CIRSE: a solvation energy estimator compatible with flexible protein docking and design applications

We present the Coordinate Internal Representation of Solvation Energy (CIRSE) for computing the solvation energy of protein configurations in terms of pairwise interactions between their atoms with analytic derivatives. Currently, CIRSE is trained to a Poisson/surface-area benchmark, but CIRSE is not meant to fit this benchmark exclusively. CIRSE predicts the overall solvation energy of protein structures from 331 NMR ensembles with 0.951+/-0.047 correlation and predicts relative solvation energy changes between members of individual ensembles with an accuracy of 15.8+/-9.6 kcal/mol. The energy of individual atoms in any of CIRSE's 17 types is predicted with at least 0.98 correlation. We apply the model in energy minimization, rotamer optimization, protein design, and protein docking applications. The CIRSE model shows some propensity to accumulate errors in energy minimization as well as rotamer optimization, but these errors are consistent enough that CIRSE correctly identifies the relative solvation energies of designed sequences as well as putative docked complexes. We analyze the errors accumulated by the CIRSE model during each type of simulation and suggest means of improving the model to be generally useful for all-atom simulations.     

Modeling of branching structures of plants

Previous studies of branching structures generally focused on arteries. Four cost models minimizing total surface area, total volume, total drag and total power losses at a junction point have been proposed to study branching structures. In this paper, we highlight the branching structures of plants and examine which model fits data of branching structures of plants the best. Though the effect of light (e.g. phototropism) and other possible factors are not included in these cost models, a simple cost model with physiological significance, needs to be verified before further research on modeling of branching structures is conducted. Therefore, data are analysed in this paper to determine the best cost model. Branching structures of plants are studied by measuring branching angles and diameters of 234 junctions from four species of plants. The sample includes small junctions, large junctions, two- and three-dimensional junctions, junctions with three branches joining at a point and those with four branches joining at a point. First, junction exponents (x) were determined. Second, log-log plots indicate that model of volume minimization fits data better than other models. Third, one-sided t -tests were used to compare the fitness of four models. It is found that model of volume minimization fits data better than other cost models.     

Brain organization: wiring economy works for the large and small

The highest-resolution test to date of the wire minimization hypothesis has found that this principle works well for brain regions with a volume just over 400 μm(3). What is the wire minimization hypothesis, and why should anyone care about it?     

Optimization of diameters and bifurcation angles in lung and vascular tree structures

An optimization model is described for lung and vascular tree structures. The model extends Murray's model, which is derived from minimal power dissipation due to the frictional resistance of laminar flow and the volume of the duct system. Instead of just laminar flow, it takes into account all types of steady flow, e.g. turbulent and laminar flow, and predicts which structural changes will occur among different parts of trees having different types of flow. The sensitivity of the optimal values is indicated and the model, predictions are compared with literature data.     

Protein structure fitting and refinement guided by cryo-EM density

For many macromolecular assemblies, both a cryo-electron microscopy map and atomic structures of its component proteins are available. Here we describe a method for fitting and refining a component structure within its map at intermediate resolution (<15 A). The atomic positions are optimized with respect to a scoring function that includes the crosscorrelation coefficient between the structure and the map as well as stereochemical and nonbonded interaction terms. A heuristic optimization that relies on a Monte Carlo search, a conjugate-gradients minimization, and simulated annealing molecular dynamics is applied to a series of subdivisions of the structure into progressively smaller rigid bodies. The method was tested on 15 proteins of known structure with 13 simulated maps and 3 experimentally determined maps. At approximately 10 A resolution, Calpha rmsd between the initial and final structures was reduced on average by approximately 53%. The method is automated and can refine both experimental and predicted atomic structures.     

Information processing limits on generating neuroanatomy: global optimization of rat olfactory cortex and amygdala

A pattern of widespread connection optimization in the nervous system has become evident: deployment of some neural interconnections attains optimality, sometimes without detectable limits. New results for optimization of layout of connected areas of rat olfactory cortex and of rat amygdala are reported here. One larger question concerns mechanisms—how such minimization is attained. A next question is why a nervous system would optimize rather than just moderately satisfice. A morphogenic proposal that relates these questions is that the means of organizing neural wiring happens also to yield optimization. Some neuroanatomy is generated via “saving wire,” and this optimizing is via simple physical processes rather than DNA-mediated mechanisms. Such “non-genomic nativism” is thereby a path around fundamental limitations on generating brains, some of the most complex structures in the known universe.     

