451 research outputs found
Some Remarks on Nonuniqueness of Minimizers for Discrete Minimization Problems
We investigate the issue of uniqueness and nonuniqueness of minimizers for the approximation of variational problems. We show that when the continuous problem does not admit a minimizer its approximation by finite elements may lead to several discrete minimizer
On the numerical analysis of some variational problems with nonhomogeneous boundary conditions
The goal of this note is to expose a new techniques to get energy estimates for nonconvex problems with nonlinear boundary conditions in term of the mesh size of a Lagrange finite elements metho
Singular perturbations of some nonlinear problems
We deal with singular perturbations of nonlinear problems depending on a small parameter Δâ>â0. First we consider the abstract theory of singular perturbations of variational inequalities involving some nonlinear operators, defined in Banach spaces, and describe the asymptotic behavior of these solutions as Δâââ0. Then these abstract results are applied to some boundary value problems. Bibliography: 15 title
On an elliptic Kirchhoff-type problem depending on two parameters
In this paper, we consider the Dirichlet problem associated to an elliptic
Kirchhoff-type equation depending on two parameters. Under rather general and
natural assumptions, we prove that, for certain values of the parameters, the
problem has at least three solutions
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
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
Quasivariational solutions for first order quasilinear equations with gradient constraint
We prove the existence of solutions for an evolution quasi-variational
inequality with a first order quasilinear operator and a variable convex set,
which is characterized by a constraint on the absolute value of the gradient
that depends on the solution itself. The only required assumption on the
nonlinearity of this constraint is its continuity and positivity. The method
relies on an appropriate parabolic regularization and suitable {\em a priori}
estimates. We obtain also the existence of stationary solutions, by studying
the asymptotic behaviour in time. In the variational case, corresponding to a
constraint independent of the solution, we also give uniqueness results
QMCube (QM3): An allâpurpose suite for multiscale QM/MM calculations
QMCube (QM3) is a suite written in the Python programming language, initially focused on multiscale QM/MM simulations of biological systems, but open enough to address other kinds of problems. It allows the user to combine highly efficient QM and MM programs, providing unified access to a wide range of computational methods. The suite also supplies additional modules with extra functionalities. These modules facilitate common tasks such as performing the setup of the models or process the data generated during the simulations. The design of QM3 has been carried out considering the least number of external dependencies (only an algebra library, already included in the distribution), which makes it extremely portable. Also, the modular structure of the suite should help to expand and develop new computational methods
Origin of Native Driving Force in Protein Folding
We derive an expression with four adjustable parameters that reproduces well
the 20x20 Miyazawa-Jernigan potential matrix extracted from known protein
structures. The numerical values of the parameters can be approximately
computed from the surface tension of water, water-screened dipole interactions
between residues and water and among residues, and average exposures of
residues in folded proteins.Comment: LaTeX file, Postscript file; 4 pages, 1 figure (mij.eps), 2 table
Mechanism of the allosteric activation of the ClpP protease machinery by substrates and active-site inhibitors
Coordinated conformational transitions in oligomeric enzymatic complexes modulate function in response to substrates and play a crucial role in enzyme inhibition and activation. Caseinolytic protease (ClpP) is a tetradecameric complex, which has emerged as a drug target against multiple pathogenic bacteria. Activation of different ClpPs by inhibitors has been independently reported from drug development efforts, but no rationale for inhibitor-induced activation has been hitherto proposed. Using an integrated approach that includes x-ray crystallography, solid- and solution-state nuclear magnetic resonance, molecular dynamics simulations, and isothermal titration calorimetry, we show that the proteasome inhibitor bortezomib binds to the ClpP active-site serine, mimicking a peptide substrate, and induces a concerted allosteric activation of the complex. The bortezomib-activated conformation also exhibits a higher affinity for its cognate unfoldase ClpX. We propose a universal allosteric mechanism, where substrate binding to a single subunit locks ClpP into an active conformation optimized for chaperone association and protein processive degradation
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