We applied the transition path sampling (TPS) method to study the translocation step of the catalytic mechanism of galactofuranosyl transferase 2 (GlfT2). Using TPS in the field of enzymatic reactions is still relatively rare, and we show its effectiveness on this enzymatic system. We decipher an unknown mechanism of the translocation step and, thus, provide a complete understanding of the catalytic mechanism of GlfT2 at the atomistic level. The GlfT2 enzyme is involved in the formation of the mycobacterial cell wall and transfers galactofuranose (Galf) from UDP-Galf onto a growing acceptor Galf chain. The biosynthesis of the galactan chain is accomplished in a processive manner, with the growing acceptor substrate remaining bound to GlfT2. The glycosidic bond formed by GlfT2 between the two Galf residues alternates between β-(1-6) and β-(1-5) linkages. The translocation of the growing galactan between individual additions of Galf residues is crucial for the function of GlfT2. Analysis of unbiased trajectory ensembles revealed that the translocation proceeds differently depending on the glycosidic linkage between the last two Galf residues. We also showed that the protonation state of the catalytic residue Asp372 significantly influences the translocation. Approximate transition state structures and potential energy reaction barriers of the translocation process were determined. The calculated potential reaction barriers in the range of 6-14 kcal/mol show that the translocation process is not the rate-limiting step in galactan biosynthesis.
- Publication type
- Journal Article MeSH
The local time of a stochastic process quantifies the amount of time that sample trajectories x(τ) spend in the vicinity of an arbitrary point x. For a generic Hamiltonian, we employ the phase-space path-integral representation of random walk transition probabilities in order to quantify the properties of the local time. For time-independent systems, the resolvent of the Hamiltonian operator proves to be a central tool for this purpose. In particular, we focus on the local times of Lévy random walks (Lévy flights), which correspond to fractional diffusion equations.
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- Journal Article MeSH
Consider the short-time probability distribution P(H,t) of the one-point interface height difference h(x=0,τ=t)-h(x=0,τ=0)=H of the stationary interface h(x,τ) described by the Kardar-Parisi-Zhang (KPZ) equation. It was previously shown that the optimal path, the most probable history of the interface h(x,τ) which dominates the upper tail of P(H,t), is described by any of two ramplike structures of h(x,τ) traveling either to the left, or to the right. These two solutions emerge, at a critical value of H, via a spontaneous breaking of the mirror symmetry x↔-x of the optimal path, and this symmetry breaking is responsible for a second-order dynamical phase transition in the system. We simulate the interface configurations numerically by employing a large-deviation Monte Carlo sampling algorithm in conjunction with the mapping between the KPZ interface and the directed polymer in a random potential at high temperature. This allows us to observe the optimal paths, which determine each of the two tails of P(H,t), down to probability densities as small as 10^{-500}. At short times we observe mirror-symmetry-broken traveling optimal paths for the upper tail, and a single mirror-symmetric path for the lower tail, in good quantitative agreement with analytical predictions. At long times, even at moderate values of H, where the optimal fluctuation method is not supposed to apply, we still observe two well-defined dominating paths. Each of them violates the mirror symmetry x↔-x and is a mirror image of the other.
- Publication type
- Journal Article MeSH
Guanine quadruplexes (GQs) play crucial roles in various biological processes, and understanding their folding pathways provides insight into their stability, dynamics, and functions. This knowledge aids in designing therapeutic strategies, as GQs are potential targets for anticancer drugs and other therapeutics. Although experimental and theoretical techniques have provided valuable insights into different stages of the GQ folding, the structural complexity of GQs poses significant challenges, and our understanding remains incomplete. This study introduces a novel computational protocol for folding an entire GQ from single-strand conformation to its native state. By combining two complementary enhanced sampling techniques, we were able to model folding pathways, encompassing a diverse range of intermediates. Although our investigation of the GQ free energy surface (FES) is focused solely on the folding of the all-anti parallel GQ topology, this protocol has the potential to be adapted for the folding of systems with more complex folding landscapes.
- Keywords
- DNA quadruplex, computational folding, enhanced sampling, kinetic partitioning mechanism, metadynamics, molecular dynamics, nudged elastic band, pathCV, transition path sampling,
- MeSH
- DNA chemistry MeSH
- G-Quadruplexes * MeSH
- Nucleic Acid Conformation MeSH
- Molecular Dynamics Simulation MeSH
- Thermodynamics MeSH
- Publication type
- Journal Article MeSH
- Names of Substances
- DNA MeSH
Photoabsorption spectra of He N + ${{\rm{He}}_N^ + }$ clusters, N=5-9, have been calculated using a diatomics-in-molecules like electronic structure model and a path-integral Monte Carlo sampling method. A qualitative change in the calculated spectra has been observed at N=9, which has been interpreted in terms of a structural transformation in the clusters consisting in a transition from trimer-like ionic cores observed for N≤7 to dimer-like ionic cores prevailing in He 9 + ${{\rm{He}}_9^ + }$ through an intermediate state (comparable abundances of both types of ionic cores) observed in He 8 + ${{\rm{He}}_8^ + }$ . The calculated spectra have been thoroughly compared with an earlier calculation on He 3 + ${{\rm{He}}_3^ + }$ , He 4 + ${{\rm{He}}_4^ + }$ , and He 10 + ${{\rm{He}}_{10}^ + }$ reported from our group and data available for the same cluster sizes from an experiment.
