AlphaFold2 (AF2) to predict protein conformational motions. Starting from ground state static structures, this integrative method generates alternative structures as well as pathways of protein conformational motions, using a progressive enhancement of the energetic frustration features in the input multiple sequence alignment sequences. For a model protein adenylate kinase, we show that the generated conformational motions are consistent with available experimental and molecular dynamics simulation data. Applying the method to another two proteins KaiB and ribose-binding protein, which involve large-amplitude conformational changes, can also successfully generate the alternative conformations. We also show how to extract overall features of the AF2 energy landscape topography, which has been considered by many to be black box. Incorporating physical knowledge into deep-learning-based structure prediction algorithms provides a useful strategy to address the challenges of dynamic structure prediction of allosteric proteins. 

Protein folding and evolution are intimately linked phenomena. Here, we revisit the concept of exons as potential protein folding modules across a set of 38 abundant and conserved protein families. Taking advantage of genomic exon–intron organization and extensive protein sequence data, we explore exon boundary conservation and assess the foldon-like behavior of exons using energy landscape theoretic measurements. We found deviations in the exon size distribution from exponential decay indicating selection in evolution. We show that when taken together there is a pronounced tendency to independent foldability for segments corresponding to the more conserved exons, supporting the idea of exon–foldon correspondence. While 45% of the families follow this general trend when analyzed individually, there are some families for which other stronger functional determinants, such as preserving frustrated active sites, may be acting. We further develop a systematic partitioning of protein domains using exon boundary hotspots, showing that minimal common exons correspond with uninterrupted alpha and/or beta elements for the majority of the families but not for all of them. 

Protein evolution is guided by structural, functional, and dynamical constraints ensuring organismal viability. Pseudogenes are genomic sequences identified in many eukaryotes that lack translational activity due to sequence degradation and thus over time have undergone “devolution.” Previously pseudogenized genes sometimes regain their protein-coding function, suggesting they may still encode robust folding energy landscapes despite multiple mutations. We study both the physical folding landscapes of protein sequences corresponding to human pseudogenes using the Associative Memory, Water Mediated, Structure and Energy Model, and the evolutionary energy landscapes obtained using direct coupling analysis (DCA) on their parent protein families. We found that generally mutations that have occurred in pseudogene sequences have disrupted their native global network of stabilizing residue interactions, making it harder for them to fold if they were translated. In some cases, however, energetic frustration has apparently decreased when the functional constraints were removed. We analyzed this unexpected situation for Cyclophilin A, Profilin-1, and Small Ubiquitin-like Modifier 2 Protein. Our analysis reveals that when such mutations in the pseudogene ultimately stabilize folding, at the same time, they likely alter the pseudogenes’ former biological activity, as estimated by DCA. We localize most of these stabilizing mutations generally to normally frustrated regions required for binding to other partners. 

The ultimate regularity of quantum mechanics creates a tension with the assumption of classical chaos used in many of our pictures of chemical reaction dynamics. Out-of-time-order correlators (OTOCs) provide a quantum analog to the Lyapunov exponents that characterize classical chaotic motion. Maldacena, Shenker, and Stanford have suggested a fundamental quantum bound for the rate of information scrambling, which resembles a limit suggested by Herzfeld for chemical reaction rates. Here, we use OTOCs to study model reactions based on a double-well reaction coordinate coupled to anharmonic oscillators or to a continuum oscillator bath. Upon cooling, as one enters the tunneling regime where the reaction rate does not strongly depend on temperature, the quantum Lyapunov exponent can approach the scrambling bound and the effective reaction rate obtained from a population correlation function can approach the Herzfeld limit on reaction rates: Tunneling increases scrambling by expanding the state space available to the system. The coupling of a dissipative continuum bath to the reaction coordinate reduces the scrambling rate obtained from the early-time OTOC, thus making the scrambling bound harder to reach, in the same way that friction is known to lower the temperature at which thermally activated barrier crossing goes over to the low-temperature activationless tunneling regime. Thus, chemical reactions entering the tunneling regime can be information scramblers as powerful as the black holes to which the quantum Lyapunov exponent bound has usually been applied.