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The extension of the 3D computational model presented sheds light on some questions about spindle assembly’s speed and accuracy, such as the effect of chromosome size, number, geometry, and polar ejection force.

Single-molecule force spectroscopy has become a powerful tool for the exploration of dynamic processes that involve proteins; yet, meaningful interpretation of the experimental data remains challenging. Owing to low signal-to-noise ratio, experimental force-extension spectra contain force signals due to nonspecific interactions, tip or substrate detachment, and protein desorption. Unravelling of complex protein structures results in the unfolding transitions of different types. Here, we test the performance of Support Vector Machines (SVM) and Expectation Maximization (EM) approaches in statistical learning from dynamic force experiments. When the output from molecular modeling in silico (or other studies) is used as a training set, SVM and EM can be applied to understand the unfolding force data. The maximal margin or maximum likelihood classifier can be used to separate experimental test observations into the unfolding transitions of different types, and EM optimization can then be utilized to resolve the statistics of unfolding forces: weights, average forces, and standard deviations. We designed an EM-based approach, which can be directly applied to the experimental data without data classification and division into training and test observations. This approach performs well even when the sample size is small and when the unfolding transitions are characterized by overlapping force ranges.

RNA oligonucleotides are crucial for a range of biological functions and in many biotechnological applications. Herein, we measured, for the first time, the conductance of individual double-stranded (ds)RNA molecules and compared it with the conductance of single DNA:RNA hybrids. The average conductance values are similar for both biomolecules, but the distribution of conductance values shows an order of magnitude higher variability for dsRNA, indicating higher molecular flexibility of dsRNA. Microsecond Molecular Dynamics simulations explain this difference and provide structural insights into the higher stability of DNA:RNA duplex with the atomic level of detail. The rotations of 2’-OH groups of the ribose rings and the bases in RNA strands destabilize the duplex structure by weakening base stacking interactions, affecting charge transport, and making single-molecule conductance of dsRNA more variable (dynamic disorder). The results demonstrate that a powerful combination of state-of-the-art biomolecular electronics techniques and computational approaches can provide valuable insights into biomolecules’ biophysics with unprecedented spatial resolution.

Fibrin polymerization involves thrombin-mediated exposure of knobs on one monomer that bind to holes available on another, leading to the formation of fibers. In silico evidence has suggested that the classical A:a knob-hole interaction is enhanced by surrounding residues not directly involved in the binding pocket of hole a, via noncovalent interactions with knob A. We assessed the importance of extended knob-hole interactions by performing biochemical, biophysical, and in silico modeling studies on recombinant human fibrinogen variants with mutations at residues responsible for the extended interactions. Three single fibrinogen variants, γD297N, γE323Q, and γK356Q, and a triple variant γDEK (γD297N/γE323Q/γK356Q) were produced in a CHO (Chinese Hamster Ovary) cell expression system. Longitudinal protofibril growth probed by atomic force microscopy was disrupted for γD297N and enhanced for the γK356Q mutation. Initial polymerization rates were reduced for all variants in turbidimetric studies. Laser scanning confocal microscopy showed that γDEK and γE323Q produced denser clots, whereas γD297N and γK356Q were similar to wild type. Scanning electron microscopy and light scattering studies showed that fiber thickness and protofibril packing of the fibers were reduced for all variants. Clot viscoelastic analysis showed that only γDEK was more readily deformable. In silico modeling suggested that most variants displayed only slip-bond dissociation kinetics compared with biphasic catch-slip kinetics characteristics of wild type. These data provide new evidence for the role of extended interactions in supporting the classical knob-hole bonds involving catch-slip behavior in fibrin formation, clot structure, and clot mechanics.

We introduce a Stochastic Reaction-Diffusion-Dynamics Model (SRDDM) for simulations of cellular mechanochemical processes with high spatial and temporal resolution. The SRDDM is mapped into the CellDynaMo package, which couples the spatially inhomogeneous reaction-diffusion master equation to account for biochemical reactions and molecular transport within the Langevin Dynamics (LD) framework to describe dynamic mechanical processes. This computational infrastructure allows the simulation of hours of molecular machine dynamics in reasonable wall-clock time. We apply SRDDM to test performance of the Search-and-Capture of mitotic spindle assembly by simulating, in three spatial dimensions, dynamic instability of elastic microtubules anchored in two centrosomes, movement and deformations of geometrically realistic centromeres with flexible kinetochores and chromosome arms. Furthermore, the SRDDM describes the mechanics and kinetics of Ndc80 linkers mediating transient attachments of microtubules to the chromosomal kinetochores. The rates of these attachments and detachments depend upon phosphorylation states of the Ndc80 linkers, which are regulated in the model by explicitly accounting for the reactions of Aurora A and B kinase enzymes undergoing restricted diffusion. We find that there is an optimal rate of microtubule-kinetochore detachments which maximizes the accuracy of the chromosome connections, that adding chromosome arms to kinetochores improve the accuracy by slowing down chromosome movements, that Aurora A and kinetochore deformations have a small positive effect on the attachment accuracy, and that thermal fluctuations of the microtubules increase the rates of kinetochore capture and also improve the accuracy of spindle assembly.

