Treadmilling of actin filaments via Brownian dynamics simulations

Actin polymerization is coupled to the hydrolysis of adenosine triphosphate (ATP) into adenosine diphosphate (ADP) and inorganic phosphate (P(i)). Therefore, each protomer within an actin filament can attain three different nucleotide states corresponding to bound ATP, ADP/P(i), and ADP. These protomer states form spatial patterns on the growing (or shrinking) filaments. Using Brownian dynamics simulations, the growth behavior of long filaments is studied, together with the associated protomer patterns, as a function of ATP-actin monomer concentration, C(T), within the surrounding solution. For concentrations close to the critical concentration C(T)=C(T,cr), the filaments undergo treadmilling, i.e., they grow at the barbed and shrink at the pointed end, which leads to directed translational motion of the whole filament. The corresponding nonequilibrium states are characterized by several global fluxes and by spatial density and flux profiles along the filaments. We focus on a certain set of transition rates as deduced from in vitro experiments and find that the associated treadmilling (or turnover) rate is about 0.08 monomers per second.     

Polymerization of actin filaments coupled with adenosine triphosphate hydrolysis: Brownian dynamics and theoretical analysis

Polymerization dynamics of single actin filaments coupled with adenosine triphosphate (ATP) hydrolysis is investigated via both theoretical analysis and Brownian dynamics simulations. Brownian dynamics simulations have been applied recently to study the growth behaviors of long filaments as a function of the free actin monomer concentrations, C(T), which is found to be in agreement with the associated experiments. In the present study, both ATP cap length and length diffusivity are studied as a function of the free ATP-actin monomer concentrations, C(T). The exact analytical expressions are found to be in perfect consistency with Brownian dynamics simulations. Likewise, we find that the length diffusion coefficient is peaked near the critical concentration, C(T,cr). It is, therefore, expected that the dependence of length diffusivity on ATP-actin monomer concentrations is utilized to analyze the surprising experiments on the length fluctuations of individual actin filaments.     

布朗动力学理论模拟动态肌动蛋白纤维的增长

肌动蛋白的聚合耦合三磷酸腺酐(ATP)分子水解成二磷酸腺苷(ADP)分子和磷酸(Pi)的释放两个过程. 因此, 肌动蛋白纤维上的原聚体存在三种不同状态, 即分别结合ATP, ADP/Pi和ADP分子. 原聚体的不同状态导致纤维具有不同的空间图谱, 这些状态的空间分布将影响纤维的各种行为. 为此,建立了相应的分子模型,在布朗动力学模拟中实现了遵循时间演化的连续马尔可夫随机过程的解聚和水解反应; 重点阐述了如何实现纤维两端的聚合和解聚达到化学平衡的方法, 并系统研究了纤维在结合ATP分子的肌动蛋白单体溶液中的增长行为.     

Supramolecular Peptide Nanostructures Regulate Catalytic Efficiency and Selectivity

We report three constitutionally isomeric tetrapeptides, each comprising one glutamic acid (E) residue, one histidine (H) residue, and two lysine (K_S) residues functionalized with side-chain hydrophobic S-aroylthiooxime (SATO) groups. Depending on the order of amino acids, these amphiphilic peptides self-assembled in aqueous solution into different nanostructures:nanoribbons, a mixture of nanotoroids and nanoribbons, or nanocoils. Each nanostructure catalyzed hydrolysis of a model substrate, with the nanocoils exhibiting the greatest rate enhancement and the highest enzymatic efficiency. Coarse-grained molecular dynamics simulations, analyzed with unsupervised machine learning, revealed clusters of H residues in hydrophobic pockets along the outer edge of the nanocoils, providing insight for the observed catalytic rate enhancement. Finally, all three supramolecular nanostructures catalyzed hydrolysis of the l -substrate only when a pair of enantiomeric Boc-l /d -Phe-ONp substrates were tested. This study highlights how subtle molecular-level changes can influence supramolecular nanostructures, and ultimately affect catalytic efficiency.     

