On the Statistical Calibration of Physical Models

We introduce a novel statistical calibration framework for physical models, relying on probabilistic embedding of model discrepancy error within the model. For clarity of illustration, we take the measurement errors out of consideration, calibrating a chemical model of interest with respect to a more detailed model, considered as “truth” for the present purpose. We employ Bayesian statistical methods for such model‐to‐model calibration and demonstrate their capabilities on simple synthetic models, leading to a well‐defined parameter estimation problem that employs approximate Bayesian computation. The method is then demonstrated on two case studies for calibration of kinetic rate parameters for methane air chemistry, where ignition time information from a detailed elementary‐step kinetic model is used to estimate rate coefficients of a simple chemical mechanism. We show that the calibrated model predictions fit the data and that uncertainty in these predictions is consistent in a mean‐square sense with the discrepancy from the detailed model data.     

Time lapse confocal microscopy studies of bacterial adhesion to self-assembled monolayers and confirmation of a novel approach to the thermodynamic model

In this study, we use thermodynamic theory to develop a novel model that allows for the quantitative determination of the Gibbs free energy of adhesion for the initial bacterial attachment process. This model eliminates the need to calculate interfacial free energies and instead relies on easily measurable contact angles to determine DeltaG(adh). We experimentally verify our model using real-time observation of the initial attachment of Pseudomonas putida to methyl- and hydroxyl-terminated self-assembled monolayers. We also test the applicability of our model to a variety of experimental conditions using data available in the literature. We show that the initial attachment process is governed by dispersion forces and is accurately predicted by our model. Also, we find that our model is simple to apply and accurate for a variety of experimental conditions.     

Ellipsoidal potential parameterization for bisphenol-A polycarbonate

We present a coarse-grained parameterization for the intra- and intermolecular potential for bisphenol-A polycarbonate (BPA-PC). The parameterization is based on the ellipsoidal-shaped monomer unit model applied to BPA-PC. Because of the symmetries of the model a Lennard-Jones type or even a mere repulsive potential with the usual parameters suffices to model the non-bonded interactions. We determined the potential parameters from ab-initio quantum calculations for the BPA-PC monomer. Results of molecular dynamics simulations using our model compare favourably with experimental data.     

Density functional theory for efficient ab initio molecular dynamics simulations in solution

We present a density functional for first-principles molecular dynamics simulations that includes the electrostatic effects of a continuous dielectric medium. It allows for numerical simulations of molecules in solution in a model polar solvent. We propose a smooth dielectric model function to model solvation into water and demonstrate its good numerical properties for total energy calculations and constant energy molecular dynamics.     

A molecular model for flow induced crystallization of polymers

We present in this paper a thermodynamic model for flow induced crystallization of a thermoplastic. The thermomechanical framework (generalized standard materials) allows us to couple in a very natural way the kinetics of crystallization with the mechanical history experienced by the thermoplastic^[1]. In describing the viscoelastic properties of the polymer with a molecular theory, we obtain a model for flow-induced crystallization that couples the chain conformation to the kinetics of crystallization. This model intends to be valid both for shearing and elongation. We present the equations for two cases: Maxwell and Pom-Pom constitutive equations. We finally illustrate our model with injection molding simulations achieved with a dedicated Finite Element code.     

Modeling and simulation of equation of state for nonadditive hard disk mixtures

We present exact results for mixtures of nonadditive hard disks and use some of them to derive a consistent model for the equation of state. We also performed molecular dynamics simulation for hard disks over a wide range of size ratios. Comparison of the model to the data shows that the model is accurate for all densities in the case of additive and slightly nonadditive (nonadditivity parameter within ±0.1) mixtures. For large nonadditivity, the model is accurate for low to moderate densities only, and starts to deteriorate at high densities.     

Photon counting histogram: one-photon excitation.

The photon counting histogram (PCH) analysis is a fluorescence fluctuation method that is able to characterize the brightness and concentration of different fluorescent species present in a liquid sample. We find that the PCH model using a three-dimensional Gaussian observation volume profile is inadequate for fitting experimental data obtained from a confocal setup with one-photon excitation. We propose an imoroved model, which is based on the correction to the observation volume profile for the out-of-focus emission. We demonstrate that this model is able to resolve different species present under a wide range of conditions. Attention is given to how this model allows the examination of the effects of different instrumental setups on the resolvability.     