Structural mechanisms underlying the mechanical properties of fibrin fibers are elusive. We combined tensile testing of uncrosslinked fibrin polymers in vitro and in silico to explore their material properties. The experimental stress ( σ ) – strain ( e ) curves for fibrin fibers are characterized by elastic deformations with a weaker elastic response for e e >160% owing to unfolding of the coiled coils and γ nodules in fibrin monomers. Fiber rupture for strains e >212% is due to dissociation of the knob-hole bonds and rupture of D:D interfaces. We developed the Fluctuating Bilinear Spring model to interpret the σ − e profiles in terms of the free energy for protofibril alignment Δ G 0 = 10.1–11.5 k B T, Young's moduli for protofibril alignment Y u = 1.9-3.2 MPa and stretching Y a = 5.7–9.7 MPa, strain scale e ˜ ≈ 12–40% for fiber rupture, and protofibril cooperativity m = 3.6–8. We applied the model to characterize the fiber strength σ c r ≈ 12-13 MPa, deformability e c r ≈ 222%, and rupture toughness U ≈ 9 MJ/m3, and to resolve thermodynamic state functions, 96.9 GJ/mol entropy change for protofibril alignment (at room temperature) and 113.6 GJ/mol enthalpy change for protofibril stretching, which add up to 210.5 GJ/mol free-energy change. Fiber elongation is associated with protofibril dehydration and sliding mechanism to create an ordered protofibril array. Fibrin fibers behave like a hydrogel; protofibril dehydration and water expulsion account for ∼94-98% of the total free-energy changes for fiber elongation and rupture. Statement of significance Structural mechanisms underlying the mechanical properties of fibrin fibers, major components of blood clots and obstructive thrombi, are elusive. We performed tensile testing of uncrosslinked fibrin polymers in vitro and in silico to explore their material properties. Fluctuating Bilinear Spring theory was developed to interpret the stress-strain profiles in terms of the energy for protofibril alignment, elastic moduli for protofibril alignment and stretching, and strain scale for fiber rupture, and to probe the limits of fiber strength, extensibility and toughness. Fibrin fibers behave like a hydrogel. Fiber elongation is defined by the protofibril dehydration and sliding. Structural rearrangements in water matrix control fiber elasticity. These results contribute to fundamental understanding of blood clot breakage that underlies thrombotic embolization.

Fibrin is the major determinant of the mechanical stability and integrity of blood clots and thrombi. To explore the rupture of blood clots, emulating thrombus breakage, we stretched fibrin gels with single-edge cracks of varying size. Ultrastructural alterations of the fibrin network correlated with three regimes of stress vs. strain profiles: the weakly non-linear regime due to alignment of fibrin fibers; linear regime owing to further alignment and stretching of fibers; and the rupture regime for large deformations reaching the critical strain and stress, at which irreversible breakage of fibers ahead of the crack tip occurs. To interpret the stress-strain curves, we developed a new Fluctuating Spring model, which maps the fibrin alignment at the characteristic strain, network stretching with the Young modulus, and simultaneous cooperative rupture of coupled fibrin fibers into a theoretical framework to obtain the closed-form expressions for the strain-dependent stress profiles. Cracks render network rupture stochastic, and the free energy change for fiber deformation and rupture decreases with the crack length, making network rupture more spontaneous. By contrast, mechanical cooperativity due to the presence of inter-fiber contacts strengthens fibrin networks. The results obtained provide a fundamental understanding of blood clot breakage that underlies thrombotic embolization. STATEMENT OF SIGNIFICANCE: Fibrin, a naturally occurring biomaterial, is the major determinant of mechanical stability and integrity of blood clots and obstructive thrombi. We tested mechanically fibrin gels with single-edge cracks and followed ultrastructural alterations of the fibrin network. Rupture of fibrin gel involves initial alignment and elastic stretching of fibers followed by their eventual rupture for deformations reaching the critical level. To interpret the stress-strain curves, we developed Fluctuating Spring model, which showed that cracks render rupture of fibrin networks more spontaneous; yet, coupled fibrin fibers reinforce cracked fibrin networks. The results obtained provide fundamental understanding of blood clot breakage that underlies thrombotic embolization. Fluctuating Spring model can be applied to other protein networks with cracks and to interpret the stress-strain profiles.

We developed the Fluctuating Nonlinear Spring (FNS) model to describe the dynamics of mechanical deformation of biological particles, such as virus capsids. The theory interprets the force-deformation spectra in terms of the "Hertzian stiffness" (non-linear regime of a particle's small-amplitude deformations), elastic constant (large-amplitude elastic deformations), and force range in which the particle's fracture occurs. The FNS theory enables one to quantify the particles' elasticity (Young's moduli for Hertzian and bending deformations), and the limits of their strength (critical forces, fracture toughness) and deformability (critical deformations) as well as the probability distributions of these properties, and to calculate the free energy changes for the particle's Hertzian, elastic, and plastic deformations, and eventual fracture. We applied the FNS theory to describe the protein capsids of bacteriophage P22, Human Adenovirus, and Herpes Simplex virus characterized by deformations before fracture that did not exceed 10-19% of their size. These nanoshells are soft (~1-10-GPa elastic modulus), with low ~50-480-kPa toughness - a regime of material behavior that is not well understood, and with the strength increasing while toughness decreases with their size. The particles' fracture is stochastic, with the average values of critical forces, critical deformations, and fracture toughness comparable with their standard deviations. The FNS theory predicts 0.7-MJ/mol free energy for P22 capsid maturation, and it could be extended to describe uniaxial deformation of cylindrical microtubules and ellipsoidal cellular organelles.

