Determination of best-fit potential parameters for a reactive force field using a genetic algorithm

The ReaxFF interatomic potential, used for organic materials, involves more than 600 adjustable parameters, the best-fit values of which must be determined for different materials. A new method of determining the set of best-fit parameters for specific molecules containing carbon, hydrogen, nitrogen and oxygen is presented, based on a parameter reduction technique followed by genetic algorithm (GA) minimization. This work has two novel features. The first is the use of a parameter reduction technique to determine which subset of parameters plays a significant role for the species of interest; this is necessary to reduce the optimization space to manageable levels. The second is the application of the GA technique to a complex potential (ReaxFF) with a very large number of adjustable parameters, which implies a large parameter space for optimization. In this work, GA has been used to optimize the parameter set to determine best-fit parameters that can reproduce molecular properties to within a given accuracy. As a test problem, the use of the algorithm has been demonstrated for nitromethane and its decomposition products.     

Protein structure prediction force fields: Parametrization with quasi-newtonian dynamics

We present an unusual method for parametrizing low-resolution force fields of the type used for protein structure prediction. Force field parameters were-determined by assigning each a fictitious mass and using a quasi-molecular dynamics algorithm in parameter space. The quasi-energy term favored folded native structures and specifically penalized folded nonnative structures. The force field was generated after optimizing less than 70 adjustable parameters, but shows a strong ability to discriminate between native structures and compact misfolded-alternatives. The functional form of the force field was chosen as in molecular mechanics and is not table-driven. It is continuous with continuous derivatives and is thus suitable for use with algorithms such as energy minimization or newtonian dynamics. Proteins 27:367–384, 1997. © 1997 Wiley-Liss, Inc.     

Determinants of protein side-chain packing.

The problem of protein side-chain packing for a given backbone trace is investigated using 3 different prediction models. The first requires an exhaustive search of all possible combinations of side-chain conformers, using the dead-end elimination theorem. The second considers only side-chain-backbone interactions, whereas the third neglects side-chain-backbone interactions and instead keeps side-chain-side-chain interactions. Predictions of side-chain conformations for 11 proteins using all 3 models show that removal of side-chain-side-chain interactions does not cause a large decrease in the prediction accuracy, whereas the model having only side-chain-side-chain interactions still retains a significant level of accuracy. These results suggest that the 2 classes of interactions, side-chain-backbone and side-chain-side-chain, are consistent with each other and work concurrently to stabilize the native conformations. This is confirmed by analyses of energy spectra of the side-chain conformations derived from the fourth prediction model, the Independent model, which gives almost the same quality of the prediction as the dead-end elimination. The analyses indicate that the 2 classes of interactions simultaneously increase the energy difference between the native and nonnative conformations.     

Theoretical studies on the behavior of carotid sinus baroreceptors

An approach to mathematical modeling of the baroreceptor that appears suitable for modeling mechanoreceptors in general is discussed. It differs from earlier works reported in the literature in the fact that it divides the baroreceptor into different functional components and attempts to describe mathematically the functioning of each component. The model consists of three first-order ordinary differential equations, one of which is linear; and there are ten free parameters. The ability of the model to fit different sets of experimental data with a single set of parameter values for a given class of inputs is demonstrated.     

Equilibrium electropotentials in electrolyte systems

The determinationof electric potentials in finite regions of symmetrical electrolyte in one-dimensional equilibrium situations requires the solution of the one-dimensional Poisson-Boltzmann equation in which the dependent variable is linearly related to the electric potential and contains unknown parameters. These require evaluation as part of the solution to a given boundary value problem. The general solution of the equation is presented. This involves elliptic functions and integrals and is sectionally isomorphic with respect to an integration parameter. The application to problems posed in terms of both initial values and two-point boundary values is discussed. The solution is used to determine the potential and concentration distributions between two flat-faced charged particles immersed in an electrolyte liquid and having interacting double layers.     