Nano-biomachine from actin and myosin gels

We introduce here an ATP (adenosine triphosphate)-fueled nano-biomachine constructed from actin and myosin gels. Various types of chemically cross-linked actin gel, which are tens of times larger in size than native actin filaments (F-actin), were formed by complexing with cation-polymers and placed on a chemically cross-linked myosin gel. By adding dilute solution of ATP, they moved along the myosin gel with a velocity as high as that of native F-actin by coupling to ATP hydrolysis. Formation mechanism and structure of actin complexes as well as those of myosin gels were studied in detail and elucidated with the specific characteristics of the motility. These results demonstrate that one can construct nano-biomachines fueled by chemical energy of ATP with controlled motility. The text was submitted by the authors in English.     

Evaluation the synergistic antitumor effect of methotrexate–camptothecin codelivery prodrug from self-assembly process to acid-catalyzed both drugs release: A comprehensive theoretical study

Therapeutic efficiency of amphiphilic methotrexate–camptothecin (MTX-CPT) prodrug compared to free drug mixture (MTX/CPT) has been investigated using all-atom molecular dynamics simulation and first principles density functional theory calculations. This comparison revealed that MTX–CPT prodrug tends to form spherical self-assembled nanoparticle (NP), while free MTX/CPT mixture forms rod-shape NP. These observations are attributed to a structural defect in the MTX–CPT prodrug and solvation free energies of MTX, CPT and MTX-CPT molecules. The results provided evidence that noncovalent interactions (NCIs) among the pharmaceutical drugs play a very important role in anticancer agents aggregation process, leading to enhanced stability of the self-assembled NPs. It is found that the stability of MTX–CPT self-assembled NP is greater than the MTX/CPT NP due to the synergistic effect of hydrogen bonding between monomers and solvent (water). Moreover, the noncatalyzed as well as catalyzed hydrolysis reactions of MTX–CPT prodrug are theoretically studied at the PCM(water)//M06-2X/6−31G(d,p) computational level to shed additional light on the role of acidic condition in tumor tissues. We found that the ester hydrolysis in mild acidic solutions is a concerted reaction. In an agreement between theory and experiment, we also confirmed that the activation energies of the catalyzed-hydrolysis steps are much lower than the activation energies of the corresponding steps in the noncatalyzed reaction. Thus, the MTX–CPT prodrug reveals very promising properties as a pH-controlled drug delivery system.     

Effect of bicarbonate ions on the crystallization of calcite on self-assembled monolayers

We use molecular dynamics simulations to investigate the nucleation of calcite crystals on self-assembled monolayers. We show how the presence of bicarbonate ions adsorbed on the monolayer surface can both aid nucleation and control the orientation of the growth of the crystal. Using a simple model of the nucleation process and calculated interfacial energies, we calculate the enhancement (with respect to the homogeneous nucleation rate) of the nucleation of calcite on the (012) and (0001) faces. The calculations show clearly that the (012) face is favored over the (0001) face and that the nucleation rate is enhanced for self-assembled monolayers made from molecules containing an even number of carbon atoms in the alkyl chain over those containing an odd number.     

Quantitative analysis of protein adsorption via atomic force microscopy and surface plasmon resonance

Surface properties have a significant influence on the performance of biomedical devices. The influence of surface chemistry on the amount and distribution of adsorbed proteins has been evaluated by a combination of atomic force microscopy (AFM) and surface plasmon resonance (SPR). Adsorption of albumin, fibrinogen, and fibronectin was analyzed under static and dynamic conditions, employing self-assembled monolayers (SAMs) as model surfaces. AFM was performed in tapping mode with antibody-modified tips. Phase-contrast images showed protein distribution on SAMs and phase-shift entity provided information on protein conformation. SPR analysis revealed substrate-specific dynamics in each system investigated. When multi-protein solutions and diluted human plasma interacted with SAMs, SPR data suggested that surface chemistry governs the equilibrium composition of the protein layer.     

