CellDynaMo-stochastic reaction-diffusion-dynamics model: Application to search-and-capture process of mitotic spindle assembly.

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.

Fibrin protofibril packing and clot stability are enhanced by extended knob-hole interactions and catch-slip bonds.

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.

Microtubule assembly and disassembly dynamics model: Exploring dynamic instability and identifying features of Microtubules' Growth, Catastrophe, Shortening, and Rescue.

Microtubules (MTs), a cellular structure element, exhibit dynamic instability and can switch stochastically from growth to shortening; but the factors that trigger these processes at the molecular level are not understood. We developed a 3D Microtubule Assembly and Disassembly DYnamics (MADDY) model, based upon a bead-per-monomer representation of the αß-tubulin dimers forming an MT lattice, stabilized by the lateral and longitudinal interactions between tubulin subunits. The model was parameterized against the experimental rates of MT growth and shortening, and pushing forces on the Dam1 protein complex due to protofilaments splaying out. Using the MADDY model, we carried out GPU-accelerated Langevin simulations to access dynamic instability behavior. By applying Machine Learning techniques, we identified the MT characteristics that distinguish simultaneously all four kinetic states: growth, catastrophe, shortening, and rescue. At the cellular 25 µM tubulin concentration, the most important quantities are the MT length L , average longitudinal curvature κ long , MT tip width w , total energy of longitudinal interactions in MT lattice U long , and the energies of longitudinal and lateral interactions required to complete MT to full cylinder U long add and U lat add . At high 250 µM tubulin concentration, the most important characteristics are L , κ long , number of hydrolyzed αß-tubulin dimers n hyd and number of lateral interactions per helical pitch n lat in MT lattice, energy of lateral interactions in MT lattice U lat , and energy of longitudinal interactions in MT tip u long . These results allow greater insights into what brings about kinetic state stability and the transitions between states involved in MT dynamic instability behavior.

Heterogeneous parallelization and acceleration of molecular dynamics simulations in GROMACS.

The introduction of accelerator devices such as graphics processing units (GPUs) has had profound impact on molecular dynamics simulations and has enabled order-of-magnitude performance advances using commodity hardware. To fully reap these benefits, it has been necessary to reformulate some of the most fundamental algorithms, including the Verlet list, pair searching, and cutoffs. Here, we present the heterogeneous parallelization and acceleration design of molecular dynamics implemented in the GROMACS codebase over the last decade. The setup involves a general cluster-based approach to pair lists and non-bonded pair interactions that utilizes both GPU and central processing unit (CPU) single instruction, multiple data acceleration efficiently, including the ability to load-balance tasks between CPUs and GPUs. The algorithm work efficiency is tuned for each type of hardware, and to use accelerators more efficiently, we introduce dual pair lists with rolling pruning updates. Combined with new direct GPU-GPU communication and GPU integration, this enables excellent performance from single GPU simulations through strong scaling across multiple GPUs and efficient multi-node parallelization.

Molecular packing structure of fibrin fibers resolved by X-ray scattering and molecular modeling.

Fibrin is the major extracellular component of blood clots and a proteinaceous hydrogel used as a versatile biomaterial. Fibrin forms branched networks 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 of fibrin fibers. Here the packing structure of fibrin fibers is quantitatively assessed by combining Small Angle X-ray Scattering (SAXS) measurements of fibrin reconstituted under a wide range of conditions with computational molecular modeling of fibrin protofibrils. 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.

Sharing Data from Molecular Simulations.

Given the need for modern researchers to produce open, reproducible scientific output, the lack of standards and best practices for sharing data and workflows used to produce and analyze molecular dynamics (MD) simulations has become an important issue in the field. There are now multiple well-established packages to perform molecular dynamics simulations, often highly tuned for exploiting specific classes of hardware, each with strong communities surrounding them, but with very limited interoperability/transferability options. Thus, the choice of the software package often dictates the workflow for both simulation production and analysis. The level of detail in documenting the workflows and analysis code varies greatly in published work, hindering reproducibility of the reported results and the ability for other researchers to build on these studies. An increasing number of researchers are motivated to make their data available, but many challenges remain in order to effectively share and reuse simulation data. To discuss these and other issues related to best practices in the field in general, we organized a workshop in November 2018 ( https://bioexcel.eu/events/workshop-on-sharing-data-from-molecular-simulations/ ). Here, we present a brief overview of this workshop and topics discussed. We hope this effort will spark further conversation in the MD community to pave the way toward more open, interoperable, and reproducible outputs coming from research studies using MD simulations.

Mechanical properties of tubulin intra- and inter-dimer interfaces and their implications for microtubule dynamic instability.

