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PubMed1995

Use of energy cost and variability in stride length to assess an optimal running adaptation.

The aim of this study was to analyse how subjects' running adaptation was affected after a training overload. 14 middle-distance runners were tested before and after a training protocol of 15 days conducted only at one training pace. The efficacy of this training protocol to improve energy cost of running was observed only at the training pace. This improvement was correlated with a particular systematic variation in stride length whereas no changes in stability of stride length were recorded. The data were interpreted in terms of specificity of training for which energy cost and stability of stride length could be considered criteria of an optimal adaptation to the training pace.

Adult↗

PubMed2006

Derivative-free generation and interpolation of convex Pareto optimal IMRT plans.

In inverse treatment planning for intensity-modulated radiation therapy (IMRT), beamlet intensity levels in fluence maps of high-energy photon beams are optimized. Treatment plan evaluation criteria are used as objective functions to steer the optimization process. Fluence map optimization can be considered a multi-objective optimization problem, for which a set of Pareto optimal solutions exists: the Pareto efficient frontier (PEF). In this paper, a constrained optimization method is pursued to iteratively estimate the PEF up to some predefined error. We use the property that the PEF is convex for a convex optimization problem to construct piecewise-linear upper and lower bounds to approximate the PEF from a small initial set of Pareto optimal plans. A derivative-free Sandwich algorithm is presented in which these bounds are used with three strategies to determine the location of the next Pareto optimal solution such that the uncertainty in the estimated PEF is maximally reduced. We show that an intelligent initial solution for a new Pareto optimal plan can be obtained by interpolation of fluence maps from neighbouring Pareto optimal plans. The method has been applied to a simplified clinical test case using two convex objective functions to map the trade-off between tumour dose heterogeneity and critical organ sparing. All three strategies produce representative estimates of the PEF. The new algorithm is particularly suitable for dynamic generation of Pareto optimal plans in interactive treatment planning.

Algorithms↗

PubMed1991

Constrained optimization and protein structure determination.

Energy minimization is one of the main approaches to the computational determination of macromolecular structure. Due to the approximations in the empirical free-energy functions and due to the computational difficulties in locating their global minima, the problem is at present intractable when the only information available is the sequence of subunits forming the molecule. A less-demanding problem in terms of both physics and mathematics is constrained optimization, which uses additional but incomplete experimental information such as distances between certain atoms. This paper reviews methods for generating molecular structure using bond lengths and angles as variables and shows how the structure can be fully specified in terms of local geometry. The analysis permits precise statements to be made about the minimum set of distances that specify a unique structure without recourse to energy minimization. We then discuss the complementary situation, i.e., structure prediction with energy minimization based only on sequence information. Finally, we show how distance constraints can be incorporated into energy minimization methods.

Algorithms↗

PubMed2006

Dramatic performance enhancements for the FASTER optimization algorithm.

FASTER is a combinatorial optimization algorithm useful for finding low-energy side-chain configurations in side-chain placement and protein design calculations. We present two simple enhancements to FASTER that together improve the computational efficiency of these calculations by as much as two orders of magnitude with no loss of accuracy. Our results highlight the importance of choosing appropriate initial configurations, and show that efficiency can be improved by stringently limiting the number of positions that are allowed to relax in response to a perturbation. The changes we describe improve the quality of solutions found for large-scale designs, and allow them to be found in hours rather than days. The improved FASTER algorithm finds low-energy solutions more efficiently than common optimization schemes based on the dead-end elimination theorem and Monte Carlo. These advances have prompted investigations into new methods for force field parameterization and multiple state design.

Algorithms↗

PubMed1975

Chemotaxis of a motile Streptococcus toward sugars and amino acids.

A motile Streptococcus was isolated and its chemotactic behavior toward sugars and amino acids was studied. Motility was optimal in the presence of an exogenous energy source and a nonionic detergent, e.g., Tween 80 or Brij-36. Both glucose and pyruvate could serve as energy source. Chemotaxis toward leucine was optimal at pH 7 to 8.5 and a temperature between 30 and 37 C. The Streptococcus showed a chemotactic response toward a variety of sugars. All commonly occurring L-amino acids, except alanine, asparagine, aspartate, glutamate, arginine, and lysine, were attractants. From concentration response curves the thresholds, peak concentrations, and optimal responses were determined.