- Keywords
- charged helium clusters, diatomics-in-molecules, geometric structure, path-integral Monte Carlo, photoabsorption spectra,
- Publication type
- Journal Article MeSH
We report the preparation, X-ray structure, chemical properties, and electron paramagnetic resonance (EPR) studies at Q and X-bands and temperature (mainly) T = 293 K of powder and oriented single crystal samples of the new compound [Cu(N',N'-dimethyl-N'-benzoylthiourea)(2,2'-bipyridine)Cl], called CuBMB. The EPR spectra of single crystal samples at the Q-band display abrupt merging and narrowing of the peaks corresponding to two rotated copper sites as a function of magnetic field (B0) orientation. This behaviour indicates a quantum transition from an array of quasi-isolated spins to a quantum-entangled spin array associated with exchange narrowing processes and produced by weak intermolecular exchange interactions Ji between neighbour copper spins. This transition occurs when the magnitudes of the anisotropic contributions to the Zeeman couplings, tuned with the direction of B0, approach these |Ji| and produce level crossings. The exchange couplings between neighbour spins are estimated from the angular variation of the single crystal EPR results at the Q-band. We analyse the quantum behaviour and phase transitions of the spin system and discuss the magnitudes of the exchange couplings in terms of the structure of the chemical paths connecting Cu neighbours. The single crystal data at the Q-band indicates an uncommon ground electronic state of CuII which is discussed and compared with the results of DFT calculations. The spectrum of polycrystalline (powder) samples at the Q-band is a sum of contributions of microcrystals in each phase, and the fraction F of the entangled phase depends on the microwave frequency. The X-band spectrum is compatible with the Q-band results, but does not display a transition, and the spin system is in the quantum-entangled phase for all field orientations. This behaviour is further studied with a simple geometric model giving basic predictions. The crystal structure of CuBMB is monoclinic, space group P21/n, with a = 11.9790(3) Å, b = 14.0236(5) Å, c = 12.1193(3) Å, β = 104.952(2)° and Z = 4, and the copper ions are equatorially bonded to the benzoylthiourea and bipyridine ligands in a heavily distorted square pyramidal structure.
- Publication type
- Journal Article MeSH
Although machine learning potentials have recently had a substantial impact on molecular simulations, the construction of a robust training set can still become a limiting factor, especially due to the requirement of a reference ab initio simulation that covers all the relevant geometries of the system. Recognizing that this can be prohibitive for certain systems, we develop the method of transition tube sampling that mitigates the computational cost of training set and model generation. In this approach, we generate classical or quantum thermal geometries around a transition path describing a conformational change or a chemical reaction using only a sparse set of local normal mode expansions along this path and select from these geometries by an active learning protocol. This yields a training set with geometries that characterize the whole transition without the need for a costly reference trajectory. The performance of the method is evaluated on different molecular systems with the complexity of the potential energy landscape increasing from a single minimum to a double proton-transfer reaction with high barriers. Our results show that the method leads to training sets that give rise to models applicable in classical and path integral simulations alike that are on par with those based directly on ab initio calculations while providing the computational speedup we have come to expect from machine learning potentials.
- Publication type
- Journal Article MeSH
Metamorphic diamonds hosted by major and accessory phases in ultrahigh-pressure (UHP) metamorphic terranes represent important indicators of deep subduction and exhumation of continental crust at convergent plate boundaries. However, their nucleation and growth mechanisms are not well understood due to their small size and diversity. The Bohemian microdiamond samples represent a unique occurrence of monocrystalline octahedral and polycrystalline cubo-octahedral microdiamonds in two different metasedimentary rock types. By combining new and published data on microdiamonds (morphology, resorption, associated phases, carbon isotope composition) with P-T constraints from their host rocks, we demonstrate that the peak P-T conditions for the diamond-bearing UHP rocks cluster along water activity-related phase transitions that determine the microdiamond features. With increasing temperature, the diamond-forming medium changes from aqueous fluid to hydrous melt, and diamond morphology evolves from cubo-octahedral to octahedral. The latter is restricted to the UHP-UHT rocks exceeding 1100 °C, which is above the incongruent melting of phengite, where microdiamonds nucleate along a prograde P-T path in silicate-carbonate hydrous melt. The observed effect of temperature on diamond morphology supports experimental data on diamond growth and can be used for examining growth conditions of cratonic diamonds from kimberlites, which are dominated by octahedra and their resorbed forms.
- Publication type
- Journal Article MeSH
We investigate the local (or occupation) time of a discrete-time random walk on a generic graph, and present a general method for calculating sample-path averages of local time functionals in terms of the resolvent of the transition matrix.
- Publication type
- Journal Article MeSH
Photoabsorption spectra of small HgN clusters (N = 2-5) have been calculated using a diatomics-in-molecules interaction model and an atoms-in-molecules approach for transition probability calculations. Absorption cross-sections are provided over a broad range of photon energies, Ephot = 4.0-7.5 eV, as calculated for various cluster temperatures ranging between T = 0 K and T = 40 K. Quantum as well as temperature-induced delocalization of nuclear positions has been taken into account at various levels using classical and quantum (path-integral) Monte Carlo methods as well as sampling from the square of cluster vibrational ground-state wavefunctions. A thorough comparison of the calculated data with available experimental records is also provided.
- Publication type
- Journal Article MeSH