Competition for enzymes in metabolic pathways: implications for optimal distributions of enzyme concentrations and for the distribution of flux control

The structures of biochemical pathways are assumed to be determined by evolutionary optimization processes. In the framework of mathematical models, these structures should be explained by the formulation of optimization principles. In the present work, the principle of minimal total enzyme concentration at fixed steady state fluxes is applied to metabolic networks. According to this principle there exists a competition of the reactions for the available amount of enzymes such that all biological functions are maintained. In states which fulfil these optimization criteria the enzyme concentrations are distributed in a non-uniform manner among the reactions. This result has consequences for the distribution of flux control. It is shown that the flux control matrix c, the elasticity matrix epsilon, and the vector e of enzyme concentrations fulfil in optimal states the relations c(T)e = e and epsilon(T)e = 0. Starting from a well-balanced distribution of enzymes the minimization of total enzyme concentration leads to a lowering of the SD of the flux control coefficients.     

A generic method of pesticide dose expression: Application to broadcast spraying of apple trees

The recommended dose for many pesticides is expressed as a constant mass or volume per unit ground area covered by the crop. This method of dose expression is well suited to boom spraying where a reasonably uniform horizontal distribution of deposit can be achieved with a well‐adjusted sprayer. However, in many practical situations (e.g. broadcast spraying of apple trees or other row structures where the spray application is made from within the canopy) the horizontal deposit distribution is strongly influenced by the crop area density and other crop structural parameters. This paper describes a generic method of pesticide dose expression to investigate these effects. The method incorporates a model of the spray volume deposition process. The model assumes that the pesticide deposit is proportional to the tank‐mix concentration of pesticide. The model also assumes that spray volume deposit is proportional to the applied spray volume per unit row length and is inversely proportional to a crop length scaling function L (i.e. a parameter with the units of length that is expressed as a generic function of different crop parameters). The useful working range of this model is bounded by the condition for high spray volume where target losses become significant due to saturation and the condition for very low volume where evaporative transport losses become significant. Within this framework, four different models are formulated using first‐order approximations for the length‐scale as functions of the following crop parameters: tree row spacing, tree row height, tree area density and tree row volume to ground area ratio. Published measurements of crop structure and spray volume deposit on apple trees are compared with the output from these models. Light detection and range (LIDAR) measurements of apple orchards are presented and used in conjunction with the different models to predict pesticide use associated with different methods of dose expression. The results demonstrate the relative potential for varying the pesticide application rate according to the different crop parameters. The results enable the identification of reference orchards that could be used to establish worst‐case pesticide application rates for registration purposes. The results also enable the identification of other orchards and growth stages where pesticide application rate might be reduced by up to a factor of five and give the same pesticide deposit as the reference structure.     

Molecular modeling of proteins: a strategy for energy minimization by molecular mechanics in the AMBER force field.

Energy minimization is an important step in molecular modeling of proteins. In this study, we sought to develop a minimization strategy which would give the best final structures with the shortest computer time in the AMBER force field. In the all-atom model, we performed energy minimization of the melittin (mostly alpha-helical) and cardiotoxin (mostly beta-sheet and beta-turns) crystal structures by both constrained and unconstrained pathways. In the constrained path, which has been recommended in the energy minimization of proteins, hydrogens were relaxed first, followed by the side chains of amino acid residues, and finally the whole molecule. Despite the logic of this approach, however, the structures minimized by the unconstrained path fit the experimental structures better than those minimized by constrained paths. Moreover, the unconstrained path saved considerable computer time. We also compared the effects of the steepest descents and conjugate gradients algorithms in energy minimization. Previously, steepest descents has been used in the initial stages of minimization and conjugate gradients in the final stages of minimization. We therefore studied the effect on the final structure of performing an initial minimization by steepest descents. The structures minimized by conjugate gradients alone resembled the structures minimized initially by the steepest descents and subsequently by the conjugate gradients algorithms. Thus an initial minimization using steepest descents is wasteful and unnecessary, especially when starting from the crystal structure. Based on these results, we propose the use of an unconstrained path and conjugate gradients for energy minimization of proteins. This procedure results in low energy structures closer to the experimental structures, and saves about 70-80% of computer time. This procedure was applied in building models of lysozyme mutants. The crystal structure of native T4 lysozyme was mutated to three different mutants and the structures were minimized. The minimized structures closely fit the crystal structures of the respective mutants (less than 0.3 A root-mean-square, RMS, deviation in the position of all heavy atoms). These results confirm the efficiency of the proposed minimization strategy in modeling closely related homologs. To determine the reliability of the united atom approximation, we also performed all of the above minimizations with united atom models. This approximation gave structures with similar but slightly higher RMS deviations than the all-atom model, but gave further savings of 60-70% in computer time. However, we feel further investigation is essential to determine the reliability of this approximation.(ABSTRACT TRUNCATED AT 400 WORDS)     

