Confidence limits,error bars and method comparison in molecular modeling. Part 1: The calculation of confidence intervals

Computational chemistry is a largely empirical field that makes predictions with substantial uncertainty. And yet the use of standard statistical methods to quantify this uncertainty is often absent from published reports. This article covers the basics of confidence interval estimation for molecular modeling using classical statistics. Alternate approaches such as non-parametric statistics and bootstrapping are discussed.     

What do we know and when do we know it?

Two essential aspects of virtual screening are considered: experimental design and performance metrics. In the design of any retrospective virtual screen, choices have to be made as to the purpose of the exercise. Is the goal to compare methods? Is the interest in a particular type of target or all targets? Are we simulating a ‘real-world’ setting, or teasing out distinguishing features of a method? What are the confidence limits for the results? What should be reported in a publication? In particular, what criteria should be used to decide between different performance metrics? Comparing the field of molecular modeling to other endeavors, such as medical statistics, criminology, or computer hardware evaluation indicates some clear directions. Taken together these suggest the modeling field has a long way to go to provide effective assessment of its approaches, either to itself or to a broader audience, but that there are no technical reasons why progress cannot be made.     

Macrocycles containing azo groups: recognition,assembly and application

In this review the authors present an overview of different molecular modeling campaigns dealing with the study and characterization of cyclodextrins (CDs) inclusion complexes with applicability to diverse biomedical and technological domains. The aim of this review is to present in a concise manner the new tendencies towards CDs molecular modeling studies in the context of a scientific computing era characterized by detailed and exhaustively validated molecular modeling protocols combined with and enormous and continuously growing computing power. Therefore, the present review covers research efforts reported in the last 5 years, including the simulation of native and modified CDs in a new and more detailed manner than what was possible in the past as well as their inclusion complexes with bioactive molecules studied by detailed protocols and exhaustive free-energy of binding calculations. Also, particular emphasis is devoted to the molecular modeling simulation of CDs included as part of drug delivery matrixes and intelligent nanodevices such as CD-based molecular motors.     

The use of nuclear techniques in source apportionment studies, exemplified by recent studies in Turkey

Nuclear analytical methods are very important atmospheric tools as they provide multielement data, which is essential for receptor modeling. In this study, the application of receptor modeling is discussed on rural data to determine source regions affecting chemical composition of aerosols in the Eastern Mediterranean. The factor analysis revealed 4 sources, two of which represent anthropogenic component in aerosol mass. The source regions that determine the composition of particles is investigated using trajectory statistics. This revised version was published online in August 2006 with corrections to the Cover Date.     

Unexpected steric effects of "remote" alkyl groups on the rate of conjugate additions to alkyl alpha,beta-ethylenic sulfones, sulfoxides, and esters

Examination of conjugated ethylenic sulfones, sulfoxides, and esters in Michael-type addition reactions reveals, for the first time, that the size of the heteroatom-attached alkyl group affects the rate of conjugate addition. Molecular modeling strongly suggests that what are generally considered to be "remote" alkyl groups in -CbetaH=CalphaHS(O)n-alkyl systems and -CH2CbetaH=CalphaHCOO-alkyl systems are actually not remote from the beta-carbon atom of the Michael accepting unit. Molecular modeling clearly shows that the alkyl groups in these Michael acceptors shield the beta-carbons in the following order: Eti-Pr>t-Bu.     

On the calculation of single-particle time correlation functions from Bose-Einstein centroid dynamics

The calculation of single-particle time correlation functions using the Bose-Einstein centroid dynamics formalism is discussed. A new definition of the quasidensity operator is used to calculate the centroid force on a given particle for an anharmonic system. The force includes correlation effects due to quantum statistics and is used for the calculation of the classical-like dynamics of phase-space centroid variables within the centroid molecular dynamics approximation. Time correlation functions are then obtained for single-particle quantities. These correspond to the double-Kubo transform of exact quantum-mechanical correlation functions. The centroid dynamics results are compared to those of exact basis-set calculations and a good agreement is found. The level of accuracy is in fact the same as what was observed earlier for the calculation of center-of-mass correlation functions for Fermi-Dirac and Bose-Einstein statistics, and for any correlation function for Boltzmann statistics. These results show that it is now possible to use Bose-Einstein centroid molecular dynamics to calculate single-particle correlation functions for systems where quantum exchange effects are present.     