ORCHIDEE‐STICS,a process‐based model of sugarcane biomass production: calibration of model parameters governing phenology

Agro‐Land Surface Models (agro‐LSM) combine detailed crop models and large‐scale vegetation models (DGVMs) to model the spatial and temporal distribution of energy, water, and carbon fluxes within the soil–vegetation–atmosphere continuum worldwide. In this study, we identify and optimize parameters controlling leaf area index (LAI) in the agro‐LSM ORCHIDEE‐STICS developed for sugarcane. Using the Morris method to identify the key parameters impacting LAI, at eight different sugarcane field trial sites, in Australia and La Reunion island, we determined that the three most important parameters for simulating LAI are (i) the maximum predefined rate of LAI increase during the early crop development phase, a parameter that defines a plant density threshold below which individual plants do not compete for growing their LAI, and a parameter defining a threshold for nitrogen stress on LAI. A multisite calibration of these three parameters is performed using three different scoring functions. The impact of the choice of a particular scoring function on the optimized parameter values is investigated by testing scoring functions defined from the model‐data RMSE, the figure of merit and a Bayesian quadratic model‐data misfit function. The robustness of the calibration is evaluated for each of the three scoring functions with a systematic cross‐validation method to find the most satisfactory one. Our results show that the figure of merit scoring function is the most robust metric for establishing the best parameter values controlling the LAI. The multisite average figure of merit scoring function is improved from 67% of agreement to 79%. The residual error in LAI simulation after the calibration is discussed.     

Statistical mechanics of protein folding by exhaustive enumeration

It is hard to construct theories for the folding of globular proteins because they are large and complicated molecules having enormous numbers of nonnative conformations and having native states that are complicated to describe. Statistical mechanical theories of protein folding are constructed around major simplifying assumptions about the energy as a function of conformation and/or simplifications of the representation of the polypeptide chain, such as one point per residue on a cubic lattice. It is not clear how the results of these theories are affected by their various simplifications. Here we take a very different simplification approach where the chain is accurately represented and the energy of each conformation is calculated by a not unreasonable empirical function. However, the set of amino acid sequences and allowed conformations is so restricted that it becomes computationally feasible to examine them all. Hence we are able to calculate melting curves for thermal denaturation as well as the detailed kinetic pathway of refolding. Such calculations are based on a novel representation of the conformations as points in an abstract 12-dimensional Euclidean conformation space. Fast folding sequences have relatively high melting temperatures, native structures with relatively low energies, small kinetic barriers between local minima, and relatively many conformations in the global energy minimum's watershed. In contrast to other folding theories, these models show no necessary relationship between fast folding and an overall funnel shape to the energy surface, or a large energy gap between the native and the lowest nonnative structure, or the depth of the native energy minimum compared to the roughness of the energy landscape. Proteins 32:425–437, 1998. © 1998 Wiley-Liss, Inc.     

Quantitative analysis of the mechanism of negative staining with native collagen fibrils and polar tropomyosin paracrystals

The mechanism of formation of the negatively stained image in electron microscopy was infestigated with native collagen fibrils as a model. The negatively stained image was simulated from the primary structure by using the values of volume or bulkiness of each amino acid residue as a parameter for stain-excluding capacity. The pattern simulated from the bulkiness values gave an excellent fit with the negatively stained image. Since some contribution of positive staining components to negative staining has been suggested, positive staining with uranyl acetate was tested with various washing solutions of different pH. While acidic conditions did not produce any stained image, a positively stained image was easily obtained at alkaline pH. On the other hand, negatively stained images with stains of different charge character remained essentially the same as those obtained with acidic uranyl stains. It was concluded that the contribution of positive components to the negatively stained image is negligible under the conventional conditions for negative staining with uranyl acetate. In order to demonstrate the utility of the analytical method employing the values of "bulkiness," we studied the unknown molecular packing in the polar lead paracrystal of rabbit skeletal tropomyosin. Utilizing the primary sequence data for alpha-tropomyosin we successfully showed the polar paracrystal to be an array of molecules which are parallel and in register. Further, our analysis made it possible to deduce the position of a given residue in the negatively stained pattern of the polar paracrystal.     

Statistical mechanics of protein folding with separable energy functions

We have initiated an entirely new approach to statistical mechanical models of strongly interacting systems where the configurational parameters and the potential energy function are both constructed so that the canonical partition function can be evaluated analytically. For a simplified model of proteins consisting of a single, fairly short polypeptide chain without cross-links, we can adjust the energy parameters to favor the experimentally determined native state of seven proteins having diverse types of folds. Then 497 test proteins are predicted to have stable native folds, even though they are also structurally diverse, and 480 of them have no significant sequence similarity to any of the training proteins.     