Development of antidotes against botulism requires understanding of the enzymatically active conformations of Botulinum neurotoxin serotype A (BoNT/A) light chain (LCA). We performed small angle X-ray scattering (SAXS) to characterize the solution structures of truncated light chain (tLCA). The 34-37 A radius of gyration of tLCA was 1.5-times greater than the averaged 22-23-A radius from the crystal structures. The bimodal distribution of interatomic distances P(r) indicated the two-domain tLCA structure with 129-133 A size, and Kratky plots indicated the tLCA partial unfolding in the 25-37 °C temperature range. To interpret these data, we employed molecular dynamics simulations and machine learning. Excellent agreement between experimental and theoretical P(r) profiles helped to resolve conformational subpopulations of tLCA in solution. Partial unfolding of the C-terminal portion of tLCA (residues 339-425) results in formation of extended conformations with the larger globular domain (residues 2-298) and the smaller unstructured domain (339-425). The catalytic domain, buried 20 A-deep inside the crystal structure, becomes accessible in extended solution conformations (8-9 A deep). The C- and N-termini containing different functional sequence motifs are maximally separated in the extended conformations. Our results offer physical insights into the molecular basis of BoNT/A function and stress the importance of reversible unfolding-refolding transitions and hydrophobic interactions.

Fibrin is the major extracellular component of blood clots and a proteinaceous hydrogel used as a versatile biomaterial. Fibrin forms branched networks of polymeric fibers, built of laterally associated double-stranded protofibrils. This multiscale hierarchical structure is crucial for the extraordinary mechanical resilience of blood clots. Yet, the structural basis of clot mechanical properties remains largely unclear due, in part, to the unresolved molecular packing structure of fibrin fibers. Here we quantitatively assess the packing structure of fibrin fibers by combining Small Angle X-ray Scattering (SAXS) measurements of fibrin networks reconstituted under a wide range of conditions with computational molecular modeling of fibrin oligomers. The number, positions, and intensities of the Bragg peaks observed in the SAXS experiments were reproduced computationally based on the all-atom molecular structure of reconstructed fibrin protofibrils. Specifically, the model correctly predicts the intensities of the reflections of the 22.5 nm axial repeat, corresponding to the half-staggered longitudinal arrangement of fibrin molecules. In addition, the SAXS measurements showed that protofibrils within fibrin fibers have a partially ordered lateral arrangement with a characteristic transverse repeat distance of 13 nm, irrespective of the fiber thickness. These findings provide fundamental insights into the molecular structure of fibrin clots that underlies their biological and physical properties.

Fibrin formation and mechanical stability are essential in thrombosis and hemostasis. To reveal how mechanical load impacts fibrin, we carried out optical trap-based single-molecule forced unbinding experiments. The strength of noncovalent A:a knob-hole bond stabilizing fibrin polymers first increases with tensile force (catch bonds) and then decreases with force when the force exceeds a critical value (slip bonds). To provide the structural basis of catch–slip-bond behavior, we analyzed crystal structures and performed molecular modeling of A:a knob-hole complex. The movable flap (residues [Formula: see text] 295 to [Formula: see text] 305) containing the weak calcium-binding site [Formula: see text] 2 serves as a tension sensor. Flap dissociation from the B domain in the [Formula: see text]-nodule and translocation to knob ‘A’ triggers hole ‘a’ closure, resulting in the increase of binding affinity and prolonged bond lifetimes. The discovery of biphasic kinetics of knob-hole bond rupture is quantitatively explained by using a theory, formulated in terms of structural transitions in the binding pocket between the low-affinity (slip) and high-affinity (catch) states. We provide a general framework to understand the mechanical response of protein pairs capable of tension-induced remodeling of their association interface. Strengthening of the A:a knob-hole bonds at 30- to 40-pN forces might favor formation of nascent fibrin clots subject to hydrodynamic shear in vivo.

We carried out dynamic force manipulations in silico on a variety of coiled-coil protein fragments from myosin, chemotaxis receptor, vimentin, fibrin, and phenylalanine zippers that vary in size and topology of their α-helical packing. When stretched along the superhelical axis, all superhelices show elastic, plastic, and inelastic elongation regimes and undergo a dynamic transition from the α-helices to the β-sheets, which marks the onset of plastic deformation. Using the Abeyaratne-Knowles formulation of phase transitions, we developed a new theoretical methodology to model mechanical and kinetic properties of protein coiled-coils under mechanical nonequilibrium conditions and to map out their energy landscapes. The theory was successfully validated by comparing the simulated and theoretical force-strain spectra. We derived the scaling laws for the elastic force and the force for α-to-β transition, which can be used to understand natural proteins' properties as well as to rationally design novel biomaterials of required mechanical strength with desired balance between stiffness and plasticity.

