459 research outputs found
Correctors for some asymptotic problems
In the theory of anisotropic singular perturbation boundary value problems, the solution u É does not converge, in the H 1-norm on the whole domain, towards some u 0. In this paper we construct correctors to have good approximations of u É in the H 1-norm on the whole domain. Since the anisotropic singular perturbation problems can be connected to the study of the asymptotic behaviour of problems defined in cylindrical domains becoming unbounded in some directions, we transpose our results for such problems
Escorted Free Energy Simulations: Improving Convergence by Reducing Dissipation
Nonequilibrium, ``fast switching'' estimates of equilibrium free energy
differences, Delta F, are often plagued by poor convergence due to dissipation.
We propose a method to improve these estimates by generating trajectories with
reduced dissipation. Introducing an artificial flow field that couples the
system coordinates to the external parameter driving the simulation, we derive
an identity for Delta F in terms of the resulting trajectories. When the flow
field effectively escorts the system along a near-equilibrium path, the free
energy estimate converges efficiently and accurately. We illustrate our method
on a model system, and discuss the general applicability of our approach.Comment: 4 pages, including 2 figures, accepted for publication in Phys Rev
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Time-independent free energies from metadynamics via Mean Force Integration
Inspired by thermodynamic integration, we propose a method for the
calculation of time-independent free energy profiles from history-dependent
biased simulations via Mean Force Integration (MFI). MFI circumvents the need
for computing the ensemble average of the bias acting on the system c(t) and
can be applied to different variants of metadynamics. Moreover, MFI naturally
extends to aggregate information obtained from independent metadynamics
simulations, allowing to converge free energy surfaces without the need to
sample recrossing events in a single continuous trajectory. We validate MFI
against one- and two-dimensional analytical potentials and by computing the
conformational free energy landscape of ibuprofen in the bulk of its most
common crystal phase.Comment: 8 pages, 4 figure
Differential Dynamics at Glycosidic Linkages of an Oligosaccharide as Revealed by 13C NMR Spin Relaxation and Stochastic Modeling
Among biomolecules, carbohydrates are unique in that not only can linkages be formed through different positions but the structures may also be branched. The trisaccharide \uf062-D-Glcp-(1\uf0ae3)[\uf062-D-Glcp-(1\uf0ae2)]-\uf061-D-Manp-OMe represents a model of a branched vicinally disubstituted structure. A 13C site-specific isotopologue with labeling in each of the two terminal glucosyl residues enabled acquisition of high-quality 13C NMR relaxation parameters T1, T2 and heteronuclear NOE, with standard deviations of \uf0a3 0.5%. For interpretation of the experimental NMR data a diffusive chain model was used in which the dynamics of the glycosidic linkages is coupled to the global reorientation motion of the trisaccharide. Brownian dynamics simulations relying on the potential of mean force at the glycosidic linkages were employed to evaluate spectral densities of the spin probes. Calculated NMR relaxation parameters showed very good agreement with experimental data, deviating < 3%. The resulting dynamics is described by correlation times of 196 ps and 174 ps for the \uf062-(1\uf0ae2)- and \uf062-(1\uf0ae3)-linked glucosyl residues, respectively, i.e., different and linkage dependent. Notably, the devised computational protocol was performed without any fitting of parameters
Efficient construction of free energy profiles of breathing metalâorganic frameworks using advanced molecular dynamics simulations
In order to reliably predict and understand the breathing behavior of highly flexible metalâorganic frameworks from thermodynamic considerations, an accurate estimation of the free energy difference between their different metastable states is a prerequisite. Herein, a variety of free energy estimation methods are thoroughly tested for their ability to construct the free energy profile as a function of the unit cell volume of MIL-53(Al). The methods comprise free energy perturbation, thermodynamic integration, umbrella sampling, metadynamics, and variationally enhanced sampling. A series of molecular dynamics simulations have been performed in the frame of each of the five methods to describe structural transformations in flexible materials with the volume as the collective variable, which offers a unique opportunity to assess their computational efficiency. Subsequently, the most efficient method, umbrella sampling, is used to construct an accurate free energy profile at different temperatures for MIL-53(Al) from first principles at the PBE+D3(BJ) level of theory. This study yields insight into the importance of the different aspects such as entropy contributions and anharmonic contributions on the resulting free energy profile. As such, this thorough study provides unparalleled insight in the thermodynamics of the large structural deformations of flexible materials