Molecular dynamics simulations of supramolecular polymer rheology

Using equilibrium and nonequilibrium molecular dynamics simulations, we studied the equilibrium and rheological properties of dilute and semidilute solutions of head-to-tail associating polymers. In our simulation model, a spontaneous complementary reversible association between the donor and the acceptor groups at the ends of oligomers was achieved by introducing a combination of truncated pseudo-Coulombic attractive potential and Lennard Jones repulsive potential between donor, acceptor, and neighboring groups. We have calculated the equilibrium properties of supramolecular polymers, such as the ring/chain equilibrium, average molecular weight, and molecular weight distribution of self-assembled chains and rings, which all agree well with previous analytical and computer modeling results. We have investigated shear thinning of solutions of 8- and 20-bead associating oligomers with different association energies at different temperatures and oligomer volume fractions. All reduced viscosity data for a given oligomer length can be collapsed into one master curve, exhibiting two power-law regions of shear-thinning behavior with an exponent of -0.55 at intermediate ranges of the reduced shear rate β and -0.8 (or -0.9) at larger shear rates. The equilibrium viscosity of supramolecular solutions with different oligomer lengths and associating energies is found to obey a power-law scaling dependence on oligomer volume fraction with an exponent of 1.5, in agreement with the experimental observations for several dilute or semidilute solutions of supramolecular polymers. This implies that dilute and semidilute supramolecular polymer solutions exhibit high polydispersity but may not be sufficiently entangled to follow the reptation mechanism of relaxation.     

Self-assembling DNA dendrimers: a numerical study

DNA is increasingly used as a specific linker to template nanostructured materials. We present a molecular dynamics simulation study of a simple DNA-dendrimer model designed to capture the basic characteristics of the biological interactions, where selectivity and strong cooperativity play an important role. Exploring a large set of densities and temperatures, we follow the progressive formation of a percolating large-scale network whose connectivity can be described by random percolation theory. We identify the relative regions of network formation and kinetic arrest versus phase separation and show that the location of the two-phase region can be interpreted in the same framework as reduced valency models. This correspondence provides guidelines for designing stable, equilibrium self-assembled low-density networks. Finally, we demonstrate a relation between bonding and dynamics, by showing that the temperature dependence of the diffusion constant is controlled by the number of fully unbonded dendrimers.     

Self-assembled dynamics of silver nanoparticles and self-assembled dynamics of 1,4-benzenedithiol adsorbed on silver nanoparticles: Surface-enhanced Raman scattering study

Self-assembled dynamics of silver nanoparticles and self-assembled dynamics of 1,4-benzenedithiol (1,4-BDT) adsorbed on silver nanoparticles were investigated experimentally with surface-enhanced Raman scattering (SERS) and theoretically with density functional theory (DFT) and finite difference time domain (FDTD) method. The absorption spectroscopy of 1,4-BDT in silver sol at different time intervals was measured, which give the indirect evidence of self-assembled dynamics of silver nanoparticles and self-assembled dynamics of 1,4-benzenedithiol (1,4-BDT) adsorbed on silver nanoparticles. To obtain the direct evidence of self-assembled dynamics of silver nanoparticles and self-assembled dynamics of 1,4-benzenedithiol (1,4-BDT) adsorbed on silver nanoparticles, the SERS of 1,4-BDT were measured experimentally and investigated theoretically. The appearances of S–S stretching band (revealing the formation of multilayers of 1,4-BDT), and strongly enhanced S–C stretching, C–C ring stretching vibrational modes clearly show self-assembled dynamics of 1,4-BDT.     

Tensegrity and motor-driven effective interactions in a model cytoskeleton

Actomyosin networks are major structural components of the cell. They provide mechanical integrity and allow dynamic remodeling of eukaryotic cells, self-organizing into the diverse patterns essential for development. We provide a theoretical framework to investigate the intricate interplay between local force generation, network connectivity, and collective action of molecular motors. This framework is capable of accommodating both regular and heterogeneous pattern formation, arrested coarsening and macroscopic contraction in a unified manner. We model the actomyosin system as a motorized cat's cradle consisting of a crosslinked network of nonlinear elastic filaments subjected to spatially anti-correlated motor kicks acting on motorized (fibril) crosslinks. The phase diagram suggests there can be arrested phase separation which provides a natural explanation for the aggregation and coalescence of actomyosin condensates. Simulation studies confirm the theoretical picture that a nonequilibrium many-body system driven by correlated motor kicks can behave as if it were at an effective equilibrium, but with modified interactions that account for the correlation of the motor driven motions of the actively bonded nodes. Regular aster patterns are observed both in Brownian dynamics simulations at effective equilibrium and in the complete stochastic simulations. The results show that large-scale contraction requires correlated kicking.     