High-sensitivity detection using isotachophoresis with variable cross-section geometry

We present a theoretical and experimental study on increasing the sensitivity of ITP assays by varying channel cross-section. We present a simple, unsteady, diffusion-free model for plateau mode ITP in channels with axially varying cross-section. Our model takes into account detailed chemical equilibrium calculations and handles arbitrary variations in channel cross-section. We have validated our model with numerical simulations of a more comprehensive model of ITP. We show that using strongly convergent channels can lead to a large increase in sensitivity and simultaneous reduction in assay time, compared to uniform cross-section channels. We have validated our theoretical predictions with detailed experiments by varying channel geometry and analyte concentrations. We show the effectiveness of using strongly convergent channels by demonstrating indirect fluorescence detection with a sensitivity of 100 nM. We also present simple analytical relations for dependence of zone length and assay time on geometric parameters of strongly convergent channels. Our theoretical analysis and experimental validations provide useful guidelines on optimizing chip geometry for maximum sensitivity under constraints of required assay time, chip area and power supply.     

What I like about Hückel theory

We start with some biographical notes on Erich Hückel, in the context of which we also mention the merits of Otto Schmidt, the inventor of the free-electron model. The basic assumptions behind the HMO (Hückel Molecular Orbital) model are discussed, and those aspects of this model are reviewed that make it still a powerful tool in Theoretical Chemistry. We ask whether HMO should be regarded as semiempirical or parameter-free. We present closed solutions for special classes of molecules, review the important concept of alternant hydrocarbons and point out how useful perturbation theory within the HMO model is. We then come to bond alternation and the question whether the pi or the sigma bonds are responsible for bond delocalization in benzene and related molecules. M?bius hydrocarbons and diamagnetic ring currents are other topics. We come to optimistic conclusions as to the further role of the HMO model, not as an approximation for the solution of the Schr?dinger equation, but as a way towards the understanding of some aspects of the Chemical Bond.     

On the equation of state for thermal polymer solutions and melts with attractive interaction

We perform Monte Carlo simulations of a lattice model for polymer melts, i. e., the bond fluctuation model in three dimensions. By using an energy parameter that prefers relatively long bonds, the model exhibits a glass transition at low temperatures, in close qualitative similarity to experiment. We modify this model by adding an attractive interaction of variable strength. We demonstrate that a small interaction strength has only a very small effect on the static properties of the melt. For a fixed strength of the potential, the chemical potential is measured by a modified particle-insertion method over a large range of temperatures and densities. The osmotic pressure is obtained by thermodynamic integration. In contrast to the original version our extended model exhibits a positive thermal expansion.     

Quantitative modeling of the behaviour of microfluidic autoregulatory devices

We develop a theoretical model for a fluidic current source consisting of a via, a detour channel, and a push-up type micro-valve. The model accurately describes the non-linear behaviour of this type of device, which has been previously measured experimentally. We show how various structural parameters and material properties of the device influence the saturated flow rate and the minimum driving pressure required for the device to function as a current source. Conversely, the model can be used to design a fluidic current source with a desired saturated flow rate and low operational pressure. The present model can be straightforwardly applied to microfluidic circuits composed of many functional autoregulatory devices.     

Molecular Modeling of Adsorption in Activated Carbon: Comparison of Monte Carlo Simulations with Experiment

We present Mont Carlo computer simulation results for a molecular model of fluids adsorbed in porous carbon materials. The model carbon used is based on the platelet model for carbon of Segarra and Glandt (1994). The model we use has a single basal plane per platelet and the structure is isotropic, disordered, with weak short-range correlations between the platelets. We have performed grand canonical Monte Carlo simulations of the adsorption isotherms for methane, ethane, and their mixtures in this model carbon. We find generally good agreement with experimental and the mixture results are quite accurately described by the ideal adsorbed solution theory. An exception to this is the behavior for the mixture at the highest pressures. In this case the experimental data show significant deviations from ideal adsorbed solution theory and the simulation results.     

An atomistic model of passive membrane permeability: application to a series of FDA approved drugs

We apply an atomistic model of passive membrane permeability to a series of weakly basic drugs. The computational model uses conformational sampling in combination with an all-atom force field and implicit solvent model to estimate relative passive membrane permeabilities. The model does not require the use of training data for rank-ordering compounds, and as such represents a different approach from the more commonly employed QSPR models. We compare the computational results to previously published experimental PAMPA and Caco-2 permeabilities.     