Background A natural product analog, 3-(4-nitrophenyl)-7H-furo[3,2-g]chromen-7-one, which is a nitrophenyl psoralen (NPP) was found to be an effective inhibitor of botulinum neurotoxin type A (BoNT/A). Methods In this work, we performed enzyme inhibition kinetics and employed biochemical techniques such as isothermal calorimetry (ITC) and fluorescence spectroscopy as well as molecular modeling to examine the kinetics and binding mechanism of NPP inhibitor with BoNT/A LC. Results Studies of inhibition mechanism and binding dynamics of NPP to BoNT/A light chain (BoNT/A LC) showed that NPP is a mixed type inhibitor for the zinc endopeptidase activity, implying that at least part of the inhibitor-enzyme binding site may be different from the substrate-enzyme binding site. By using biochemical techniques, we demonstrated NPP forms a stable complex with BoNT/A LC. These observations were confirmed by Molecular Dynamics (MD) simulation, which demonstrates that NPP binds to the site near the active site. Conclusion The NPP binding interferes with BoNT/A LC binding to the SNAP-25, hence, inhibits its cleavage. Based on these results, we propose a modified strategy for designing a molecule to enhance the efficiency of the inhibition against the neurotoxic effect of BoNT. General significance Insights into the interactions of NPP with BoNT/A LC using biochemical and computational approaches will aid in the future development of effective countermeasures and better pharmacological strategies against botulism.

We studied the hydrodynamic behavior of fibrinogen, a blood plasma protein involved in blood clotting, in a broad 0.3–60 mg/mL range of concentration and 5–42 °C temperature using pulsed-field gradient 1H NMR-diffusometry. Arrhenius plots revealed the activation energy for fibrinogen diffusion Ed = 21.3 kJ/mol at 1.4 mg/mL and 28.4 kJ/mol at 38 mg/mL. We found a dramatic slowdown in fibrinogen self-diffusion with concentration beginning at 1.7–3.4 mg/mL, which deviated from the standard hard-particle behavior, suggesting a remarkable intermolecular entanglement. This concentration dependence was observed regardless of the absence or presence of the GPRP peptide (inhibitor of fibrin polymerization), and also in samples free of fibrin oligomers. By contrast, diffusivity of fibrinogen variant I-9 with truncated C-terminal portions of the Aα chains was much less concentration-dependent, indicating the importance of intermolecular linkages formed by the αC regions. Theoretical models combined with all-atom mol...

Fibrin is a filamentous network made in blood to stem bleeding; it forms when fibrinogen is converted into fibrin monomers that self-associate into oligomers and then to polymers. To gather structural insights into fibrin formation and properties, we combined high-resolution atomic force microscopy of fibrin(ogen) oligomers and molecular modeling of crystal structures of fibrin(ogen) and its fragments. We provided a structural basis for the intermolecular flexibility of single-stranded fibrin(ogen) oligomers and identified a hinge region at the D:D inter-monomer junction. Following computational reconstruction of the missing portions, we recreated the full-atomic structure of double-stranded fibrin oligomers that was validated by quantitative comparison with the experimental images. We characterized previously unknown intermolecular binding contacts at the D:D and D:E:D interfaces, which drive oligomerization and reinforce the intra- and inter-strand connections in fibrin besides the known knob-hole bonds. The atomic models provide valuable insights into the submolecular mechanisms of fibrin polymerization.

Summary The space-filling fibrin network is a major part of clots and thrombi formed in blood. Fibrin polymerization starts when fibrinogen, a plasma protein, is proteolytically converted to fibrin, which self-assembles to form double-stranded protofibrils. When reaching a critical length, these intermediate species aggregate laterally to transform into fibers arranged into branched fibrin network. We combined multiscale modeling in silico with atomic force microscopy (AFM) imaging to reconstruct complete atomic models of double-stranded fibrin protofibrils with γ-γ crosslinking, A:a and B:b knob-hole bonds, and αC regions—all important structural determinants not resolved crystallographically. Structures of fibrin oligomers and protofibrils containing up to 19 monomers were successfully validated by quantitative comparison with high-resolution AFM images. We characterized the protofibril twisting, bending, kinking, and reversibility of A:a knob-hole bonds, and calculated hydrodynamic parameters of fibrin oligomers. Atomic structures of protofibrils provide a basis to understand mechanisms of early stages of fibrin polymerization.

Microtubules are found in most eukaryotic cells, with homologs in eubacteria and archea, and they have functional roles in mitosis, cell motility, intracellular transport, and the maintenance of cell shape. Numerous efforts have been expended over the last two decades to characterize the interactions between microtubules and the wide variety of microtubule associated proteins that control their dynamic behavior in cells resulting in microtubules being assembled and disassembled where and when they are required by the cell. We present the main findings regarding microtubule polymerization and depolymerization and review recent work about the molecular motors that modulate microtubule dynamics by inducing either microtubule depolymerization or severing. We also discuss the main experimental and computational approaches used to quantify the thermodynamics and mechanics of microtubule filaments.

