Shallow Local Minima Research Articles

Chaperone-protein interactions in live zebrafish larvae.

Functional protein-protein interaction, in particular transient “quinary structure,” is sensitive to small changes in the local environment, occurring in the form of pH, crowding, electrostatic and other interactions with neighboring molecules. One reason for this sensitivity is reflected in their energy landscape, characterized by a shallow local minima in the neighborhood of the functional configurations. This motivates our study of a functional protein-protein interaction in its native environment - different cell types in a living organism. We study the binding of the metabolic enzyme phosphoglycerate kinase (PGK) to the chaperone Hsp70 of which it is a client, to quantify binding in individual cells of larval zebrafish. Using a customized temperature-control setup, we subject the organism expressing fluorescently labelled PGK and Hsp70 in selected cell types to a range of temperatures to induce a controlled heat shock. Using fluorescence resonance energy transfer (FRET), we detect the Hsp70 chaperone response via an increase in the affinity between the two proteins near the melting point of PGK

Understanding the roles of amino acid residues in tertiary structure formation of chignolin by using molecular dynamics simulation

Chignolin is a 10-residue peptide (GYDPETGTWG) that forms a stable beta-hairpin structure in water. However, its design template, GPM12 (GYDDATKTFG), does not have a specific structure. To clarify which amino acids give it the ability to form the beta-hairpin structure, we calculated the folding free-energy landscapes of chignolin, GPM12, and their chimeric peptides using multicanonical molecular dynamics (MD) simulation. Cluster analysis of the conformational ensembles revealed that the native structure of chignolin was the lowest in terms of free energy while shallow local minima were widely distributed in the free energy landscape of GPM12, in agreement with experimental observations. Among the chimeric peptides, GPM12(D4P/K7G) stably formed the same beta-hairpin structure as that of chignolin in the MD simulation. This was confirmed by nuclear magnetic resonance (NMR) spectroscopy. A comparison of the free-energy landscapes showed that the conformational distribution of the Asp3-Pro4 sequence was inherently biased in a way that is advantageous both to forming hydrogen bonds with another beta-strand and to initiating loop structure. In addition, Gly7 helps stabilize the loop structure by having a left-handed alpha-helical conformation. Such a conformation is necessary to complete the loop structure, although it is not preferred by other amino acids. Our results suggest that the consistency between the short-range interactions that determine the local geometries and the long-range interactions that determine the global structure is important for stable tertiary structure formation.

Efficient Reconstruction of Piecewise Constant Images Using Nonsmooth Nonconvex Minimization

We consider the restoration of piecewise constant images where the number of the regions and their values are not fixed in advance, with a good difference of piecewise constant values between neighboring regions, from noisy data obtained at the output of a linear operator (e.g., a blurring kernel or a Radon transform). Thus we also address the generic problem of unsupervised segmentation in the context of linear inverse problems. The segmentation and the restoration tasks are solved jointly by minimizing an objective function (an energy) composed of a quadratic data-fidelity term and a nonsmooth nonconvex regularization term. The pertinence of such an energy is ensured by the analytical properties of its minimizers. However, its practical interest used to be limited by the difficulty of the computational stage which requires a nonsmooth nonconvex minimization. Indeed, the existing methods are unsatisfactory since they (implicitly or explicitly) involve a smooth approximation of the regularization term and often get stuck in shallow local minima. The goal of this paper is to design a method that efficiently handles the nonsmooth nonconvex minimization. More precisely, we propose a continuation method where one tracks the minimizers along a sequence of approximate nonsmooth energies $\{J_\eps\}$, the first of which being strictly convex and the last one the original energy to minimize. Knowing the importance of the nonsmoothness of the regularization term for the segmentation task, each $J_\eps$ is nonsmooth and is expressed as the sum of an $\ell_1$ regularization term and a smooth nonconvex function. Furthermore, the local minimization of each $J_{\eps}$ is reformulated as the minimization of a smooth function subject to a set of linear constraints. The latter problem is solved by the modified primal-dual interior point method, which guarantees the descent direction at each step. Experimental results are presented and show the effectiveness and the efficiency of the proposed method. Comparison with simulated annealing methods further shows the advantage of our method.