Analyzing mechanisms and microscopic reversibility of self-assembly

We use computer simulations to investigate self-assembly in a system of model chaperonin proteins, and in an Ising lattice gas. We discuss the mechanisms responsible for rapid and efficient assembly in these systems, and we use measurements of dynamical activity and assembly progress to compare their propensities for kinetic trapping. We use the analytic solution of a simple minimal model to illustrate the key features associated with such trapping, paying particular attention to the number of ways that particles can misbind. We discuss the relevance of our results for the design and control of self-assembly in general.     

Quantitative characterization of DNA films by X-ray photoelectron spectroscopy

We describe the use of self-assembled films of thiolated (dT)25 single-stranded DNA (ssDNA) on gold as a model system for quantitative characterization of DNA films by X-ray photoelectron spectroscopy (XPS). We evaluate the applicability of a uniform and homogeneous overlayer-substrate model for data analysis, examine model parameters used to describe DNA films (e.g., density and electron attenuation length), and validate the results. The model is used to obtain quantitative composition and coverage information as a function of immobilization time. We find that when the electron attenuation effects are properly included in the XPS data analysis, excellent agreement is obtained with Fourier transform infrared (FTIR) measurements for relative values of the DNA coverage, and the calculated absolute coverage is consistent with a previous radiolabeling study. Based on the effectiveness of the analysis procedure for model (dT)25 ssDNA films, it should be generally valid for direct quantitative comparison of DNA films prepared under widely varying conditions.     

Homochiral oligopeptides by chiral amplification: interpretation of experimental data with a copolymerization model

We present a differential rate equation model of chiral polymerization based on a simple copolymerization scheme in which the enantiomers are added to, or removed from, the homochiral or heterochiral chains (reversible stepwise isodesmic growth or dissociation). The model is set up for closed systems and takes into account the corresponding thermodynamic constraints implied by the reversible monomer attachments, while obeying a constant mass constraint. In its simplest form, the model depends on a single variable rate constant, the maximum chain length N, and the initial concentrations. We have fit the model to the experimental data from the Rehovot group on lattice-controlled chiral amplification of oligopeptides. We find in all the chemical systems employed, except for one, that the model fits the measured relative abundances of the oligopeptides with higher degrees of correlation than from a purely random polymerization process.     

Addressing the challenges of modeling the scattering from bottlebrush polymers in solution

Small-angle scattering measurements of complex macromolecules in solution are used to establish relationships between chemical structure and conformational properties. Interpretation of the scattering data requires an inverse approach where a model is chosen and the simulated scattering intensity from that model is iterated to match the experimental scattering intensity. This raises challenges in the case where the model is an imperfect approximation of the underlying structure, or where there are significant correlations between model parameters. We examine three bottlebrush polymers (consisting of polynorbornene backbone and polystyrene side chains) in a good solvent using a model commonly applied to this class of polymers: the flexible cylinder model. Applying a series of constrained Monte-Carlo Markov Chain analyses demonstrates the severity of the correlations between key parameters and the presence of multiple close minima in the goodness of fit space. We demonstrate that a shape-agnostic model can fit the scattering with significantly reduced parameter correlations and less potential for complex, multimodal parameter spaces. We provide recommendations to improve the analysis of complex macromolecules in solution, highlighting the value of Bayesian methods. This approach provides richer information for understanding parameter sensitivity compared to methods which produce a single, best fit.     

Collaborative filtering on a family of biological targets

Building a QSAR model of a new biological target for which few screening data are available is a statistical challenge. However, the new target may be part of a bigger family, for which we have more screening data. Collaborative filtering or, more generally, multi-task learning, is a machine learning approach that improves the generalization performance of an algorithm by using information from related tasks as an inductive bias. We use collaborative filtering techniques for building predictive models that link multiple targets to multiple examples. The more commonalities between the targets, the better the multi-target model that can be built. We show an example of a multi-target neural network that can use family information to produce a predictive model of an undersampled target. We evaluate JRank, a kernel-based method designed for collaborative filtering. We show their performance on compound prioritization for an HTS campaign and the underlying shared representation between targets. JRank outperformed the neural network both in the single- and multi-target models.