Numerical recipes: the art of scientific computing

Press, W. H.; Flannery, Brian P.; Teukolsky, Saul A.; Vetterling, William T.; Chipperfield, J.R.

doi:10.1016/s0003-2670(00)82860-3

Cited by 3,441 publications

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“…41,42 The significance of the correlation between experimental and theoretical values is deduced from Kendall's nonparametric . 39 Because one does not know a priori the probability distribution of the experimental B-factors, a significance for the agreement between the two data sets cannot be computed from the value of the linear correlation coefficient. On the other hand, the rank correlation given by is independent from the distribution.…”

Section: Temperature Factors and Heme Modelingsupporting

confidence: 75%

Modeling truncated hemoglobin vibrational dynamics

Marsella

2005

Proteins

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We present a study on the near equilibrium dynamics of two small proteins in the family of truncated hemoglobins, developed under the framework of a Gaussian network approach. Effective beta carbon atoms are taken into account besides Calphas for all residues but glycines in the coarse-graining procedure, without leading to an increase in the degrees of freedom (beta Gaussian Model). Normalized covariance matrix and deformation along slowest modes with collective character are analyzed, pointing out anticorrelations between functionally relevant sites for the proteins under study. In particular, we underline the functional motions of an extended tunnel-cavity system running inside the protein matrix, which provide a pathway for small ligands binding with the iron in the heme group. We give a rough estimate of the order of magnitude of the relaxation times of the slowest two overdamped modes and compare results with previous studies on globins.

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Section: Temperature Factors and Heme Modelingsupporting

confidence: 75%

Modeling truncated hemoglobin vibrational dynamics

Marsella

2005

Proteins

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“…The Matlab routine bvp4c (implementing the three-stage Lobatto IIIa formula) was used to solve the two-point boundary-value problem (4.42) -(4.46) forfðsÞ andf 1 , subject to (4.48) -(4.52) ats ¼ e ( 1 and (4.47) ats ¼S ) 1. Numerical results were verified by comparison with a Cþþ shooting program that implements Runge -Kutta integration and Newton's method (based on algorithms from Numerical recipes [77]) and integration with ode45 in Matlab. Condition (4.47) is applied at a large valueS ofs: in practice, S ¼ 20 proved more than sufficient for far-field behaviour to become clear.…”

Section: Methodsmentioning

confidence: 99%

Arenavirus budding resulting from viral-protein-associated cell membrane curvature

Schley

Whittaker

Neuman

2013

J. R. Soc. Interface.

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Viral replication occurs within cells, with release (and onward infection) primarily achieved through two alternative mechanisms: lysis, in which virions emerge as the infected cell dies and bursts open; or budding, in which virions emerge gradually from a still living cell by appropriating a small part of the cell membrane. Virus budding is a poorly understood process that challenges current models of vesicle formation. Here, a plausible mechanism for arenavirus budding is presented, building on recent evidence that viral proteins embed in the inner lipid layer of the cell membrane. Experimental results confirm that viral protein is associated with increased membrane curvature, whereas a mathematical model is used to show that localized increases in curvature alone are sufficient to generate viral buds. The magnitude of the protein-induced curvature is calculated from the size of the amphipathic region hypothetically removed from the inner membrane as a result of translation, with a change in membrane stiffness estimated from observed differences in virion deformation as a result of protein depletion. Numerical results are based on experimental data and estimates for three arenaviruses, but the mechanisms described are more broadly applicable. The hypothesized mechanism is shown to be sufficient to generate spontaneous budding that matches well both qualitatively and quantitatively with experimental observations.

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“…Murphy, 2012;Bishop, 2006;Rasmussen, 2006), books about the Bayesian approach (usually also containing a chapter about the frequentist viewpoint; Gregory, 2005;Sivia & Skilling, 2006), books that compare probability theories (Samaniego, 2010;Hacking, 2006), as well as books about other scientific topics (e.g. Press, 2007). In the following only the principal inference schemes, as relevant for our problem, are discussed from which the main differences between the two approaches become clear.…”

Section: Statistical Inferencementioning

confidence: 99%

Indirect Fourier transform in the context of statistical inference

et al. 2016

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Inferring structural information from the intensity of a small-angle scattering (SAS) experiment is an ill-posed inverse problem. Thus, the determination of a solution is in general non-trivial. In this work, the indirect Fourier transform (IFT), which determines the pair distance distribution function from the intensity and hence yields structural information, is discussed within two different statistical inference approaches, namely a frequentist one and a Bayesian one, in order to determine a solution objectively From the frequentist approach the cross-validation method is obtained as a good practical objective function for selecting an IFT solution. Moreover, modern machine learning methods are employed to suppress oscillatory behaviour of the solution, hence extracting only meaningful features of the solution. By comparing the results yielded by the different methods presented here, the reliability of the outcome can be improved and thus the approach should enable more reliable information to be deduced from SAS experiments.

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Numerical recipes: the art of scientific computing

Cited by 3,441 publications

References 0 publications

Modeling truncated hemoglobin vibrational dynamics

Modeling truncated hemoglobin vibrational dynamics

Arenavirus budding resulting from viral-protein-associated cell membrane curvature

Indirect Fourier transform in the context of statistical inference

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