Proteins. Structures and molecular properties, T.E. Creighton. W. H. Freeman and Company, New York (1984), 515, $36.95

In this note, we propose partially linear models with least squares support vector machines (LS-SVMs) for nonlinear ARX models. We illustrate how full black-box models can be improved when prior information about model structure is available. A real-life example, based on the Silverbox benchmark data, shows significant improvements in the generalization ability of the structured model with respect to the full black-box model, reflected also by a reduction in the effective number of parameters.

Kernel based partially linear models and nonlinear identification

Much work has been done in the past decade to quantify the phenomenon of allosteric communication in proteins. Every new study unveils an extra piece of the puzzle in our search for an understanding of allostery that allows us to make predictions on the response of a protein to medically relevant stimuli such as pathological mutations or drug binding. This review summarizes recent advances in the analysis of mechanisms of allosteric communication in proteins, and combines this new knowledge to offer a perspective of allostery which is consistent with chemical views of molecular processes. First, we review recent work, particularly computational, on the characterization of signal propagation and conformational changes in allosteric proteins. We then compare different models of allostery, and discuss the significance of the concept of an allosteric pathway. We argue that allostery can be rationalized in terms of pathways of residues that efficiently transmit energy between different binding sites. We then p...

A Chemical Perspective on Allostery.

A novel transacetylase (TAase) function of glutamine synthetase (GS) in bacterial species such as Mycobacterium smegmatis and Mycobacterium tuberculosis H37Rv was established by us, termed as mycobacterial TAase (MTAase). Several polyphenolic acetates (PAs) were found to be substrates for MTAase by inhibiting certain receptor proteins such as glutathione S-transferase by way of acetylation. The present work describes the descriptor-based 2D-QSAR studies developed for a series of PA synthesized by us and evaluated for MTAase and antimycobacterial activity using stepwise multiple linear regression method with the kinetic constants and the minimum inhibitory constant (MIC) as the dependent variables, to address the fact that TAase activity was leading to the antimycobacterial activity. Further, blind docking methods using AutoDock were carried out to study the interaction of potent PA with the crystal structure of M. tuberculosis GS. PAs were predicted to bind M. tuberculosis GS on the protein surface away from the known active site of GS. Subsequent focussed/refined docking of potent PA with GS showed that the -amino group of Lys4 of GS formed a cation- interaction with the benzene ring of PA. Also, ADMET-related descriptors were calculated to predict the pharmacokinetic properties for the selection of the effective and bioavailable compounds.

/pdf/2d-qsar-docking-studies-and-in-silico-admet-prediction-of-1tay2y2wkf.pdf

2D-QSAR, Docking Studies, and In Silico ADMET Prediction of Polyphenolic Acetates as Substrates for Protein Acetyltransferase Function of Glutamine Synthetase of Mycobacterium tuberculosis

Finding optimal three-dimensional molecular configurations based on a limited amount of experimental and/or theoretical data requires efficient nonlinear optimization algorithms. Optimization methods must be able to find atomic configurations that are close to the absolute, or global, minimum error and also satisfy known physical constraints such as minimum separation distances between atoms (based on van der Waals interactions). The most difficult obstacles in these types of problems are that 1) using a limited amount of input data leads to many possible local optima and 2) introducing physical constraints, such as minimum separation distances, helps to limit the search space but often makes convergence to a global minimum more difficult. We introduce a constrained global optimization algorithm that is robust and efficient in yielding near-optimal three-dimensional configurations that are guaranteed to satisfy known separation constraints. The algorithm uses an atom-based approach that reduces the dimensionality and allows for tractable enforcement of constraints while maintaining good global convergence properties. We evaluate the new optimization algorithm using synthetic data from the yeast phenylalanine tRNA and several proteins, all with known crystal structure taken from the Protein Data Bank. We compare the results to commonly applied optimization methods, such as distance geometry, simulated annealing, continuation, and smoothing. We show that compared to other optimization approaches, our algorithm is able combine sparse input data with physical constraints in an efficient manner to yield structures with lower root mean squared deviation.

/pdf/constrained-global-optimization-for-estimating-molecular-4573mt0n5n.pdf

Constrained global optimization for estimating molecular structure from atomic distances.