Amino Acids↗

PubMed2002

Fast and accurate side-chain topology and energy refinement (FASTER) as a new method for protein structure optimization.

We have developed an original method for global optimization of protein side-chain conformations, called the Fast and Accurate Side-Chain Topology and Energy Refinement (FASTER) method. The method operates by systematically overcoming local minima of increasing order. Comparison of the FASTER results with those of the dead-end elimination (DEE) algorithm showed that both methods produce nearly identical results, but the FASTER algorithm is 100-1000 times faster than the DEE method and scales in a stable and favorable way as a function of protein size. We also show that low-order local minima may be almost as accurate as the global minimum when evaluated against experimentally determined structures. In addition, the new algorithm provides significant information about the conformational flexibility of individual side-chains. We observed that strictly rigid side-chains are concentrated mainly in the core of the protein, whereas highly flexible side-chains are found almost exclusively among solvent-oriented residues.

Algorithms↗

PubMed2003

Fold recognition with minimal gaps.

Here we present a simplified form of threading that uses only a 20 x 20 two-body residue-based potential and restricted number of gaps. Despite its simplicity and transparency the Monte Carlo-based threading algorithm performs very well in a rigorous test of fold recognition. The results suggest that by simplifying and constraining the decoy space, one can achieve better fold recognition. Fold recognition results are compared with and supplemented by a PSI-BLAST search. The statistical significance of threading results is rigorously evaluated from statistics of extremes by comparison with optimal alignments of a large set of randomly shuffled sequences. The statistical theory, based on the Random Energy Model, yields a cumulative statistical parameter, epsilon, that attests to the likelihood of correct fold recognition. A large epsilon indicates a significant energy gap between the optimal alignment and decoy alignments and, consequently, a high probability that the fold is correctly recognized. For a particular number of gaps, the epsilon parameter reaches its maximal value, and the fold is recognized. As the number of gaps further increases, the likelihood of correct fold recognition drops off. This is because the decoy space is small when gaps are restricted to a small number, but the native alignment is still well approximated, whereas unrestricted increase of the number of gaps leads to rapid growth of the number of decoys and their statistical dominance over the correct alignment. It is shown that best results are obtained when a combination of one-, two-, and three-gap threading is used. To this end, use of the epsilon parameter is crucial for rigorous comparison of results across the different decoy spaces belonging to a different number of gaps.

Algorithms↗

PubMed1996

From structure to sequence and back again.

With a simple lattice model and sequence design algorithm, we can design sequences to fit arbitrary compact globular structures. We judged the success of the design algorithm by performing exhaustive conformational searches to determine if a designed sequence's lowest energy conformation matched the target for which it was designed. Designed sequences tend to be much better optimized for their targets than a natural sequence is optimized for its lowest energy model conformation. We examined the effect of varying the number of available amino acid types on the success of the design method. It was more difficult but not impossible to successfully design discriminating sequences using fewer amino acid types.

Algorithms↗

PubMed2005

Optimization of biomass, vitamins, and carotenoid yield on light energy in a flat-panel reactor using the A-stat technique.

Acceleration-stat (A-stat) cultivations in which the dilution rate is continuously changed at a constant acceleration rate, leading to different average light intensities inside the photobioreactor, can supply more information and reduce experimental time compared with chemostat cultivations. The A-stat was used to optimize the biomass and product yield of continuous cultures of the microalgae D. tertiolecta in a flat-panel reactor. In this study, four different accelerations were studied, a pseudo steady state was maintained at acceleration rates of 0.00016 and 0.00029 h(-2) and results were similar to those of the chemostat. An increase in the acceleration rate led to an increase in the deviation between results obtained in the A-stat and in the chemostats. We concluded that it is advantageous to use the A-stat instead of chemostats to determine culture characteristics and optimize a specific photobioreactor. The effect of average light intensity inside the photobioreactor on the production of vitamins C and E, lutein, and beta-carotene was studied using the A-stat. The highest concentrations of these products were 3.48 +/- 0.46, 0.33 +/- 0.06, 5.65 +/- 0.24, and 2.36 +/- 0.38 mg g(-1), respectively. These results were obtained at different average light intensities, showing the importance of optimizing each product on light intensity.