Binding of soluble fibrinogen to the activated conformation of the integrin αIIbβ3 is required for platelet aggregation and is mediated exclusively by the C-terminal AGDV-containing dodecapeptide (γC-12) sequence of the fibrinogen γ chain. However, peptides containing the Arg-Gly-Asp (RGD) sequences located in two places in the fibrinogen Aα chain inhibit soluble fibrinogen binding to αIIbβ3 and make substantial contributions to αIIbβ3 binding when fibrinogen is immobilized and when it is converted to fibrin. Here, we employed optical trap-based nanomechanical measurements and computational molecular modeling to determine the kinetics, energetics, and structural details of cyclic RGDFK (cRGDFK) and γC-12 binding to αIIbβ3. Docking analysis revealed that NMR-determined solution structures of cRGDFK and γC-12 bind to both the open and closed αIIbβ3 conformers at the interface between the αIIb β-propeller domain and the β3 βI domain. The nanomechanical measurements revealed that cRGDFK binds to αIIbβ3 at least as tightly as γC-12. A subsequent analysis of molecular force profiles and the number of peptide-αIIbβ3 binding contacts revealed that both peptides form stable bimolecular complexes with αIIbβ3 that dissociate in the 60-120 pN range. The Gibbs free energy profiles of the αIIbβ3-peptide complexes revealed that the overall stability of the αIIbβ3-cRGDFK complex was comparable with that of the αIIbβ3-γC-12 complex. Thus, these results provide a mechanistic explanation for previous observations that RGD- and AGDV-containing peptides are both potent inhibitors of the αIIbβ3-fibrinogen interactions and are consistent with the observation that RGD motifs, in addition to AGDV, support interaction of αIIbβ3 with immobilized fibrinogen and fibrin.

The transition from -helices to -strands under external mechanical force in fibrin molecule containing coiled-coils is studied and free energy landscape is resolved. The detailed theoretical modeling of each stage of coiled-coils fragment pulling process was performed. The plots of force (F) as a function of molecule expansion (X) for two symmetrical fibrin coiled-coils (each 17 nm in length) show three distinct modes of mechanical behaviour: (1) linear (elastic) mode when coiled-coils behave like entropic springs (F100-125 pN and X7-8 nm), (2) viscous (plastic) mode when molecule resistance force does not increase with increase in elongation length (F150 pN and X10-35 nm) and (3) nonlinear mode (F175-200 pN and X40-50 nm). In linear mode the coiled-coils unwind at 2 radian angle, but no structural transition occurs. Viscous mode is characterized by the phase transition from the triple -spirals to three-stranded parallel -sheet. The critical tension of -helices is 0.25 nm per turn, and the characteristic energy change is equal to 4.9 kcal/mol. Changes in internal energy u, entropy s and force capacity cf per one helical turn for phase transition were also computed. The observed dynamic behavior of -helices and phase transition from -helices to -sheets under tension might represent a universal mechanism of regulation of fibrillar protein structures subject to mechanical stresses due to biological forces.

Hydrodynamic interactions (HI) are incorporated into Langevin dynamics of the Cα‐based protein model using the Truncated Expansion approximation (TEA) to the Rotne–Prager–Yamakawa diffusion tensor. Computational performance of the obtained GPU realization demonstrates the model's capability for describing protein systems of varying complexity (102–105 residues), including biological particles (filaments, virus shells). Comparison of numerical accuracy of the TEA versus exact description of HI reveals similar results for the kinetics and thermodynamics of protein unfolding. The HI speed up and couple biomolecular transitions through cross‐communication among protein domains, which result in more collective displacements of structure elements governed by more deterministic (less variable) dynamics. The force‐extension/deformation spectra from nanomanipulations in silico exhibit sharper force signals that match well the experimental profiles. Hence, biomolecular simulations without HI overestimate the role of tension/stress fluctuations. Our findings establish the importance of incorporating implicit water‐mediated many‐body effects into theoretical modeling of dynamic processes involving biomolecules. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

Using a combined experimental and theoretical approach named binding-unbinding correlation spectroscopy (BUCS), we describe the two-dimensional kinetics of interactions between fibrinogen and the integrin αIIbβ3, the ligand-receptor pair essential for platelet function during hemostasis and thrombosis. The methodology uses the optical trap to probe force-free association of individual surface-attached fibrinogen and αIIbβ3 molecules and forced dissociation of an αIIbβ3-fibrinogen complex. This novel approach combines force clamp measurements of bond lifetimes with the binding mode to quantify the dependence of the binding probability on the interaction time. We found that fibrinogen-reactive αIIbβ3 pre-exists in at least two states that differ in their zero force on-rates (k(on1) = 1.4 × 10(-4) and k(on2) = 2.3 × 10(-4) μm(2)/s), off-rates (k(off1) = 2.42 and k(off2) = 0.60 s(-1)), and dissociation constants (K(d)(1) = 1.7 × 10(4) and K(d)(2) = 2.6 × 10(3) μm(-2)). The integrin activator Mn(2+) changed the on-rates and affinities (K(d)(1) = 5 × 10(4) and K(d)(2) = 0.3 × 10(3) μm(-2)) but did not affect the off-rates. The strength of αIIbβ3-fibrinogen interactions was time-dependent due to a progressive increase in the fraction of the high affinity state of the αIIbβ3-fibrinogen complex characterized by a faster on-rate. Upon Mn(2+)-induced integrin activation, the force-dependent off-rates decrease while the complex undergoes a conformational transition from a lower to higher affinity state. The results obtained provide quantitative estimates of the two-dimensional kinetic rates for the low and high affinity αIIbβ3 and fibrinogen interactions at the single molecule level and offer direct evidence for the time- and force-dependent changes in αIIbβ3 conformation and ligand binding activity, underlying the dynamics of fibrinogen-mediated platelet adhesion and aggregation.

