Expectation-Maximization of the Potential of Mean Force and Diffusion Coefficient in Langevin Dynamics from Single Molecule FRET Data Photon by Photon

The dynamics of a protein along a well-defined coordinate can be formally projected onto the form of an overdamped Lagevin equation. Here, we present a comprehensive statistical-learning framework for simultaneously quantifying the deterministic force (the potential of mean force, PMF) and the stochastic force (characterized by the diffusion coefficient, <i>D</i>) from single-molecule Förster-type resonance energy transfer (smFRET) experiments. The likelihood functional of the Langevin parameters, PMF and <i>D</i>, is expressed by a path integral of the latent smFRET distance that follows Langevin dynamics and realized by the donor and the acceptor photon emissions. The solution is made possible by an eigen decomposition of the time-symmetrized form of the corresponding Fokker–Planck equation coupled with photon statistics. To extract the Langevin parameters from photon arrival time data, we advance the expectation-maximization algorithm in statistical learning, originally developed for and mostly used in discrete-state systems, to a general form in the continuous space that allows for a variational calculus on the continuous PMF function. We also introduce the regularization of the solution space in this Bayesian inference based on a maximum trajectory-entropy principle. We use a highly nontrivial example with realistically simulated smFRET data to illustrate the application of this new method

Degree of Polymerization of Glucan Chains Shapes the Structure Fluctuations and Melting Thermodynamics of a Cellulose Microfibril

A Staggered LATtice (SLAT) model is developed for modeling cellulose microfibrils. The simple representation of molecular packing and interactions employed in SLAT allows simulations of structure fluctuations and phase transition of cellulose microfibrils at sufficiently long and large scales for comparison with experiments. Glucan chains in the microfibril are modeled as connected monomers, each corresponding to a cellobiose subunit, and the surrounding space around the cellulose is composed of solvent cells. Interaction parameters of monomer–monomer interactions were parametrized based on the results of atomistic molecular dynamics simulations. The monomer–solvent interaction was optimized to give a melting temperature of ∼695 K for the 36-glucan chain model cellulose microfibril, which is consistent with the estimation based on experimental data. Monte Carlo simulations of the SLAT model also capture experimentally measured X-ray diffraction patterns of cellulose as a function of temperature, including the region of melting transition, as well as predict the highly flexible regions in the microfibril. Beyond the diameter of ∼3 nm, we found that melting temperature of the cellulose microfibril is not significantly shifted by changing the thickness. On the other hand, a slight decrease in the degree of polymerization of glucan chains is shown to enhance structure fluctuations through the ends of glucan chains, i.e., the defect sites, and thereby significantly reduce the melting temperature. Analysis of the sizes, densities, and lifetimes of defect structures in the microfibril indicates a significant extent of fluctuations on the surfaces even at room temperature and that defect statistics are strong but distinct functions of temperature and solvent quality. The SLAT model is the first of its kind for simulating cellulosic materials, and this work shows that it can be used to incorporate information obtained from atomistic simulations and experimental data to enable the aforementioned findings through computation

Preferential Interactions between Lithium Chloride and Glucan Chains in <i>N</i>,<i>N</i>‑Dimethylacetamide Drive Cellulose Dissolution

Naturally occurring cellulose is crystalline as a consequence of the strong interactions between the glucan chains that comprise it and therefore is insoluble in most solvents. One of the few solvent systems able to dissolve cellulose is lithium chloride (LiCl) dissolved in <i>N</i>,<i>N</i>-dimethylacetamide (DMA). By an integrated application of all-atom molecular dynamics (MD) simulations, reaction path optimization, free-energy calculations, and a force-matching analysis of coarse-grained atomistic simulations, we establish that DMA-mediated preferential interactions of Li⁺ cations and Cl^– anions with glucan chains enable cellulose dissolution in LiCl/DMA. The relatively weak solvation of Li⁺, Cl^–, and glucan chains by DMA results in strong effective interactions of Li⁺ and Cl^– ions with the glucans, leading to cellulose dissolution. The small size of the Li⁺ cations allows them to strongly couple to multiple interaction sites on the glucan chains of cellulose, including the spatially restricted regions around the ether linkages connecting neighboring glucose residues. Li⁺ cations were thus identified as the main component responsible for driving cellulose dissolution. The mechanism for explaining the solubility of cellulose in the LiCl/DMA system deduced from the analysis of atomistic-scale simulations conducted in this work is also consistent with most of the empirical observations related to cellulose dissolution in salt/amide solvent systems