Theory of crosslinked bundles of helical filaments: intrinsic torques in self-limiting biopolymer assemblies

Inspired by the complex influence of the globular crosslinking proteins on the formation of biofilament bundles in living organisms, we study and analyze a theoretical model for the structure and thermodynamics of bundles of helical filaments assembled in the presence of crosslinking molecules. The helical structure of filaments, a universal feature of biopolymers such as filamentous actin, is shown to generically frustrate the geometry of crosslinking between the "grooves" of two neighboring filaments. We develop a coarse-grained model to investigate the interplay between the geometry of binding and mechanics of both linker and filament distortion, and we show that crosslinking in parallel bundles of helical filaments generates intrinsic torques, of the type that tend to wind the bundle superhelically about its central axis. Crosslinking mediates a non-linear competition between the preference for bundle twist and the size-dependent mechanical cost of filament bending, which in turn gives rise to feedback between the global twist of self-assembled bundles and their lateral size. Finally, we demonstrate that above a critical density of bound crosslinkers, twisted bundles form with a thermodynamically preferred radius that, in turn, increases with a further increase in crosslinking bonds. We identify the stiffness of crosslinking bonds as a key parameter governing the sensitivity of bundle structure and assembly to the availability and affinity of crosslinkers.     

ATP Drives the Formation of a Catalytic Hydrazone through an Energy Ratchet Mechanism

An energy ratchet mechanism is exploited for the synthesis of a molecule. In the presence of adenosine triphosphate (ATP), hydrazone-bond formation between an aldehyde and hydrazide is accelerated and the composition at thermodynamic equilibrium is shifted towards the hydrazone. Enzymatic hydrolysis of ATP installs a kinetically stable state, at which hydrazone is present at a higher concentration compared to the composition at thermodynamic equilibrium in the presence of the degradation products of ATP. It is shown that the kinetic state has an enhanced catalytic activity in the hydrolysis of an RNA-model compound.     

Fluorescence correlation spectroscopy analysis of segmental dynamics in actin filaments

We adapt fluorescence correlation spectroscopy (FCS) formalism to the studies of the dynamics of semiflexible polymers and derive expressions relating FCS correlation function to the longitudinal and transverse mean-square displacements of polymer segments. The obtained relations do not depend on any specific model of polymer dynamics. We use the derived expressions to measure the dynamics of actin filaments in two experimental situations: filaments labeled at distinct positions and homogeneously labeled filaments. Both approaches give consistent results and allow to measure the temporal dependence of the segmental mean-square displacement over almost five decades in time, from approximately 40 micros to approximately 2 s. These noninvasive measurements allow for a detailed quantitative comparison of the experimental data to the current theories of semiflexible polymer dynamics. Good quantitative agreement is found between the experimental results and theories explicitly accounting for the hydrodynamic interactions between polymer segments.     

Mathematical modeling of kinetics of adenosine-5’-triphosphate hydrolysis catalyzed by the Zn2+ ion in the pH range 8.5–9.0

The kinetics of adenosine-5’-triphosphate (ATP) hydrolysis catalyzed by Zn²⁺ at pH 8.5–9.0 is analyzed by numerical simulation. The rates of product formation (adenosine diphosphate (ADP) and adenosine monophosphate (AMP)) are determined by a conformational transformation. In the sequence of steps of mutual transformations of cyclic (Cy) pH-dependent species, which are active in ATP hydrolysis to ADP, and open (Op) species, the rate-limiting step is the slow isomerization of ZnATP²-complexes. This slow step is determined by the abstraction of the OH^- group from a pentacovalent intermediate catalyzed by H₃O⁺. In the Op species,Zn ²⁺ is bound to the phosphate chain. In the Cy species, which can be hydrolized to ADP, Zn²⁺ coordinates a nitrogen atom in position 7 and γ-phosphate. The mutual transformations of conformers occur via pentacovalent intermediates with the participation of γ-phosphorus and include pseudotransformations. In the direct transformation CyOH^-⦚r OpOH^-, pseudotransformation is a rate-controlling step. The deprotonated open monomeric form OpOH^- is inactive in hydrolysis. Within the framework of the dimeric model and a more complex model that accounts for the role of trimeric associates ZnATP^2-, the general scheme of intermediate transformations is considered that accounts for the existence of a pH-independent pathway of hydrolysis. The rate and equilibrium constants are estimated. Concentration profiles for intermediate products during hydrolysis are described.     