Thirteen tubulin protofilaments, made of αß-tubulin heterodimers, interact laterally to produce cytoskeletal microtubules. Microtubules exhibit the striking property of dynamic instability, manifested in their intermittent growth and shrinkage at both ends. This behavior is key to many cellular processes, such as cell division, migration, maintenance of cell shape, etc. Although assembly and disassembly of microtubules is known to be linked to hydrolysis of a guanosine triphosphate molecule in the pocket of ß-tubulin, detailed mechanistic understanding of corresponding conformational changes is still lacking. Here we take advantage of the recent generation of in-microtubule structures of tubulin to examine the properties of protofilaments, which serve as important microtubule assembly and disassembly intermediates. We find that initially straight tubulin protofilaments, relax to similar non-radially curved and slightly twisted conformations. Our analysis further suggests that guanosine triphosphate hydrolysis primarily affects the flexibility and conformation of the inter-dimer interface, without a strong impact on the shape or flexibility of αß-heterodimer. Inter-dimer interfaces are significantly more flexible compared to intra-dimer interfaces. We argue that such a difference in flexibility could be key for distinct stability of the plus and minus microtubule ends. The higher flexibility of the inter-dimer interface may have implications for development of pulling force by curving tubulin protofilaments during microtubule disassembly, a process of major importance for chromosome motions in mitosis.

Regulatory element in fibrin triggers tension-activated transition from catch to slip bonds.

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 γ295 to γ305) containing the weak calcium-binding site γ2 serves as a tension sensor. Flap dissociation from the B domain in the γ-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.

Atomic Structural Models of Fibrin Oligomers.

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.

Dynamic Transition from α-Helices to ß-Sheets in Polypeptide Coiled-Coil Motifs.

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 ß-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-ß 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.

Conformational Flexibility and Self-Association of Fibrinogen in Concentrated Solutions.

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 molecular dynamics simulations revealed partially bent fibrinogen solution conformations that interpolate between a flexible chain and a rigid rod observed in the crystal. The results obtained illuminate the important role of the αC regions in modulating the fibrinogen molecular shape through formation of weak intermolecular linkages that control the bulk properties of fibrinogen solutions.

Structural Basis of Interfacial Flexibility in Fibrin Oligomers.

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.

Botulinum neurotoxin: unique folding of enzyme domain of the most-poisonous poison.

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 → I1 [Formula: see text] I2 [Formula: see text] U, 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.

Molecular mechanisms, thermodynamics, and dissociation kinetics of knob-hole interactions in fibrin.

Polymerization of fibrin, the primary structural protein of blood clots and thrombi, occurs through binding of knobs 'A' and 'B' in the central nodule of fibrin monomer to complementary holes 'a' and 'b' in the γ- and ß-nodules, respectively, of another monomer. We characterized the A:a and B:b knob-hole interactions under varying solution conditions using molecular dynamics simulations of the structural models of fibrin(ogen) fragment D complexed with synthetic peptides GPRP (knob 'A' mimetic) and GHRP (knob 'B' mimetic). The strength of A:a and B:b knob-hole complexes was roughly equal, decreasing with pulling force; however, the dissociation kinetics were sensitive to variations in acidity (pH 5-7) and temperature (T = 25-37 °C). There were similar structural changes in holes 'a' and 'b' during forced dissociation of the knob-hole complexes: elongation of loop I, stretching of the interior region, and translocation of the moveable flap. The disruption of the knob-hole interactions was not an "all-or-none" transition as it occurred through distinct two-step or single step pathways with or without intermediate states. The knob-hole bonds were stronger, tighter, and more brittle at pH 7 than at pH 5. The B:b knob-hole bonds were weaker, looser, and more compliant than the A:a knob-hole bonds at pH 7 but stronger, tighter, and less compliant at pH 5. Surprisingly, the knob-hole bonds were stronger, not weaker, at elevated temperature (T = 37 °C) compared with T = 25 °C due to the helix-to-coil transition in loop I that helps stabilize the bonds. These results provide detailed qualitative and quantitative characteristics underlying the most significant non-covalent interactions involved in fibrin polymerization.

Comparative simulation studies of native and single-site mutant human beta-defensin-1 peptides.