Endoglucanase Peripheral Loops Facilitate Complexation of Glucan Chains on Cellulose via Adaptive Coupling to the Emergent Substrate Structures

We examine how the catalytic domain of a glycoside hydrolase family 7 endoglucanase catalytic domain (Cel7B CD) facilitates complexation of cellulose chains from a crystal surface. With direct relevance to the science of biofuel production, this problem also represents a model system of biopolymer processing by proteins in Nature. Interactions of Cel7B CD with a cellulose microfibril along different paths of complexation are characterized by mapping the atomistic fluctuations recorded in free-energy simulations onto the parameters of a coarse-grain model. The resulting patterns of protein–biopolymer couplings also uncover the sequence signatures of the enzyme in peeling off glucan chains from the microfibril substrate. We show that the semiopen active site of Cel7B CD exhibits similar barriers and free energies of complexation over two distinct routes; namely, scooping of a chain into the active-site cleft and threading from the chain end into the channel. On the other hand, the complexation energetics strongly depends on the surface packing of the targeted chain and the resulting interaction sites with the enzyme. A revealed principle is that Cel7B CD facilitates cellulose deconstruction via adaptive coupling to the emergent substrate. The flexible, peripheral segments of the protein outside of the active-site cleft are able to accommodate the varying features of cellulose along the simulated paths of complexation. The general strategy of linking physics-based molecular interactions to protein sequence could also be helpful in elucidating how other protein machines process biopolymers

Endoglucanase Peripheral Loops Facilitate Complexation of Glucan Chains on Cellulose via Adaptive Coupling to the Emergent Substrate Structures

We examine how the catalytic domain of a glycoside hydrolase family 7 endoglucanase catalytic domain (Cel7B CD) facilitates complexation of cellulose chains from a crystal surface. With direct relevance to the science of biofuel production, this problem also represents a model system of biopolymer processing by proteins in Nature. Interactions of Cel7B CD with a cellulose microfibril along different paths of complexation are characterized by mapping the atomistic fluctuations recorded in free-energy simulations onto the parameters of a coarse-grain model. The resulting patterns of protein–biopolymer couplings also uncover the sequence signatures of the enzyme in peeling off glucan chains from the microfibril substrate. We show that the semiopen active site of Cel7B CD exhibits similar barriers and free energies of complexation over two distinct routes; namely, scooping of a chain into the active-site cleft and threading from the chain end into the channel. On the other hand, the complexation energetics strongly depends on the surface packing of the targeted chain and the resulting interaction sites with the enzyme. A revealed principle is that Cel7B CD facilitates cellulose deconstruction via adaptive coupling to the emergent substrate. The flexible, peripheral segments of the protein outside of the active-site cleft are able to accommodate the varying features of cellulose along the simulated paths of complexation. The general strategy of linking physics-based molecular interactions to protein sequence could also be helpful in elucidating how other protein machines process biopolymers

Endoglucanase Peripheral Loops Facilitate Complexation of Glucan Chains on Cellulose via Adaptive Coupling to the Emergent Substrate Structures

We examine how the catalytic domain of a glycoside hydrolase family 7 endoglucanase catalytic domain (Cel7B CD) facilitates complexation of cellulose chains from a crystal surface. With direct relevance to the science of biofuel production, this problem also represents a model system of biopolymer processing by proteins in Nature. Interactions of Cel7B CD with a cellulose microfibril along different paths of complexation are characterized by mapping the atomistic fluctuations recorded in free-energy simulations onto the parameters of a coarse-grain model. The resulting patterns of protein–biopolymer couplings also uncover the sequence signatures of the enzyme in peeling off glucan chains from the microfibril substrate. We show that the semiopen active site of Cel7B CD exhibits similar barriers and free energies of complexation over two distinct routes; namely, scooping of a chain into the active-site cleft and threading from the chain end into the channel. On the other hand, the complexation energetics strongly depends on the surface packing of the targeted chain and the resulting interaction sites with the enzyme. A revealed principle is that Cel7B CD facilitates cellulose deconstruction via adaptive coupling to the emergent substrate. The flexible, peripheral segments of the protein outside of the active-site cleft are able to accommodate the varying features of cellulose along the simulated paths of complexation. The general strategy of linking physics-based molecular interactions to protein sequence could also be helpful in elucidating how other protein machines process biopolymers

Endoglucanase Peripheral Loops Facilitate Complexation of Glucan Chains on Cellulose via Adaptive Coupling to the Emergent Substrate Structures