Ultrafast hydration dynamics in melittin folding and aggregation: helix formation and tetramer self-assembly

Melittin, an amphipathic peptide from honeybee venom, consists of 26 amino acid residues and adopts different conformations from a random coil, to an alpha-helix, and to a self-assembled tetramer under certain aqueous environments. We report here our systematic studies of the hydration dynamics in these conformations using single intrinsic tryptophan (W19) as a molecular probe. With femtosecond resolution, we observed the solvation dynamics occurring in 0.62 and 14.7 ps in a random-coiled primary structure. The former represents bulklike water motion, and the latter reflects surface-type hydration dynamics of proteins. As a comparison, a model tripeptide (KWK) was also studied. At a membrane-water interface, melittin folds into a secondary alpha-helical structure, and the interfacial water motion was found to take as long as 114 ps, indicating a well-ordered water structure along the membrane surface. In high-salt aqueous solution, the dielectric screening and ionic solvation promote the hydrophobic core collapse in melittin aggregation and facilitate the tetramer formation. This self-assembled tertiary structure is also stabilized by the strong hydrophilic interactions of charged C-terminal residues and associated ions with water molecules in the two assembled regions. The hydration dynamics was observed to occur in 87 ps, significantly slower than typical water relaxation at protein surfaces but similar to water motion at membrane interfaces. Thus, the observed time scale of approximately 100 ps probably implies appropriate water mobility for mediating the formation of high-order structures of melittin in an alpha-helix and a self-assembled tetramer. These results elucidate the critical role of hydration dynamics in peptide conformational transitions and protein structural stability and integrity.     

Frenkel exciton model of ultrafast excited state dynamics in AT DNA double helices

Recent ultrafast experiments have implicated intrachain base-stacking rather than base-pairing as the crucial factor in determining the fate and transport of photoexcited species in DNA chains. An important issue that has emerged concerns whether or not a Frenkel excitons is sufficient one needs charge-transfer states to fully account for the dynamics. Here we present an SU(2)  SU(2) lattice model which incorporates both intrachain and interchain electronic interactions to study the quantum mechanical evolution of an initial excitonic state placed on either the adenosine or thymidine side of a model B DNA poly(dA).poly(dT) duplex. Our calculations indicate that over several hundred femtoseconds, the adenosine exciton remains a cohesive excitonic wave packet on the adenosine side of the chain where as the thymidine exciton rapidly decomposes into mobile electron/hole pairs along the thymidine side of the chain. In both cases, the very little transfer to the other chain is seen over the time-scale of our calculations. We attribute the difference in these dynamics to the roughly 4:1 ratio of hole versus electron mobility along the thymidine chain. We also show that this difference is robust even when structural fluctuations are introduced in the form of static off-diagonal disorder.     

Distribution and dynamics of transformation of hydrolytic cationic forms of nickel(II)

A system Ni²⁺-NO₃⁻-H₂O was examined by dialysis under equilibrium conditions using step constants of hydrolysis to constructs distribution diagrams of Ni(II) cationic forms in a dependence on a pH value of a solution. We considered the reaction dynamics of hydrolytic cationic forms of nickel(II) and substantiated schemes of realized processes with a change in pH.     

Coarse-grained simulations of ABA amphiphilic triblock copolymer solutions in thin films

We study a coarse-grained model of A(10)-B(20)-A(10) amphiphilic triblock copolymers in aqueous solution under confinement. We focus on the influence of the wall interaction on the morphology of the ensuing self-assembled structures. We also study the dynamics of the polymers. All our simulations are confined between two walls. We study three different combinations of walls: hydrophobic and hydrophobic, hydrophobic and hydrophilic, hydrophilic and hydrophilic. We moreover elucidate the concentration influence. The conformation and behavior of the copolymer in strongly confined systems depend on the type of wall interaction and concentration.