Hydration properties of magnesium and calcium ions from constrained first principles molecular dynamics

We studied the solvation structures of the divalent metal cations Mg(2+) and Ca(2+) in ambient water by applying a Car-Parrinello-based constrained molecular dynamics method. By employing the metal-water oxygen coordination number as a reaction coordinate, we could identify distinct aqua complexes characterized by structural variations of the first coordination shell. In particular, our estimated free-energy profile clearly shows that the global minimum for Mg(2+) is represented by a rather stable sixfold coordination in the octahedral arrangement, in agreement with experiments. Conversely, for Ca(2+) the free-energy curve shows several shallow local minima, suggesting that the hydration structure of Ca(2+) is highly variable. Implications for water exchange reactions are also discussed.

An ab Initio Investigation of the Ground and First Two Excited Electronic States of the Difluoromethyl Radical

Ab initio calculations have been performed to determine the structure and energies of the ground and first two excited electronic states of CHF2. The 6-31+G*, 6-311++G**, aug-ccpVDZ, and aug-cc-pVTZ basis sets were utilized at the MP2 and CCSD(T) levels of theory for the structures and energies of minima and transition states on the ground electronic surface. The 6-31+G*, 6-311++G** basis sets were utilized at the CIS, CASSCF, and MRCI levels of theory for characterization of the excited electronic states. The ground state was found to be pyramidal, the first excited state is possibly dissociative and the second excited state planar. Vertical transition energies for transitions from the ground to the first and second excited states were found to range from 61 355 to 71 372 cm-1 at the CIS level of theory. Shallow local minima on the A state potential energy surface with long C−H bonds of about 2.0 A were located by using two-dimensional potential surface scans. Upon excitation to the B state, the C−H bon...

Analysis of the Origin Band of Acridine Dimer Fluorescence Excitation Spectrum - Conformations of Jet-Cooled Acridine Dimer

The analysis of rotational band contour for the origin transition of fluorescence excitation spectrum of acridine dimer, earlier observed under conditions of jet-cooling in supersonic helium expansion, has been performed.An optimized ground-state equilibrium structure of acridine dimer fits the approximation of asymmetric top rigid rotor. In this approximation rotational constants were determined and an A-type rotational band was computed. It has turned out that the computed rotational band contour is much narrower than the experimental one. In search for the reasons of this discrepancy between calculations and experiment, an analysis of relative rotational motion of acridine moieties of the dimer was carried out. It was found that minima of potential energy curves for rotational motion, although very flat, under conditions of supersonic expansion can acquire (in their shallow local minima) non-vanishing population of slightly different conformations of the dimer. It was shown that in terms of non-statistical distribution of such populations, the origin bands of individual conformations may contribute to the experimental band contour.

A Comparison of Global Optimization Methods for the Design of a High-speed Civil Transport

The conceptual design of aircraft often entails a large number of nonlinear constraints that result in a nonconvex feasible design space and multiple local optima. The design of the high-speed civil transport (HSCT) is used as an example of a highly complex conceptual design with 26 design variables and 68 constraints. This paper compares three global optimization techniques on the HSCT problem and two test problems containing thousands of local optima and noise: multistart local optimizations using either sequential quadratic programming (SQP) as implemented in the design optimization tools (DOT) program or Snyman's dynamic search method, and a modified form of Jones' DIRECT global optimization algorithm. SQP is a local optimizer, while Snyman's algorithm is capable of moving through shallow local minima. The modified DIRECT algorithm is a global search method based on Lipschitzian optimization that locates small promising regions of design space and then uses a local optimizer to converge to the optimum. DOT and the dynamic search algorithms proved to be superior for finding a single optimum masked by noise of trigonometric form. The modified DIRECT algorithm was found to be better for locating the global optimum of functions with many widely separated true local optima.