Nonequilibrium Detailed Fluctuation Theorem for Repeated Discrete Feedback
We extend the framework of forward and reverse processes commonly utilized in
the derivation and analysis of the nonequilibrium work relations to
thermodynamic processes with repeated discrete feedback. Within this framework,
we derive a generalization of the detailed fluctuation theorem, which is
modified by the addition of a term that quantifies the change in uncertainty
about the microscopic state of the system upon making measurements of physical
observables during feedback. As an application, we extend two nonequilibrium
work relations: the nonequilibrium work fluctuation theorem and the
relative-entropy work relation.Comment: 7 pages, 3 figure
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Mitochondrial ADP/ATP Carrier in Dodecylphosphocholine Binds Cardiolipins with Non-native Affinity
Biophysical investigation of membrane proteins generally requires their extraction from native sources using detergents, a step that can lead, possibly irreversibly, to protein denaturation. The propensity of docecylphosphocholine (DPC), a detergent widely utilized in NMR studies of membrane proteins, to distort their structure has been the subject of much controversy. It has been recently proposed that the binding specificity of the yeast mitochondrial ADP/ATP carrier (yAAC3) toward cardiolipins (CLs) is preserved in DPC, thereby suggesting that DPC is a suitable environment to study membrane proteins. In this communication, we used all-atom molecular dynamics simulations to investigate the specific binding of CLs to yAAC3. Our data demonstrate that the interaction interface observed in a native-like environment differs markedly from that inferred from an NMR investiga- tion in DPC, implying that in this detergent, the protein structure is distorted. We further investigated yAAC3 solubilized in DPC and in the milder dodecylmaltoside with thermal-shift assays. The loss of thermal transition observed in DPC confirms that the protein is no longer properly folded in this environment
Limits of the Stokes and Navier-Stokes equations in a punctured periodic domain
We treat three problems on a two-dimensional âpunctured periodic domainâ: we take Ωr=(âL,L)2ârK, where r>0 and K is the closure of an open connected set that is star-shaped with respect to 0 and has a C1 boundary. We impose periodic boundary conditions on the boundary of Ω=(âL,L)2, and Dirichlet boundary conditions on â(rK). In this setting we consider the Poisson equation, the Stokes equations, and the time-dependent NavierâStokes equations, all with a fixed forcing function f, and examine the behavior of solutions as râ0. In all three cases we show convergence of the solutions to those of the limiting problem, i.e. the problem posed on all of Ω with periodic boundary conditions
Ice Formation on Kaolinite: Insights from Molecular Dynamics Simulations
The formation of ice affects many aspects of our everyday life as well as
technologies such as cryotherapy and cryopreservation. Foreign substances
almost always aid water freezing through heterogeneous ice nucleation, but the
molecular details of this process remain largely unknown. In fact, insight into
the microscopic mechanism of ice formation on different substrates is difficult
to obtain even via state-of-the-art experimental techniques. At the same time,
atomistic simulations of heterogeneous ice nucleation frequently face
extraordinary challenges due to the complexity of the water-substrate
interaction and the long timescales that characterize nucleation events. Here,
we have investigated several aspects of molecular dynamics simulations of
heterogeneous ice nucleation considering as a prototypical ice nucleating
material the clay mineral kaolinite, which is of relevance in atmospheric
science. We show via seeded molecular dynamics simulations that ice nucleation
on the hydroxylated (001) face of kaolinite proceeds exclusively via the
formation of the hexagonal ice polytype. The critical nucleus size is two times
smaller than that obtained for homogeneous nucleation at the same supercooling.
Previous findings suggested that the flexibility of the kaolinite surface can
alter the time scale for ice nucleation within molecular dynamics simulations.
However, we here demonstrate that equally flexible (or non flexible) kaolinite
surfaces can lead to very different outcomes in terms of ice formation,
according to whether or not the surface relaxation of the clay is taken into
account. We show that very small structural changes upon relaxation
dramatically alter the ability of kaolinite to provide a template for the
formation of a hexagonal overlayer of water molecules at the water-kaolinite
interface, and that this relaxation therefore determines the nucleation ability
of this mineral
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