Ascorbic Acid↗

PubMed2003

Isomers of C(20): an energy profile II.

Semi-empirical calculations, at the PM3 level provided within the Winmopac v2.0 software package, are used to geometrically optimize and determine the absolute energies (heats of formation) of a variety of C(20) isomers that are predicted to exist in and around the bowl and cage isomers. Using the optimized Cartesian coordinates for the bowl and the cage isomers, a saddle-point calculation was performed. The output file generated, containing energy, distance, and geometry information, is then organized into a graphical format. The resulting graph, which plots the energy of the 20-atom system as a function of the distance from the geometric midpoint, is a two-dimensional energy profile. This profile illustrates an estimation of the contours on the potential energy surface, showing energy minima and maxima that are encountered as the bowl evolves into the cage structure, or vice-versa. To expand the surface into three dimensions, geometry optimizations were performed on the sets of Cartesian coordinates that correspond to energy minima in the bowl-cage profile. Based on these optimizations, eight additional isomers of C(20) have been identified and are predicted to be energetically stable. These additional isomers were subsequently subjected to saddle-point calculations in order to identify those isomers that lie adjacent to one another on the three-dimensional surface. Two isomers that are adjacent to each other will exhibit an energy profile that progresses smoothly from the potential well of each isomer up to the saddle point separating them. Consequently, these adjacent pairs of isomers establish a step-wise transformation between the bowl and the cage. This process, which extends out over the three-dimensional surface, is predicted to require less energy than that of the direct, two-dimensional transformation predicted in the bowl-cage profile.

Journal Article↗

PubMed2005

Bounds for the scattering length of spin-polarized helium from high-accuracy electronic structure calculations.

We developed a series of correlation-consistent, polarized multiple zeta basis sets optimized specifically for the energy of the 2 3S state of helium atom. These basis sets were subsequently augmented with diffuse functions optimized for the van der Waals constants C6 through C14 which determine the asymptotic behavior of the second-order dispersion interaction between 2 3S helium atoms at large interatomic separation R. The resulting bases were applied to compute the Born-Oppenheimer (BO) potential for the lowest 5Sigmag+ state of the helium dimer. The coupled cluster and the full configuration-interaction techniques were employed to account for the electron correlation effects. The cardinal number extrapolation technique was used to obtain the complete-basis-set limit V(R) for the interaction potential and to find its lower VL(R) and upper VU(R) bounds. The resulting potentials were fitted to an analytical function containing accurate van der Waals constants C6 through C12 (including C11). We found that the complete-basis-set BO potential has a well depth De=1048.24+/-0.36 cm-1. The highest rotationless vibrational level is bound by D14=90.2+/-4.7 MHz, much stronger than the previous most accurate estimation of 15.2 MHz. The error bounds for De and D14 were obtained using the VL(R) and VU(R) potentials. The S-wave scattering length computed using the VL(R), V(R), and VU(R) potentials (assuming atomic masses) is aL=7.41 nm, a=7.54 nm, and aU=7.69 nm, respectively. We also computed the adiabatic, relativistic, and quantum electrodynamics (QED) corrections to the BO potential. When these corrections are taken into account the values of D14 and of a (both computed assuming nuclear masses) are 87.4+/-6.7 MHz and 7.64+/-0.20 nm; the error bounds reflect now also the uncertainty of the included adiabatic, relativistic, and QED corrections. The value of the scattering length resulting from our investigation lies outside the error bounds of all experimental determinations based on the properties of Bose-Einstein condensate of spin-polarized helium atoms.

Journal Article↗

PubMed1978

Energy metabolism of Rickettsia typhi: pools of adenine nucleotides and energy charge in the presence and absence of glutamate.