This paper formulates the nonlinear system modeling problem as a scattered data interpolation problem, and develops a new method that computes interpolants that minimize a wavelet-based norm subject to interpolatory constraints. The norm is that of a Reproducing Kernel Hilbert Space (RKHS) for which the wavelet functions that form an orthonormal basis for L 2 are orthogonal. In contrast to radial basis function kernels, these kernels are not translation invariant and they may be designed to provide spatially varying resolution useful for interpolating from unevenly distributed data samples. Furthermore, the discrete wavelet transform can be exploited to efficiently compute the values of the interpolant on a uniform grid. Modeling of systems in Sobolev spaces using different interpolation methods is discussed in details as a special case of RKHS. Numerical simulations are used to demonstrate the effectiveness of the method.

Wavelet Based Modeling of Nonlinear Systems

Proteinmorphosis is a physically-based interactive modeling system for simulating large or small conformational changes of proteins and protein complexes. It takes advantage of the cross-linked one-dimensional nature of protein chains. The user can, based on her chemical knowledge, pull pairs of points (lying either on a single protein or on different molecules) together by specifying geometric distance constraints. The resulting conformation(s) of the molecule(s) of interest is computed by an efficient finite element formalism taking into account elasticity of the protein backbone, van der Waals repulsions, hydrogen bonds, salt bridges and the imposed distance constraints. The conformational change is computed incrementally and the result can be visualized as an animation; complete interactivity is provided to position and view the proteins as desired by the user. Physical properties of regions on the protein can also be chosen interactively. The conformational change of calmodulin upon peptide binding is examined as a first experiment. It is found that the result is satisfactory in reproducing the conformational change that follows on peptide binding. We use Proteinmorphosis to study the cooperative hemoglobin oxygen binding mechanism in a second, more sophisticated, experiment. Different modeling strategies are designed to understand the allosteric (cooperative) binding process in this system and the results are found to be consistent with existing hypotheses.

/pdf/proteinmorphosis-a-mechanical-model-for-protein-4r1usw0lrb.pdf

Proteinmorphosis: a mechanical model for protein conformational changes.

We present a variational approach for the simulation of large conformational changes of proteins (including multiple protein chains/ligands) which takes advantage of their cross-linked one-dimensional nature, a structure which often occurs in civil engineering. Conformational changes are computed by incremental energy minimisation. We use an efficient finite element method for finding equilibria of complexes composed of inter-linked chains; this method is based on recent advances in the description of one-dimensional elasticity. Protein backbone elasticity, van der Waals repulsions, hydrogen bonds and salt bridges are taken into account, together with user-defined geometric distance constraints that may be imposed for purposes of simulating various binding processes based on chemical knowledge. These computational methods have been integrated into a system, Proteinmorphosis, which includes interactive visualisation. The conformational change of calmodulin upon peptide binding is examined as a first experiment. Allostery in hemoglobin, which consists of a cooperative oxygen binding mechanism, is a second, more sophisticated, numerical experiment. Different modelling strategies are designed to understand the allostery. The results for both molecules are consistent with existing hypotheses, and reproduce the known atomic positions after binding to within the experimental error. The modelling system is part of an on-going program to model structural biology, from protein structure to cell and tissue properties.

A Civil Engineering Model of Protein Conformational Change

In this paper, we analyze the numerical approximation of the Navier–Stokes problem over a bounded polygonal domain in R 2 , where the initial condition is modeled by a log-normal random ﬁeld. This problem usually arises in the area of uncertainty quantiﬁcation. We aim to compute the expectation value of linear functionals of the solution to the Navier–Stokes equations and perform a rigorous error analysis for the problem. In particular, our method includes the ﬁnite element, fully-discrete discretizations, truncated Karhunen–Lo´eve expansion for the realizations of the initial condition, and lattice-based quasi-Monte Carlo (QMC) method to estimate the expected values over the parameter space. Our QMC analysis is based on randomly-shifted lattice rules for the integration over the domain in high-dimensional space, which guarantees the error decays with O ( N − 1+ δ ), where N is the number of sampling points, δ > 0 is an arbitrary small number, and the constant in the decay estimate is independent of the dimension of integration. of

Quasi-Monte Carlo finite element approximation of the Navier-Stokes equations with initial data modeled by log-normal random fields

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Wavelet Based Modeling of Nonlinear Systems

Proteinmorphosis: a mechanical model for protein conformational changes.

A Civil Engineering Model of Protein Conformational Change

Quasi-Monte Carlo finite element approximation of the Navier-Stokes equations with initial data modeled by log-normal random fields