Statistical mechanics of protein folding by cluster distance geometry

This is our second type of model for protein folding where the configurational parameters and the effective potential energy function are chosen in such a way that all conformations are described and the canonical partition function can be evaluated analytically. Structure is described in terms of distances between pairs of sequentially contiguous blocks of eight residues, and all possible conformations are grouped into 71 subsets in terms of bounds on these distances. The energy is taken to be a sum of pairwise interactions between such blocks. The 210 energy parameters were adjusted so that the native folds of 32 small proteins are favored in free energy over the denatured state. We then found 146 proteins having negligible sequence similarity to any of the training proteins, yet the free energy of the respective correct native states were favored over the denatured state.     

Prediction of protein folding from amino acid sequence over discrete conformation spaces

Predicting the three-dimensional structure of a protein given only its amino acid sequence is a long-standing goal in computational chemistry. In the thermodynamic approach, one needs a potential function of conformation that resembles the free energy of the real protein to the extent that the global minimum of the potential is attained by the native conformation and no other. In practice, this has never been achieved with certainty because even with greatly simplified representations of the polypeptide chain, there are an astronomical number of local minima to examine. If one chooses instead a protein representation with only a large but manageable number of discrete conformations, then the global preference of the potential for the native can be directly verified. Representing a protein as a walk on a two-dimensional square lattice makes it easy to see that simple functions of the interresidue contacts are sufficient to globally favor a given "native" conformation, as long as it is a compact, globular structure. Explicit representation of the solvent is not required. Another more realistic way to confine the conformational search to a finite set is to draw alternative conformations from fragments of larger proteins having known crystal structure. Then it is possible to construct a simple function of interresidue contacts in three dimensions such that only 8 proteins are required to determine the adjustable parameters, and the native conformations of 37 other proteins are correctly preferred over all alternative conformations. The deduced function favors short-range backbone-backbone contacts regardless of residue type and long-range hydrophobic associations. Interactions over long distances, such as electrostatics, are not required.     

Simplified method for the computation of parameters of power-law rate equations from time-series

Modeling biological processes from time-series data is a resourceful procedure which has received much attention in the literature. For models established in the context of non-linear differential equations, parameter-dependent phenomenological tentative response functions are tested by comparing would-be solutions of those models to the experimental time-series. Those values of the parameters for which a tested solution is a best fit are then retained. It is done with the help of some appropriate optimization algorithm which simplifies the searching procedure within the range of variability of the parameters that are to be estimated. The procedure works well in problems with a small number of adjustable parameters or/and with narrow searching ranges. However, it may start to be problematic for models with a large number of problem parameters inasmuch as convergence to the best fit is not necessarily ensured. In this case, a reduction in size of the parameter estimation problem must be undertaken. We presently address this issue by proposing a systematic procedure that does so in problems in which the system's response to a sufficiently small pulse perturbation of steady-state can be obtained. The response is then assumed to be a solution of the linearized equations, the Jacobian of which can be retrieved by a simple multilinear regression. The calculated n(2) Jacobian entries provide as many relationships among problem parameters, thus cutting substantially the size of the starting problem. After this preliminary treatment is applied, only (kappa-n(2)) of the initial kappa adjustable parameters are left for evaluation by means of a non-linear optimization procedure. The benefits of the present variant are both in economy of computation and in accuracy in determining the parameter values. The performance of the method is established under different circumstances. It is illustrated in the context of power-law rates, although this does not preclude its applicability to more general functional responses.     

Recognizing protein–protein interfaces with empirical potentials and reduced amino acid alphabets

Background  

In structural genomics, an important goal is the detection and classification of protein–protein interactions, given the structures of the interacting partners. We have developed empirical energy functions to identify native structures of protein–protein complexes among sets of decoy structures. To understand the role of amino acid diversity, we parameterized a series of functions, using a hierarchy of amino acid alphabets of increasing complexity, with 2, 3, 4, 6, and 20 amino acid groups. Compared to previous work, we used the simplest possible functional form, with residue–residue interactions and a stepwise distance-dependence. We used increased computational ressources, however, constructing 290,000 decoys for 219 protein–protein complexes, with a realistic docking protocol where the protein partners are flexible and interact through a molecular mechanics energy function. The energy parameters were optimized to correctly assign as many native complexes as possible. To resolve the multiple minimum problem in parameter space, over 64000 starting parameter guesses were tried for each energy function. The optimized functions were tested by cross validation on subsets of our native and decoy structures, by blind tests on series of native and decoy structures available on the Web, and on models for 13 complexes submitted to the CAPRI structure prediction experiment.     