Due to the very long timescales involved (ms-s), theoretical modeling of fundamental biological processes including folding, misfolding, and mechanical unraveling of biomolecules, under physiologically relevant conditions, is challenging even for distributed computing systems. Graphics Processing Units (GPUs) are emerging as an alternative programming platform to the more traditional CPUs as they provide high raw computational power that can be utilized in a wide range of scientific applications. Using a coarse-grained Self Organized Polymer (SOP) model, we have developed and tested the GPU-based implementation of Langevin simulations for proteins (SOP-GPU program). Simultaneous calculation of forces for all particles is implemented using either the particle based or the interacting pair based parallelization, which leads to a ∼90-fold acceleration compared to an optimized CPU version of the program. We assess the computational performance of an end-to-end application of the SOP-GPU program, where all steps of the algorithm are running on the GPU, by profiling the associated simulation time and memory usage for a number of small proteins, long protein fibers, and large-size protein assemblies. The SOP-GPU package can now be used in the theoretical exploration of the mechanical properties of large-size protein systems to generate the force-extension and force-indentation profiles under the experimental conditions of force application, and to relate the results of singlemolecule experiments in vitro and in silico.

Large-size biomolecular systems that spontaneously assemble, disassemble, and self-repair by controlled inputs play fundamental roles in biology. Microtubules (MTs), which play important roles in cell adhesion and cell division, are a prime example. MTs serve as ″tracks″ for molecular motors, and their biomechanical functions depend on dynamic instability-a stochastic switching between periods of rapid growing and shrinking. This process is controlled by many cellular factors so that growth and shrinkage periods are correlated with the life cycle of a cell. Resolving the molecular basis for the action of these factors is of paramount importance for understanding the diverse functions of MTs. We employed a multiscale modeling approach to study the force-induced MT depolymerization by analyzing the mechanical response of a MT protofilament to external forces. We carried out self-organized polymer (SOP) model based simulations accelerated on Graphics Processing Units (GPUs). This approach enabled us to follow the mechanical behavior of the molecule on experimental time scales using experimental force loads. We resolved the structural details and determined the physical parameters that characterize the stretching and bending modes of motion of a MT protofilament. The central result is that the severing action of proteins, such as katanin and kinesin, can be understood in terms of their mechanical coupling to a protofilament. For example, the extraction of tubulin dimers from MT caps by katanin can be achieved by pushing the protofilament toward the axis of the MT cylinder, while the removal of large protofilaments curved into ″ram's horn″ structures by kinesin is the result of the outward bending of the protofilament. We showed that, at the molecular level, these types of deformations are due to the anisotropic, but homogeneous, micromechanical properties of MT protofilaments.

Dynamic force spectroscopy has become indispensable for the exploration of the mechanical properties of proteins. In force-ramp experiments, performed by utilizing a time-dependent pulling force, the peak forces for unfolding transitions in a multimeric protein (D)(N) are used to map the free energy landscape for unfolding for a protein domain D. We show that theoretical modeling of unfolding transitions based on combining the observed first (f(1)), second (f(2)), …, N(th) (f(N)) unfolding forces for a protein tandem of fixed length N, and pooling the force data for tandems of different length, n(1)n(2)…N, leads to an inaccurate estimation of the distribution of unfolding forces for the protein D, ψ(D)(f). This problem can be overcome by using Order statistics theory, which, in conjunction with analytically tractable models, can be used to resolve the molecular characteristics that determine the unfolding micromechanics. We present a simple method of estimation of the parent distribution, ψ(D)(f), based on analyzing the force data for a tandem (D)(n) of arbitrary length n. Order statistics theory is exemplified through a detailed analysis and modeling of the unfolding forces obtained from pulling simulations of the monomer and oligomers of the all-β-sheet WW domain.

Theoretical exploration of fundamental biological processes involving the forced unraveling of multimeric proteins, the sliding motion in protein fibers and the mechanical deformation of biomolecular assemblies under physiological force loads is challenging even for distributed computing systems. Using a C(α)-based coarse-grained self organized polymer (SOP) model, we implemented the Langevin simulations of proteins on graphics processing units (SOP-GPU program). We assessed the computational performance of an end-to-end application of the program, where all the steps of the algorithm are running on a GPU, by profiling the simulation time and memory usage for a number of test systems. The ∼90-fold computational speedup on a GPU, compared with an optimized central processing unit program, enabled us to follow the dynamics in the centisecond timescale, and to obtain the force-extension profiles using experimental pulling speeds (v(f) = 1-10 μm/s) employed in atomic force microscopy and in optical tweezers-based dynamic force spectroscopy. We found that the mechanical molecular response critically depends on the conditions of force application and that the kinetics and pathways for unfolding change drastically even upon a modest 10-fold increase in v(f). This implies that, to resolve accurately the free energy landscape and to relate the results of single-molecule experiments in vitro and in silico, molecular simulations should be carried out under the experimentally relevant force loads. This can be accomplished in reasonable wall-clock time for biomolecules of size as large as 10(5) residues using the SOP-GPU package.