The obligate intracellular bacterium Rickettsia typhi was examined for its ability to generate and maintain an adenylate energy charge in an extracellular environment. Freshly purified organisms were incubated, at 34 degrees C and pH 7.4, with or without glutamate and various other metabolites, and the levels of ATP, ADP, and AMP were determined. Of the metabolites tested, glutamate and glutamine were the most effective for the generation of ATP. In the presence of glutamate, there was a rapid increase in the level of ATP, followed by a moderate decrease during 150 min of incubation. The energy charge increased from a level of 0.2 to 0.5 to about 0.7 to 0.75, and then slowly declined to about 0.45 to 0.6. In the absence of glutamate, after an occasional initial surge in ATP level as the temperature was changed from 4 to 34 degrees C, there was a sharp decline in both ATP and energy charge (to 0.1 and sometimes to 0.01). The rickettsiae maintained their ability to regenerate their energy charge upon the addition of glutamate for about 30 min, but this ability declined with further incubation. In contrast to Escherichia coli, the decline in ATP in R. typhi was accompanied by a sharp increase in the level of AMP and the total adenylate pool. No adenine or adenosine was recovered from rickettsiae incubated with labeled AMP, ADP, or ATP. From these experiments and the demonstration reported elsewhere that rickettsiae transport the adenine nucleotides, it can be concluded that the adenylate energy charge in R. typhi is governed by the salvage of the adenine nucleotides rather than their unphosphorylated precursors. Thus, R. typhi undergoes greater shifts in energy charge than other bacteria, a phenomenon which may account for their instability in an extracellular environment. Under optimal conditions the adenylate energy charge of R. typhi approaches levels that border on those generally regarded as adequate for growth.

Adenine Nucleotides↗

PubMed2004

Isomers of C20: an energy profile III.

Semiempirical calculations, at the PM3 level provided within the Winmopac v2.0 software package, are used to geometrically optimize and determine the absolute energies (heats of formation) of a variety of C(20) isomers that are predicted to exist in and around the ring and cage isomers. Using the optimized Cartesian coordinates for the ring and the cage isomers, a saddle-point calculation was performed. The resulting energy profile, consisting of a series of peaks and valleys, is used as a starting point for the identification and location of fifteen additional isomers of C(20) that are predicted to be energetically stable, both via geometry optimizations and force constant analysis. These additional isomers were subsequently determined to lie adjacent to one another on the potential surface and establish a step-wise transformation between the ring and the cage. Transition-state optimization of the Cartesian coordinates at the saddle point between adjacent isomers was performed to quantify the energy of the transition state. The step-wise process from one isomer to another, which extends out over the three-dimensional surface, is predicted to require approximately 15% less energy than that of the direct, two-dimensional transformation predicted in the bowl-cage profile. However, the net atomic rearrangement for the step-wise process is about four times greater than that of the direct process. Although less in energy, the amount of atomic rearrangement in the step-wise process would make the occurrence of such a route prohibitive. Utilizing the direct distance separating the three primary isomers (ring, bowl, cage), the method of triangulation is performed to quantitatively position other C(20) structures on the potential surface, relative to the ring, bowl, and cage isomers.

Journal Article↗

PubMed1991

Quantitative analysis of electron energy-loss spectra from ultrathin-sectioned biological material. I. Optimization of the background-fit with the use of Bio-standards.

A computer program for quantitative spectral analysis is proposed for the elemental analysis of biological material by electron energy-loss spectroscopy in a conventional transmission electron microscope, the Zeiss EM902. Bio-standards are used to test the performance of this program. The application of a simplex optimization method for curve-fitting is proposed to separate the ionization edge from the background. Making use of Ce-, Ca- and Fe-bio-standards, this method is compared with Egerton's well-known two-area method.

Calcium↗

PubMed2001

Linear programming optimization and a double statistical filter for protein threading protocols.

The design of scoring functions (or potentials) for threading, differentiating native-like from non-native structures with a limited computational cost, is an active field of research. We revisit two widely used families of threading potentials: the pairwise and profile models. To design optimal scoring functions we use linear programming (LP). The LP protocol makes it possible to measure the difficulty of a particular training set in conjunction with a specific form of the scoring function. Gapless threading demonstrates that pair potentials have larger prediction capacity compared with profile energies. However, alignments with gaps are easier to compute with profile potentials. We therefore search and propose a new profile model with comparable prediction capacity to contact potentials. A protocol to determine optimal energy parameters for gaps, using LP, is also presented. A statistical test, based on a combination of local and global Z-scores, is employed to filter out false-positives. Extensive tests of the new protocol are presented. The new model provides an efficient alternative for threading with pair energies, maintaining comparable accuracy. The code, databases, and a prediction server are available at http://www.tc.cornell.edu/CBIO/loopp.