Quantitative characterization of blood rheological behavior in transient flow with a model including a structure parameter

Transient rheological behavior of blood which involves non newtonian viscosity, elasticity and thixotropy can be modelized with a Maxwell rheological state equation which depends on a structure parameter having dimension of a shear rate. Identification of the model parameters leads to use an exponential apparent shear rate step and to use recursive filters for taking into account the impulse response of the viscometer servo-control device. Typical results for a normal blood sample are given.     

Comparison of energy components of proteins from thermophilic and mesophilic organisms

In order to infer the energetic determinants of thermophilic proteins, molecular mechanics calculations were applied to five proteins from thermophilic eubacteria and their mesophilic homologs. The energy function includes a hydration term as well as the electrostatic contribution from the solvent in addition to the usual conformational energy terms. We calculated energy values for three different states of each protein: the native, near-native, and unfolded structures. The energy difference and its components between pairs of these states were compared. The hypothetical near-native structures have almost the same backbone conformation as the native structure but with largely distorted side-chain packing, thus enabling us to extract the energy components important for stabilizing the native backbone topology itself, irrespective of structural details. It was found that the sum of the electrostatic and hydration energies, although of large positive values, were consistently lower for the thermophilic proteins than for their mesophilic counterparts. This trend was observed in the energy difference not only between the native and unfolded structures, but also between the near-native and unfolded structures. In contrast, the energy components regarding side-chain packing did not show any clear tendency. These results suggest that the thermophilic proteins are stabilized so that the precise packing of the native structure does not significantly affect the stability. Implications of this conclusion are also discussed.     

Elucidating protein thermodynamics from the three-dimensional structure of the native state using network rigidity

Given the three-dimensional structure of a protein, its thermodynamic properties are calculated using a recently introduced distance constraint model (DCM) within a mean-field treatment. The DCM is constructed from a free energy decomposition that partitions microscopic interactions into a variety of constraint types, i.e., covalent bonds, salt-bridges, hydrogen-bonds, and torsional-forces, each associated with an enthalpy and entropy contribution. A Gibbs ensemble of accessible microstates is defined by a set of topologically distinct mechanical frameworks generated by perturbing away from the native constraint topology. The total enthalpy of a given framework is calculated as a linear sum of enthalpy components over all constraints present. Total entropy is generally a nonadditive property of free energy decompositions. Here, we calculate total entropy as a linear sum of entropy components over a set of independent constraints determined by a graph algorithm that builds up a mechanical framework one constraint at a time, placing constraints with lower entropy before those with greater entropy. This procedure provides a natural mechanism for enthalpy-entropy compensation. A minimal DCM with five phenomenological parameters is found to capture the essential physics relating thermodynamic response to network rigidity. Moreover, two parameters are fixed by simultaneously fitting to heat capacity curves for histidine binding protein and ubiquitin at five different pH conditions. The three free parameter DCM provides a quantitative characterization of conformational flexibility consistent with thermodynamic stability. It is found that native hydrogen bond topology provides a key signature in governing molecular cooperativity and the folding-unfolding transition.     

Quantitative analysis of the nanopore translocation dynamics of simple structured polynucleotides

Nanopore translocation experiments are increasingly applied to probe the secondary structures of RNA and DNA molecules. Here, we report two vital steps toward establishing nanopore translocation as a tool for the systematic and quantitative analysis of polynucleotide folding: 1), Using α-hemolysin pores and a diverse set of different DNA hairpins, we demonstrate that backward nanopore force spectroscopy is particularly well suited for quantitative analysis. In contrast to forward translocation from the vestibule side of the pore, backward translocation times do not appear to be significantly affected by pore-DNA interactions. 2), We develop and verify experimentally a versatile mesoscopic theoretical framework for the quantitative analysis of translocation experiments with structured polynucleotides. The underlying model is based on sequence-dependent free energy landscapes constructed using the known thermodynamic parameters for polynucleotide basepairing. This approach limits the adjustable parameters to a small set of sequence-independent parameters. After parameter calibration, the theoretical model predicts the translocation dynamics of new sequences. These predictions can be leveraged to generate a baseline expectation even for more complicated structures where the assumptions underlying the one-dimensional free energy landscape may no longer be satisfied. Taken together, backward translocation through α-hemolysin pores combined with mesoscopic theoretical modeling is a promising approach for label-free single-molecule analysis of DNA and RNA folding.     