A new computational methodology for the accurate numerical calculation of the Cauchy stress tensor, stress invariants, principal stress components, von Mises and Tresca tensors is developed. The methodology is based on the atomic stress approach which permits the calculation of stress tensors, widely used in continuum mechanics modeling of materials properties, using the output from the MD simulations of discrete atomic and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}\end{document}Cα-based coarse-grained structural models of biological particles. The methodology mapped into the software package TensorCalculator was successfully applied to the empty cowpea chlorotic mottle virus (CCMV) shell to explore the evolution of mechanical stress in this mechanically-tested specific example of a soft virus capsid. We found an inhomogeneous stress distribution in various portions of the CCMV structure and stress transfer from one portion of the virus structure to another, which also points to the importance of entropic effects, often ignored in finite element analysis and elastic network modeling. We formulate a criterion for elastic deformation using the first principal stress components. Furthermore, we show that von Mises and Tresca stress tensors can be used to predict the onset of a viral capsid’s mechanical failure, which leads to total structural collapse. TensorCalculator can be used to study stress evolution and dynamics of defects in viral capsids and other large-size protein assemblies.

Microtubules, the primary components of the chromosome segregation machinery, are stabilized by longitudinal and lateral non-covalent bonds between the tubulin subunits. However, the thermodynamics of these bonds and the microtubule physico-chemical properties are poorly understood. Here, we explore the biomechanics of microtubule polymers using multiscale computational modeling and nanoindentations in silico of a contiguous microtubule fragment. A close match between the simulated and experimental force-deformation spectra enabled us to correlate the microtubule biomechanics with dynamic structural transitions at the nanoscale. Our mechanical testing revealed that the compressed MT behaves as a system of rigid elements interconnected through a network of lateral and longitudinal elastic bonds. The initial regime of continuous elastic deformation of the microtubule is followed by the transition regime, during which the microtubule lattice undergoes discrete structural changes, which include first the reversible dissociation of lateral bonds followed by irreversible dissociation of the longitudinal bonds. We have determined the free energies of dissociation of the lateral (6.9+/-0.4 kcal/mol) and longitudinal (14.9+/-1.5 kcal/mol) tubulin-tubulin bonds. These values in conjunction with the large flexural rigidity of tubulin protofilaments obtained (18,000-26,000 pN*nm^2), support the idea that the disassembling microtubule is capable of generating a large mechanical force to move chromosomes during cell division. Our computational modeling offers a comprehensive quantitative platform to link molecular tubulin characteristics with the physiological behavior of microtubules. The developed in silico nanoindentation method provides a powerful tool for the exploration of biomechanical properties of other cytoskeletal and multiprotein assemblies

Physical properties of capsids of plant and animal viruses are important factors in capsid self-assembly, survival of viruses in the extracellular environment, and their cell infectivity. Combined AFM experiments and computational modeling on subsecond timescales of the indentation nanomechanics of Cowpea Chlorotic Mottle Virus capsid show that the capsid's physical properties are dynamic and local characteristics of the structure, which change with the depth of indentation and depend on the magnitude and geometry of mechanical input. Under large deformations, the Cowpea Chlorotic Mottle Virus capsid transitions to the collapsed state without substantial local structural alterations. The enthalpy change in this deformation state Delta H-ind =11.5-12.8 MJ/mol is mostly due to large-amplitude out-of-plane excitations, which contribute to the capsid bending; the entropy change T Delta S-ind = 5.1-5.8 MJ/mol is due to coherent in-plane rearrangements of protein chains, which mediate the capsid stiffening. Direct coupling of these modes defines the extent of (ir)reversibility of capsid indentation dynamics correlated with its (in)elastic mechanical response to the compressive force. This emerging picture illuminates how unique physico-chemical properties of protein nanoshells help define their structure and morphology, and determine their viruses' biological function.

Atomic force measurements of unbinding rates (or off-rates) of ligands bound to a class of cell adhesion molecules from the selectin family show a transition from catch to slip bonds as the value of external force (f) is increased. At low forces (

Very short hydrogen bonds universally show large positive dependences of the deuterium NMR quadrupolar coupling constant with temperature. We present temperature dependent NMR data for eight such systems, with O⋯O distances of between 238 and 250 pm, and show we can model the temperature dependences by density functional methods, as long as proper attention is paid to intermolecular effects and intermode couplings.