Amino Acid Sequence↗

PubMed1997

Optimization of 3D conformal electron beam therapy in inhomogeneous media by concomitant fluence and energy modulation.

The possibilities of using simultaneous fluence and energy modulation techniques in electron beam therapy to shape the dose distribution and almost eliminate the influences of tissue inhomogeneities have been investigated. By using a radiobiologically based optimization algorithm the radiobiological properties of the tissues can be taken into account when trying to find the best possible dose delivery. First water phantoms with differently shaped surfaces were used to study the effect of surface irregularities. We also studied water phantoms with internal inhomogeneities consisting of air or cortical bone. It was possible to improve substantially the dose distribution by fluence modulation in these cases. In addition to the fluence modulation the most suitable single electron energy in each case was also determined. Finally, the simultaneous use of several preselected electron beam energies was also tested, each with an individually optimized fluence profile. One to six electron energies were used, resulting in a slow improvement in complication-free cure with increasing number of beam energies. To apply these techniques to a more clinically relevant situation a post-operative breast cancer patient was studied. For simplicity this patient was treated with only one anterior beam portal to clearly illustrate the effect of inhomogeneities like bone and lung on the dose distribution. It is shown that by using fluence modulation the influence of dose inhomogeneities can be significantly reduced. When two or more electron beam energies with individually optimized fluence profiles are used the dose conformality to the internal target volume is further increased, particularly for targets with complex shapes.

Algorithms↗

PubMed2003

Multiscale study of counterion-induced attraction and bundle formation of F-actin using an Ising-like mean-field model.

An Ising-like counterion-binding model is developed and solved by a mean-field method. For G-actin, the calculated affinity constants of all the binding sites ranging from loose to tight binding match the experimental data. The model is used to calculate the interaction energy between two F-actin filaments. Within a certain counterion concentration range, a rapidly decaying attractive force between two parallel filaments is produced not only by the correlation of the counterion distributions on the two filaments, but also by the correlation of the configurations of the two filaments with fixed counterion positions, which has been ignored in previous calculations. The bundling energy depends strongly on the configuration of the filaments. Upon bundling, the tightly bound counterion site is not affected, but the medium and loosely bound ones are. The model reproduces the observed minimal divalent counterion concentration for bundling, and naturally predicts the resolubilization of bundles which is seen in recent experiments. At the optimal counterion concentration, we obtain a bundling energy of approximately -0.01 eV per monomer along the filament. The counterion valence strongly affects the optimal counterion concentration, but has only minor effects on the optimal bundling energy. We show that the attractive potential between filaments can be simplified as the sum of interactions between their monomers. This simplification makes it possible to calculate the exact free energy of a two-F-actin-filament system. We are thus able to probe the effects of filament length on F-actin bundling and obtain a critical length for bundling of 59 monomers at 1 microM monomer concentration and pH=7.2.

Actin Cytoskeleton↗

PubMed2005

Muscle fiber type effects on energetically optimal cadences in cycling.

Fast-twitch (FT) and slow-twitch (ST) muscle fibers vary in their mechanical and energetic properties, and it has been suggested that muscle fiber type distribution influences energy expenditure and the energetically optimal cadence during pedaling. However, it is challenging to experimentally isolate the effects of muscle fiber type on pedaling energetics. In the present study, a modeling and computer simulation approach was used to test the dependence of muscle energy expenditure on pedaling rate during submaximal cycling. Simulations were generated using a musculoskeletal model at cadences from 40 to 120 rev min(-1), and the dynamic and energetic properties of the model muscles were scaled to represent a range of muscle fiber types. Energy expenditure and the energetically optimal cadence were found to be higher in a model with more FT fibers than a model with more ST fibers, consistent with predictions from the experimental literature. At the muscle level, mechanical efficiency was lower in the model with a greater proportion of FT fibers, but peaked at a higher cadence than in the ST model. Regardless of fiber type distribution, mechanical efficiency was low at 40 rev min(-1), increased to a broad plateau between 60 and 100 rev min(-1) , and decreased substantially at 120 rev min(-1). In conclusion, muscle fiber type distribution was confirmed as an important determinant of the energetics of pedaling.

Bicycling↗