Stabilities, Excitation Energies, and Dissociation Reactions of CF2Cl2 and CF2Br2: Quantum Chemical Computations of Heats of Formation of Fluorinated Methanes, Methyls, and Carbenes

The heats of formation of a range of chlorofluoro-, bromofluoro-, and iodofluoromethanes, methyls, and carbenes were computed using the Gaussian-3 (G3) and Gaussian-2 (G2) methods. From a number of computed isodesmic reaction enthalpies, the heats of formation (at 298 K) of the key methyl species in the decomposition reactions of difluoromethanes, namely CF2Cl, CF2Br, and CF2I, were determined as −64.7 ± 2.0, −52.3 ± 2.0, and −39.3 ± 2.0 kcal mol-1, respectively, while our recommended heat of formation for CI4 is 77.0 ± 3.0 kcal mol-1. Using the available thermochemistry the energetics of the dissociation reactions of CF2X2 (X = Cl, Br, I) corresponding to the product channels CF2X + X and CF2 + X2 (as well as CF2 + 2X) were thus computed and compared. The energetics favor the molecular channel but only by ∼10−12 kcal mol-1 in the case of CF2Cl2 and CF2Br2. However, no transition states were found in these systems for the molecular elimination of Cl2 and Br2. By contrast, H2 elimination in CF2H2 was found to be favored by ∼ 40 kcal mol-1 (at the G2 level) with the corresponding transition state predicted to be 17.3 kcal mol-1 below the radical products CHF2 + H. The vertical excitation energies of CF2Cl2 and CF2Br2 (to the lowest singlet and triplet B1, A2, B2, and A1 excited states) were computed using a range of methods including CASPT2 and EOM-CCSD in conjunction with the cc-pVTZ basis set. The results obtained for the lowest energy, viz., Ã(1B1) ← X̃(1A1), transitions are consistent with the available experimental data. The excited state potential energy surfaces, as calculated at the CASPT2 level of theory, are found to be repulsive with respect to a single C−Cl or C−Br bond stretch, but have shallow local minima in C2v symmetry, i.e., when both C−Cl or C−Br bonds are stretched to ∼2.3 Å, that suggest the existence of weakly bound metastable states.

Mixture of experts regression modeling by deterministic annealing

We propose a new learning algorithm for regression modeling. The method is especially suitable for optimizing neural network structures that are amenable to a statistical description as mixture models. These include mixture of experts, hierarchical mixture of experts (HME), and normalized radial basis functions (NRBF). Unlike recent maximum likelihood (ML) approaches, we directly minimize the (squared) regression error. We use the probabilistic framework as means to define an optimization method that avoids many shallow local minima on the complex cost surface. Our method is based on deterministic annealing (DA), where the entropy of the system is gradually reduced, with the expected regression cost (energy) minimized at each entropy level. The corresponding Lagrangian is the system's free-energy, and this annealing process is controlled by variation of the Lagrange multiplier, which acts as a temperature parameter. The new method consistently and substantially outperformed the competing methods for training NRBF and HME regression functions over a variety of benchmark regression examples.

From supramolecular photochemistry to the molecular computer

Abstract

Recovery of parametric models from range images: the case for superquadrics with global deformations

A method for recovery of compact volumetric models for shape representation of single-part objects in computer vision is introduced. The models are superquadrics with parametric deformations (bending, tapering, and cavity deformation). The input for the model recovery is three-dimensional range points. Model recovery is formulated as a least-squares minimization of a cost function for all range points belonging to a single part. During an iterative gradient descent minimization process, all model parameters are adjusted simultaneously, recovery position, orientation, size, and shape of the model, such that most of the given range points lie close to the model's surface. A specific solution among several acceptable solutions, where are all minima in the parameter space, can be reached by constraining the search to a part of the parameter space. The many shallow local minima in the parameter space are avoided as a solution by using a stochastic technique during minimization. Results using real range data show that the recovered models are stable and that the recovery procedure is fast.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>