Human defensins play important roles in a broad range of biological functions, such as microbial defense and immunity. Yet, little is known about their molecular properties, i.e. secondary structure stability, structural variability, important side chain interactions, surface charge distribution, and resistance to thermal fluctuations, and how these properties are related to their functions. To assess these factors, we studied the native human ß-defensin-1 monomer and dimer as well as several single-site mutants using molecular dynamics simulations. The results showed that disulfide bonds are important determinants in maintaining the defensins' structural integrity, as no structural transitions were observed at 300 K and only minor structural unfolding was detected upon heating to 500 K. The α-helix was less thermally stable than the core ß-sheet structure held together by hydrogen bonds and hydrophobic interactions. The monomer α-helix stability was directly correlated, whereas the end-to-end distance was inversely correlated to the experimentally measured ß-defensin-1 chemotactic activity, in the order: mutant 2 (Gln24Glu) > mutant 3 (Lys31Ala) = wild type > mutant 1 (Asn4Ala). The structural stability of the ß-defensin-1 dimer species exhibited an inverse correlation to their chemotactic activity. In dimers formed by mutants 2 and 3, we observed sliding of one monomer upon the surface of the other in the absence of unbinding. This dynamic sliding feature may enhance the molecular oligomerization of ß-defensin-1 peptides contributing to their antibacterial activity. It could also help these peptides orient correctly in the CC chemokine receptor 6 binding site, thereby initiating their chemotactic activity. In agreement with this notion, the remarkable sliding behavior was observed only for the mutants with the highest chemotactic activity.

Mechanical transition from α-helical coiled coils to ß-sheets in fibrin(ogen).

We characterized the α-to-ß transition in α-helical coiled-coil connectors of the human fibrin(ogen) molecule using biomolecular simulations of their forced elongation and theoretical modeling. The force (F)-extension (X) profiles show three distinct regimes: (1) the elastic regime, in which the coiled coils act as entropic springs (F < 100-125 pN; X < 7-8 nm); (2) the constant-force plastic regime, characterized by a force-plateau (F ≈ 150 pN; X ≈ 10-35 nm); and (3) the nonlinear regime (F > 175-200 pN; X > 40-50 nm). In the plastic regime, the three-stranded α-helices undergo a noncooperative phase transition to form parallel three-stranded ß-sheets. The critical extension of the α-helices is 0.25 nm, and the energy difference between the α-helices and ß-sheets is 4.9 kcal/mol per helical pitch. The soft α-to-ß phase transition in coiled coils might be a universal mechanism underlying mechanical properties of filamentous α-helical proteins.

Multiscale modeling of the nanomechanics of microtubule protofilaments.

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.

Mechanism of fibrin(ogen) forced unfolding.

Fibrinogen, upon enzymatic conversion to monomeric fibrin, provides the building blocks for fibrin polymer, the scaffold of blood clots and thrombi. Little has been known about the force-induced unfolding of fibrin(ogen), even though it is the foundation for the mechanical and rheological properties of fibrin, which are essential for hemostasis. We determined mechanisms and mapped the free energy landscape of the elongation of fibrin(ogen) monomers and oligomers through combined experimental and theoretical studies of the nanomechanical properties of fibrin(ogen), using atomic force microscopy-based single-molecule unfolding and simulations in the experimentally relevant timescale. We have found that mechanical unraveling of fibrin(ogen) is determined by the combined molecular transitions that couple stepwise unfolding of the γ chain nodules and reversible extension-contraction of the α-helical coiled-coil connectors. These findings provide important characteristics of the fibrin(ogen) nanomechanics necessary to understand the molecular origins of fibrin viscoelasticity at the fiber and whole clot levels.

Exploring the mechanical stability of the C2 domains in human synaptotagmin 1.

Human synaptotagmin 1 (Syt1) plays a crucial role in the bending of the membrane during neurotransmitter release at the synapse. Hence, resolving the structural details of Syt1 that underlie its biological function is fundamental for providing mechanistic insights into the nature of the synaptic response. We explored the unfolding micromechanics of Syt1 by analyzing the free energy landscape of the whole molecule and its C2A and C2B domains. We employed a self-organized polymer (SOP) model of a protein chain to carry out pulling simulations, accelerated on graphics processing units (GPUs), under experimental force loads. To resolve the atomic-level details, we complemented the SOP model simulations with atomistic simulations. On the basis of the results obtained, we hypothesize that (1) isolated single domains C2A and C2B present similar mechanical resistance against an applied pulling force but unfold following different kinetic pathways and that (2) C2B is more mechanically resistant in the C2AB complex due to stabilizing interactions with other domains. These findings correlate well with recent atomic force microscopy (AFM) studies on the Syt1 molecule, in which the increase in the unfolding force for C2B was detected when this domain was joined with C2A. Our results also suggest that the linkers (I27 domains) used in the experimental setup can modulate the mechanical behavior of this synaptic protein complex and alter not only the critical force for unfolding but also the unfolding pathways for the C2 domains. Interestingly, the presence of the C2A-C2B domain interface in the C2AB complex confers mechanical stability to either of the C2 domains. Our findings provide new insights into the relative conformational variability of the C2 domains, which we believe to be modulated, to a large extent, by intermolecular coupling with other proteins.