Fast and accurate methods for predicting short-range constraints in protein models

Protein modeling tools utilize many kinds of structural information that may be predicted from amino acid sequence of a target protein or obtained from experiments. Such data provide geometrical constraints in a modeling process. The main aim is to generate the best possible consensus structure. The quality of models strictly depends on the imposed conditions. In this work we present an algorithm, which predicts short-range distances between Cα atoms as well as a set of short structural fragments that possibly share structural similarity with a query sequence. The only input of the method is a query sequence profile. The algorithm searches for short protein fragments with high sequence similarity. As a result a statistics of distances observed in the similar fragments is returned. The method can be used also as a scoring function or a short-range knowledge-based potential based on the computed statistics.     

Modeling data from titration,amide H/D exchange,and mass spectrometry to obtain protein-ligand binding constants

We recently reported a new method for quantification of protein-ligand interaction by mass spectrometry, titration and H/D exchange (PLIMSTEX) for determining the binding stoichiometry and affinity of a wide range of protein-ligand interactions. Here we describe the method for analyzing the PLIMSTEX titration curves and evaluate the effect of various models on the precision and accuracy for determining binding constants using H/D exchange and a titration. The titration data were fitted using a 1:n protein:ligand sequential binding model, where n is the number of binding sites for the same ligand. An ordinary differential equation was used for the first time in calculating the free ligand concentration from the total ligand concentration. A nonlinear least squares regression method was applied to minimize the error between the calculated and the experimentally measured deuterium shift by varying the unknown parameters. A resampling method and second-order statistics were used to evaluate the uncertainties of the fitting parameters. The interaction of intestinal fatty-acid-binding protein (IFABP) with a fatty-acid carboxylate and that of calmodulin with Ca(2+) are used as two tests. The modeling process described here not only is a new tool for analyzing H/D exchange data acquired by ESI-MS, but also possesses novel aspects in modeling experimental titration data to determine the affinity of ligand binding.     

Chemical data,ways and means,past and future

A brief outline of various data handling methods, from linear learning machines, principal component analysis, experimental design, and modeling to visualization, optimization, and validation together with a personal view on the historical development of the use of these methods, is given. Some future trends in handling chemical data are proposed as well. Copyright © 2014 John Wiley & Sons, Ltd.     

New simulation model of multicomponent crystal growth and inhibition

We review a novel computational model for the study of crystal structures both on their own and in conjunction with inhibitor molecules. The model advances existing Monte Carlo (MC) simulation techniques by extending them from modeling 3D crystal surface patches to modeling entire 3D crystals, and by including the use of "complex" multicomponent molecules within the simulations. These advances makes it possible to incorporate the 3D shape and non-uniform surface properties of inhibitors into simulations, and to study what effect these inhibitor properties have on the growth of whole crystals containing up to tens of millions of molecules. The application of this extended MC model to the study of antifreeze proteins (AFPs) and their effects on ice formation is reported, including the success of the technique in achieving AFP-induced ice-growth inhibition with concurrent changes to ice morphology that mimic experimental results. Simulations of ice-growth inhibition suggest that the degree of inhibition afforded by an AFP is a function of its ice-binding position relative to the underlying anisotropic growth pattern of ice. This extended MC technique is applicable to other crystal and crystal-inhibitor systems, including more complex crystal systems such as clathrates.     

Colloid–chemical regression model in analyzing the relationship between dynamic surface tension and the content of total protein and albumins in blood

Mathematical statistics methods in chemistry and biology make it possible to apply certain analytical methods, e.g., interphase tensiometry, in diagnosing physiological states of humans and animals. This study is the first to use the regression method for modeling the relationship between the biochemical parameters of blood serum and dynamic surface tension (DST). We also demonstrate how the regression model can be used to determine the contents of total protein and albumins in blood serum from the known DST values at the liquid/air interface. As a result of constructing the regression model, we propose the regression equations characterizing the relationship between the DST values and the content of protein components in blood serum of animals.     

On the geometric modeling approach to empirical null distribution estimation for empirical Bayes modeling of multiple hypothesis testing

We study the geometric modeling approach to estimating the null distribution for the empirical Bayes modeling of multiple hypothesis testing. The commonly used method is a nonparametric approach based on the Poisson regression, which however could be unduly affected by the dependence among test statistics and perform very poorly under strong dependence. In this paper, we explore a finite mixture model based geometric modeling approach to empirical null distribution estimation and multiple hypothesis testing. Through simulations and applications to two public microarray data, we will illustrate its competitive performance.     