The unbinding dynamics of complexes involving cell-adhesion molecules depends on the specific ligands. Atomic force microscopy measurements have shown that for the specific P-selectin–P-selectin glycoprotein ligand (sPSGL-1) the average bond lifetime 〈 t 〉 initially increases (catch bonds) at low (≤10 pN) constant force, f , and decreases when f > 10 pN (slip bonds). In contrast, for the complex with G1 anti-P-selectin monoclonal antibody 〈 t 〉 monotonically decreases with f . To quantitatively map the energy landscape of such complexes we use a model that considers the possibility of redistribution of population from one force-free state to another force-stabilized bound state. The excellent agreement between theory and experiments allows us to extract energy landscape parameters by fitting the calculated curves to the lifetime measurements for both sPSGL-1 and G1. Surprisingly, the unbinding transition state for P-selectin–G1 complex is close (0.32 nm) to the bound state, implying that the interaction is brittle, i.e., once deformed, the complex fractures. In contrast, the unbinding transition state of the P-selectin–sPSGL-1 complex is far (≈ 1.5 nm) from the bound state, indicative of a compliant structure. Constant f energy landscape parameters are used to compute the distributions of unbinding times and unbinding forces as a function of the loading rate, r f . For a given r f , unbinding of sPSGL-1 occurs over a broader range of f with the most probable f being an order of magnitude less than for G1. The theory for cell adhesion complexes can be used to predict the outcomes of unbinding of other protein–protein complexes.

The influence of quantum bath effects on the dynamics of a quantum two-level system linearly coupled to a harmonic bath is studied when the coupling is both diagonal and off-diagonal. It is shown that the pure dephasing kernel and the non-adiabatic quantum transition rate between Born–Oppenheimer states of the subsystem can be decomposed into a contribution from thermally excited bath modes plus a zero point energy contribution. This quantum rate can be modewise factorized exactly into a product of a mixed quantum subsystem-classical bath transition rate and a quantum correction factor. This factor determines dynamics of quantum bath correlations. Quantum bath corrections to both the transition rate and the pure dephasing kernel are shown to be readily evaluated via a mixed quantum-classical simulation. Hence, quantum dynamics can be recovered from a mixed quantum-classical counterpart by incorporating the missing quantum bath corrections. Within a mixed quantum-classical framework, a simple approach for evaluating quantum bath corrections in calculation of the non-adiabatic transition rate is presented.

As an application of the complex spectral representation of the Liouvillian that gives a rigorous approach to irreversible processes, a problem of decoherence for a particle coupled with a field in the thermodynamic limit is considered. We especially focus our attention on a time evolution of the field, which is commonly neglected in phenomenological approachs to the decoherence problem. In contrast to the usual hypothesis, there is a non-negligible time evolution of the field. The result shows that the decoherence in the field is an important consequence of irreversible processes that leads dynamically to a mixed state from a pure state through a secular effect due to the resonance effect between the particle and the field.

The absorption lineshape of a two-level chromophore coupled quadratically to a collective Gaussian solvation coordinate with an arbitrary Brownian oscillator spectral density is calculated exactly using a path-integral representation of the dipole correlation function in Liouville space.

Single photon counting time distributions obtained from single molecule photon arrival trajectories are employed in the theoretical study of multistate kinetics coupled to a two-state jump bath. The bath time scale may be extracted from statistical analysis of one- and two-point time-domain optical measurements. The amplitude and shape of the distribution of interphoton arrival times reflects bath correlations. A slow bath (relative to the kinetics) results in broad distributions of arrival times reflecting bath memory. For a fast bath, the arrival time distributions narrow around shorter times, similar to motional narrowing in frequency domain spectroscopy. The variance of either kinetic rates or equilibrium population of bath states results in asymmetry of the distribution of two photon arrival times.

Multitime correlation functions of photon arrival times in single molecule fluorescence resonant energy transfer measurements are computed using a simple model representing slow conformational dynamics described by a collective stochastic Gaussian coordinate. The analogy with time domain nonlinear optical spectroscopy is explored. Various statistical measures of distributions of single photon arrival times and fluorescence lifetimes are employed to analyze non-Poissonian statistics.

Stochastic trajectories in single molecule kinetics coupled to several Gaussian Markovian coordinates are analyzed using a generating function obtained by solving the multidimensional Smoluchowski equation. Multitime correlation functions are computed and used to identify direct signatures of non-Poissonian kinetics resulting from coupling to slow coordinates. Effects of various degrees of correlation between collective coordinates with multiple time scales are studied.

Botulinum neurotoxin (BoNT), the most toxic substance known to mankind, is the first example of the fully active molten globule state. To understand its folding mechanism, we performed urea denaturation experiments and theoretical modeling using BoNT serotype A (BoNT/A). We found that the extent of BoNT/A denaturation from the native state (N) shows a nonmonotonic dependence on urea concentration indicating a unique multistep denaturation process, N → I1I2U, with two intermediate states I1 and I2. BoNT/A loses almost all its secondary structure in 3.75 M urea (I1), yet it displays a native-like secondary structure in 5 M urea (I2). This agrees with the results of theoretical modeling, which helped to determine the molecular basis of unique behavior of BoNT/A in solution. Except for I2, all the states revert back to full enzymatic activity for SNAP-25 including the unfolded state U stable in 7 M urea. Our results stress the importance of structural flexibility in the toxin’s mechanism of survival and action, an unmatched evolutionary trait from billion-year-old bacteria, which also correlates with the long-lasting enzymatic activity of BoNT inside neuronal cells. BoNT/A provides a rich model to explore protein folding in relation to functional activity.