We examine how the catalytic domain of a glycoside hydrolase family 7 endoglucanase catalytic domain (Cel7B CD) facilitates complexation of cellulose chains from a crystal surface. With direct relevance to the science of biofuel production, this problem also represents a model system of biopolymer processing by proteins in Nature. Interactions of Cel7B CD with a cellulose microfibril along different paths of complexation are characterized by mapping the atomistic fluctuations recorded in free-energy simulations onto the parameters of a coarse-grain model. The resulting patterns of protein–biopolymer couplings also uncover the sequence signatures of the enzyme in peeling off glucan chains from the microfibril substrate. We show that the semiopen active site of Cel7B CD exhibits similar barriers and free energies of complexation over two distinct routes; namely, scooping of a chain into the active-site cleft and threading from the chain end into the channel. On the other hand, the complexation energetics strongly depends on the surface packing of the targeted chain and the resulting interaction sites with the enzyme. A revealed principle is that Cel7B CD facilitates cellulose deconstruction via adaptive coupling to the emergent substrate. The flexible, peripheral segments of the protein outside of the active-site cleft are able to accommodate the varying features of cellulose along the simulated paths of complexation. The general strategy of linking physics-based molecular interactions to protein sequence could also be helpful in elucidating how other protein machines process biopolymers

Endoglucanase Peripheral Loops Facilitate Complexation of Glucan Chains on Cellulose via Adaptive Coupling to the Emergent Substrate Structures

We examine how the catalytic domain of a glycoside hydrolase family 7 endoglucanase catalytic domain (Cel7B CD) facilitates complexation of cellulose chains from a crystal surface. With direct relevance to the science of biofuel production, this problem also represents a model system of biopolymer processing by proteins in Nature. Interactions of Cel7B CD with a cellulose microfibril along different paths of complexation are characterized by mapping the atomistic fluctuations recorded in free-energy simulations onto the parameters of a coarse-grain model. The resulting patterns of protein–biopolymer couplings also uncover the sequence signatures of the enzyme in peeling off glucan chains from the microfibril substrate. We show that the semiopen active site of Cel7B CD exhibits similar barriers and free energies of complexation over two distinct routes; namely, scooping of a chain into the active-site cleft and threading from the chain end into the channel. On the other hand, the complexation energetics strongly depends on the surface packing of the targeted chain and the resulting interaction sites with the enzyme. A revealed principle is that Cel7B CD facilitates cellulose deconstruction via adaptive coupling to the emergent substrate. The flexible, peripheral segments of the protein outside of the active-site cleft are able to accommodate the varying features of cellulose along the simulated paths of complexation. The general strategy of linking physics-based molecular interactions to protein sequence could also be helpful in elucidating how other protein machines process biopolymers

Structural basis for overhang excision and terminal unwinding of DNA duplexes by TREX1

<div><p>Three prime repair exonuclease 1 (TREX1) is an essential exonuclease in mammalian cells, and numerous in vivo and in vitro data evidenced its participation in immunity regulation and in genotoxicity remediation. In these very complicated cellular functions, the molecular mechanisms by which duplex DNA substrates are processed are mostly elusive because of the lack of structure information. Here, we report multiple crystal structures of TREX1 complexed with various substrates to provide the structure basis for overhang excision and terminal unwinding of DNA duplexes. The substrates were designed to mimic the intermediate structural DNAs involved in various repair pathways. The results showed that the Leu24-Pro25-Ser26 cluster of TREX1 served to cap the nonscissile 5′-end of the DNA for precise removal of the short 3′-overhang in L- and Y-structural DNA or to wedge into the double-stranded region for further digestion along the duplex. Biochemical assays were also conducted to demonstrate that TREX1 can indeed degrade double-stranded DNA (dsDNA) to a full extent. Overall, this study provided unprecedented knowledge at the molecular level on the enzymatic substrate processing involved in prevention of immune activation and in responses to genotoxic stresses. For example, Arg128, whose mutation in TREX1 was linked to a disease state, were shown to exhibit consistent interaction patterns with the nonscissile strand in all of the structures we solved. Such structure basis is expected to play an indispensable role in elucidating the functional activities of TREX1 at the cellular level and in vivo.</p></div

X-ray data collection and refinement statistics for TREX1-DNA complexes.

<p>dI, deoxyinosine; dsDNA, double-stranded DNA; Mg²⁺, magnesium ion; r.m.s, root-mean-square; ssDNA, single-stranded DNA; TREX1, three prime repair exonuclease 1.</p