Use of decoys to optimize an all-atom force field including hydration

A novel method of parameter optimization is proposed. It makes use of large sets of decoys generated for six nonhomologous proteins with different architecture. Parameter optimization is achieved by creating a free energy gap between sets of nativelike and nonnative conformations. The method is applied to optimize the parameters of a physics-based scoring function consisting of the all-atom ECEPP05 force field coupled with an implicit solvent model (a solvent-accessible surface area model). The optimized force field is able to discriminate near-native from nonnative conformations of the six training proteins when used either for local energy minimization or for short Monte Carlo simulated annealing runs after local energy minimization. The resulting force field is validated with an independent set of six nonhomologous proteins, and appears to be transferable to proteins not included in the optimization; i.e., for five out of the six test proteins, decoys with 1.7- to 4.0-Å all-heavy-atom root mean-square deviations emerge as those with the lowest energy. In addition, we examined the set of misfolded structures created by Park and Levitt using a four-state reduced model. The results from these additional calculations confirm the good discriminative ability of the optimized force field obtained with our decoy sets.     

Refining the structure of the strongly bound actin-myosin complex by protein docking

The structure of the strongly bound complex of the globular myosin head and F-actin is a key for understanding some important details of the mechanism of the actin-myosin motor. Current knowledge about the structure is based on the docking of known atomic structures of actin and myosin heads into low-resolution EM electron density maps. To refine the structure, we suggested a new approach based on energy minimization using the ICM-Pro software. The minimization includes rigid-body movement of protein backbone and side chain optimization on the protein interface. Our best model structure is similar to that obtained from EM. It also provides the highest calculated interaction energy and agrees with a number of mutagenesis experiments. Using the structure, we suggest molecular explanations for actin activation of product release from myosin and actin-induced myosin dissociation.     

A new computational approach for real protein folding prediction

An effective and fast minimization approach is proposed for the prediction of protein folding, in which the 'relative entropy' is used as a minimization function and the off-lattice model is used. In this approach, we only use the information of distances between the consecutive Calpha atoms along the peptide chain and a generalized form of the contact potential for 20 types of amino acids. Tests of the algorithm are performed on the real proteins. The root mean square deviations of the structures of eight folded target proteins versus the native structures are in a reasonable range. In principle, this method is an improvement on the energy minimization approach.     

Application of a genetic algorithm in the conformational analysis of methylene-acetal-linked thymine dimers in DNA: Comparison with distance geometry calculations

The three-dimensional spatial structure of a methylene-acetal-linked thymine dimer presentin a 10 base-pair (bp) sense–antisense DNA duplex was studied with a geneticalgorithm designed to interpret NOE distance restraints. Trial solutions were represented bytorsion angles. This means that bond angles for the dimer trial structures are kept fixed duringthe genetic algorithm optimization. Bond angle values were extracted from a 10 bpsense–antisense duplex model that was subjected to energy minimization by means ofa modified AMBER force field. A set of 63 proton–proton distance restraints definingthe methylene-acetal-linked thymine dimer was available. The genetic algorithm minimizesthe difference between distances in the trial structures and distance restraints. A largeconformational search space could be covered in the genetic algorithm optimization byallowing a wide range of torsion angles. The genetic algorithm optimization in all cases ledto one family of structures. This family of the methylene-acetal-linked thymine dimer in theduplex differs from the family that was suggested from distance geometry calculations. It isdemonstrated that the bond angle geometry around the methylene-acetal linkage plays animportant role in the optimization.     

Methods for Baculovirus Amplification - Application to Large Scale Recombinant Protein Production in Insect Cells

Baculovirus amplification in one insect cell line Spodoptera frugiperda (Sf21) and subsequent recombinant protein production in another cell line, Trichoplusia ni, has been achieved within a single bioreactor. The advantages of this single bioreactor configuration include minimization of the virus volumes and titres required for large scale protein expression experiments as well as optimization of the infection process itself.     

The branching angles in computer-generated optimized models of arterial trees

The structure of a complex arterial tree model is generated on the computer using the newly developed method of "constrained constructive optimization." The model tree is grown step by step, at each stage of development fulfilling invariant boundary conditions for pressures and flows. The development of structure is governed by adopting minimum volume inside the vessels as target function. The resulting model tree is analyzed regarding the relations between branching angles and segment radii. Results show good agreement with morphometric measurements on corrosion casts of human coronary arteries reported in the literature.     