A model for learning human reaching movements

 Reaching movement is a fast movement towards a given target. The main characteristics of such a movement are straight path and a bell-shaped speed profile. In this work a mathematical model for the control of the human arm during ballistic reaching movements is presented. The model of the arm contains a 2 degrees of freedom planar manipulator, and a Hill-type, non-linear mechanical model of six muscles. The arm model is taken from the literature with minor changes. The nervous system is modeled as an adjustable pattern generator that creates the control signals to the muscles. The control signals in this model are rectangular pulses activated at various amplitudes and timings, that are determined according to the given target. These amplitudes and timings are the parameters that should be related to each target and initial conditions in the workspace. The model of the nervous system consists of an artificial neural net that maps any given target to the parameter space of the pattern generator. In order to train this net, the nervous system model includes a sensitivity model that transforms the error from the arm end-point coordinates to the parameter coordinates. The error is assessed only at the termination of the movement from knowledge of the results. The role of the non-linearity in the muscle model and the performance of the learning scheme are analysed, illustrated in simulations and discussed. The results of the present study demonstrate the central nervous system’s (CNS) ability to generate typical reaching movements with a simple feedforward controller that controls only the timing and amplitude of rectangular excitation pulses to the muscles and adjusts these parameters based on knowledge of the results. In this scheme, which is based on the adjustment of only a few parameters instead of the whole trajectory, the dimension of the control problem is reduced significantly. It is shown that the non-linear properties of the muscles are essential to achieve this simple control. This conclusion agrees with the general concept that motor control is the result of an interaction between the nervous system and the musculoskeletal dynamics. Received : 21 May 1996 / Accepted in revised form : 10 June 1997     

Variation between individuals and the consequences for diet selection by groups of animals

We describe a model to predict the diet selection of a population of animals, based on simple assumptions about the characteristics of the individuals in a population, including the variation between them. Individuals are characterized by three parameters with biological relevance; a nutrient (protein) requirement, an ability to discriminate between foods of different protein contents and a need to collect information about both foods. Each animal selects perfectly a diet that avoids both a deficiency and an excess of protein, where this is possible. To construct the population two further assumptions are made. The first is that the values of each parameter are drawn from uncorrelated normal distributions subject to the values being logically possible. The second is that, for different mean values for the population, the standard deviation is directly proportional to the mean so that the coefficient of variation is independent of the mean. The model was used to predict the outcomes of six hypothetical experiments, using 100 individuals on each treatment, where the values of the three parameters were systematically varied. In the experiments one food was always of low protein content while the protein content of the other was the treatment variable. The quantitative effects of varying either the mean value of the parameters, or their variation, on both the mean composition of the diet selected, and on its variation, were not possible to predict without using the model. The shape of the population response was different to that for any individual. Extensions to the model may be able to increase its relevance to practical issues of diet selection. Copyright 2000 The Association for the Study of Animal Behaviour.     

Prokaryotic gene finding based on physicochemical characteristics of codons calculated from molecular dynamics simulations

An ab initio model for gene prediction in prokaryotic genomes is proposed based on physicochemical characteristics of codons calculated from molecular dynamics (MD) simulations. The model requires a specification of three calculated quantities for each codon: the double-helical trinucleotide base pairing energy, the base pair stacking energy, and an index of the propensity of a codon for protein-nucleic acid interactions. The base pairing and stacking energies for each codon are obtained from recently reported MD simulations on all unique tetranucleotide steps, and the third parameter is assigned based on the conjugate rule previously proposed to account for the wobble hypothesis with respect to degeneracies in the genetic code. The third interaction propensity parameter values correlate well with ab initio MD calculated solvation energies and flexibility of codon sequences as well as codon usage in genes and amino acid composition frequencies in ∼175,000 protein sequences in the Swissprot database. Assignment of these three parameters for each codon enables the calculation of the magnitude and orientation of a cumulative three-dimensional vector for a DNA sequence of any length in each of the six genomic reading frames. Analysis of 372 genomes comprising ∼350,000 genes shows that the orientations of the gene and nongene vectors are well differentiated and make a clear distinction feasible between genic and nongenic sequences at a level equivalent to or better than currently available knowledge-based models trained on the basis of empirical data, presenting a strong support for the possibility of a unique and useful physicochemical characterization of DNA sequences from codons to genomes.