The character of molecular modeling

In asking what progress might occur in molecular modeling in the next 25 years it is worth asking what progress has been made in the last twenty-five. In doing so it is hard to be optimistic for the future of the field unless a greater commitment is made to basic science.     

The use of the terms formal element,initial and detailed components,and phase and chemical form in modeling of the states of homo- and heterogeneous systems

The terms formal element, initial and detailed components, and phase and chemical form and their use in chemical thermodynamic modeling of the state of substances in homo- and heterogeneous systems with taking into account local and partial equilibria are considered. The detailed component concept is introduced into fundamental equations. The use of the concept of formal elements is illustrated.     

Synthesis,properties and molecular modeling of functional hyperbranched polymers and dendrimers

The design, synthesis, properties and molecular modeling of fully conjugated dendritic molecules and conjugated hyperbranched polymers are described. It has been shown that conjugated hyperbranched molecules are much more soluble than their linear analogues while maintaining all the properties characteristic of conjugated polymers. It was found that the use of polymeric solid support in hyperbranched polymerization allows to control molecular weight and degree of branching (DB). The molecular modeling of hyperbranched conjugated molecules reveals that hyperbranched structure of conjugated molecules affects significantly neither their stability nor the conjugation. On the other hand the terminal groups affect appreciably the electronic structure of conjugated hyperbranched molecules.     

The effect of time step,thermostat, and strain rate on ReaxFF simulations of mechanical failure in diamond,graphene, and carbon nanotube

As the sophistication of reactive force fields for molecular modeling continues to increase, their use and applicability has also expanded, sometimes beyond the scope of their original development. Reax Force Field (ReaxFF), for example, was originally developed to model chemical reactions, but is a promising candidate for modeling fracture because of its ability to treat covalent bond cleavage. Performing reliable simulations of a complex process like fracture, however, requires an understanding of the effects that various modeling parameters have on the behavior of the system. This work assesses the effects of time step size, thermostat algorithm and coupling coefficient, and strain rate on the fracture behavior of three carbon‐based materials: graphene, diamond, and a carbon nanotube. It is determined that the simulated stress‐strain behavior is relatively independent of the thermostat algorithm, so long as coupling coefficients are kept above a certain threshold. Likewise, the stress‐strain response of the materials was also independent of the strain rate, if it is kept below a maximum strain rate. Finally, the mechanical properties of the materials predicted by the Chenoweth C/H/O parameterization for ReaxFF are compared with literature values. Some deficiencies in the Chenoweth C/H/O parameterization for predicting mechanical properties of carbon materials are observed. © 2015 Wiley Periodicals, Inc.     

XYZ,a program for modeling,validation, prediction and graphic display of data

A program for modeling, validation, prediction and graphic display of data is reported. The package is useful for dealing with responses that area function of a reduced number of variables. Implementation of user-defined models is easy and several very general equations can be selected. The structure of the program is shown and the use of the different modules is explained. Two typical, applications based on distinct mathematical models are shown.     

A comparison of performance statistics for proficiency testing programmes

Recently, ISO issued a new document on statistical methods for use in proficiency-testing schemes. The document presented a number of new performance statistics that involve the use of measurement uncertainties of the participants’ results and/or the assigned values for the performance evaluation. Making use of the Monte Carlo simulation technique, this paper attempts to compare selected performance statistics of different approaches. In addition, the simulation programme was extended to study the effect of multi-modality in participants’ results on the performance evaluation when different performance statistics were applied.     

R&D Intensification in Polymer Catalyst and Product Development by Using High‐Throughput Experimentation and Simulation

Currently laboratory automation is a rapidly growing field of interest in chemical process research and development. The idea of using automated and parallel methods for the optimization of chemical processes was initiated by the extensive implementation of combinatorial techniques in medicinal chemistry. The techniques applied involve all methods and concepts aimed at dramatically increasing the output of research by extensive use of automation, parallelization and miniaturization, fast analysis, advanced data handling and by efficient automated planning, scheduling and tracking. In this paper, the “Combi” or high‐throughput experimentation approach consists of the integration of parallel experimentation with four key modeling and simulation methodologies, modeling, multivariate statistics, statistical design of experimentation and empirical model generation.

Integrated automated liquid and solid handling.