Molecular Modeling of Proteins: A Strategy for Energy Minimization by Molecular Mechanics in the AMBER Force Field

Abstract

Energy minimization is an important step in molecular modeling of proteins. In this study, we sought to develop a minimization strategy which would give the best final structures with the shortest computer time in the AMBER force field. In the all-atom model, we performed energy minimization of the melittin (mostly α-helical) and cardiotoxin (mostly β-sheet and β-turns) crystal structures by both constrained and unconstrained pathways. In the constrained path, which has been recommended in the energy minimization of proteins, hydrogens were relaxed first, followed by the side chains of amino acid residues, and finally the whole molecule. Despite the logic of this approach, however, the structures minimized by the unconstrained path fit the experimental structures better than those minimized by constrained paths. Moreover, the unconstrained path saved considerable computer time. We also compared the effects of the steepest descents and conjugate gradients algorithms in energy minimization. Previously, steepest descents has been used in the initial stages of minimization and conjugate gradients in the final stages of minimization. We therefore studied the effect on the final structure of performing an initial minimization by steepest descents. The structures minimized by conjugate gradients alone resembled the structures minimized initially by the steepest descents and subsequently by the conjugate gradients algorithms. Thus an initial minimization using steepest descents is wasteful and unnecessary, especially when starting from the crystal structure. Based on these results, we propose the use of an unconstrained path and conjugate gradients for energy minimization of proteins. This procedure results in low energy structures closer to the experimental structures, and saves about 70–80% of computer time. This procedure was applied in building models of lysozyme mutants. The crystal structure of native T₄ lysozyme was mutated to three different mutants and the structures were minimized. The minimized structures closely fit the crystal structures of the respective mutants (< 0.3 Å root-mean-square, RMS, deviation in the position of all heavy atoms). These results confirm the efficiency of the proposed minimization strategy in modeling closely related homologs. To determine the reliability of the united atom approximation, we also performed all of the above minimizations with united atom models. This approximation gave structures with similar but slightly higher RMS deviations than the all-atom model, but gave further savings of60-70% in computer time. However, we feel further investigation is essential to determine the reliability of this approximation. Finally, to determine the limitation of the procedure, we built the melittin molecule interactively in an α-helical conformation and this model showed an RMS deviation greater than 2.8 Å when compared to the melittin crystal structure. This model was minimized by various strategies. None of the minimized structures converged towards the crystal structure. Thus, although the proposed method seems to give valid structures starting from closely related crystal structures, it cannot predict the native structure when the starting structure is far from the native structure. From these results, we recommend the use of the proposed strategy of minimizing by an unconstrained path using the conjugate gradients algorithm, but only for modeling of closely related structural homologs of proteins.     

The seeds of Campsiandra angustifolia (Fabaceae: Caesalpiniodeae) as a reflex of selective pressures on dispersal and establishment

We indirectly evaluated the selective pressures on dispersal and establishment of Campsiandra angustifolia, a common water-dispersed tree from the Peruvian Amazon, analyzing the variation in the relationship between the volume occupied by dispersal and establishment structures in a total of 535 seeds from 13 trees located at three different habitats. The seeds differed one order of magnitude in their total volume. However, independently of their size and the location of the maternal tree, the relationship between the volume occupied by dispersal and establishment structures was relatively constant (approximately 1) and showed a normal distribution with low skewness, indicating stabilizing selection. These results suggest that, in the habitats studied, dispersal and establishment processes may have similar importance to C. agustifolia. In species with seeds confined in pods, and therefore strongly space-limited, the relative volume of their seeds occupied by dispersal and establishment structures could be a better measure of the trade-off between these two processes than the variation in seed size.     

A Full-automatic Sequence Design Algorithm for Branched DNA Structures

Abstract

Production of various structures by self-assembling single stranded DNA molecules is a widely used technology in the filed of DNA nanotechnology. Base sequences of single strands do predict the shape of the resulting nanostructure. Therefore, sequence design is crucial for the successful structure fabrication. This paper presents a sequence design algorithm based on mismatch minimization that can be applied to every desired DNA structure. With this algorithm, junctions, loops, single as well as double stranded regions, and very large structures up to several thousand base pairs can be handled. Thereby, the algorithm is fast for the most structures. Algorithm is Java-implemented. Its implementation is called Seed and is available publicly. As an example for a successful sequence generation, this paper presents the fabrication of DNA chain molecules consisting of double-crossover (DX) tiles as well.     

Total work rate of breathing optimization in CO-2 inhalation and exercise.

The hypothesis that respiratory frequency and the relative durations of inspiration and expiration are regulated according to a total cycle work rate minimization criterion was explored. Effects of negative work performed by the respiratory muscles and dead space variation as a function of tidal volume were included in a formulation which yielded a theoretically predictable optimal frequency and relative duration of inspiration and expiration at all levels of ventilation. Predicted cycle characteristics based on measured mechanical parameters were compared with data taken during CO-2 inhalation (3 and 5%) and moderate exercise (MRR = 3 and 6) in three normal human subjects. No major difference in breathing pattern was observed between CO-2 inhalation and exercise. Results suggest that conditions for minimization of total cycle work rate are achieved asympototically as the level of ventilation rises above the resting level. At rest and at low levels of hyperpnea complete work rate optimization is not achieved.