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PubMed2004

A new pairwise folding potential based on improved decoy generation and side-chain packing.

A new force field for pairwise residue interactions as a function of C(alpha) to C(alpha) distances is presented. The force field was developed through the solution of a linear programming formulation with large sets of constraints. The constraints are based on the construction of >80,000 low-energy decoys for a set of proteins and requiring the decoy energies for each protein system to be higher than the native conformation of that particular protein. The generation of a robust force field was facilitated by the use of a novel decoy generation process, which involved the rational selection of proteins to add to the training set and included a significant energy minimization of the decoys. The force field was tested on a large set of decoys for various proteins not included in the training set and shown to perform well compared with a leading force field in identifying the native conformation for these proteins.

Algorithms↗
PubMed2006

Optimal design of protein docking potentials: efficiency and limitations.

Protein-protein docking is a challenging computational problem in functional genomics, particularly when one or both proteins undergo conformational change(s) upon binding. The major challenge is to define scoring function soft enough to tolerate these changes and specific enough to distinguish between near-native and "misdocked" conformations. Using a linear programming technique, we derived protein docking potentials (PDPs) that comply with this requirement. We considered a set of 63 nonredundant complexes to this aim, and generated 400,000 putative docked complexes (decoys) based on shape complementarity criterion for each complex. The PDPs were required to yield for the native (correctly docked) structure a potential energy lower than those of all the nonnative (misdocked) structures. The energy constraints applied to all complexes led to ca. 25 million inequalities, the simultaneous solution of which yielded an optimal set of PDPs that discriminated the correctly docked (up to 4.0 A root-mean-square deviation from known complex structure) structure among the 85 top-ranking (0.02%) decoys in 59/63 examined bound-bound cases. The high performance of the potentials was further verified in jackknife tests and by ranking putative docked conformation submitted to CAPRI. In addition to their utility in identifying correctly folded complexes, the PDPs reveal biologically meaningful features that distinguish docking potentials from folding potentials.

Antigens↗
PubMed2006

A novel high resolution Calpha--Calpha distance dependent force field based on a high quality decoy set.

This work presents a novel C(alpha)--C(alpha) distance dependent force field which is successful in selecting native structures from an ensemble of high resolution near-native conformers. An enhanced and diverse protein set, along with an improved decoy generation technique, contributes to the effectiveness of this potential. High quality decoys were generated for 1489 nonhomologous proteins and used to train an optimization based linear programming formulation. The goal in developing a set of high resolution decoys was to develop a simple, distance-dependent force field that yields the native structure as the lowest energy structure and assigns higher energies to decoy structures that are quite similar as well as those that are less similar. The model also includes a set of physical constraints that were based on experimentally observed physical behavior of the amino acids. The force field was tested on two sets of test decoys not in the training set and was found to excel on all the metrics that are widely used to measure the effectiveness of a force field. The high resolution force field was successful in correctly identifying 113 native structures out of 150 test cases and the average rank obtained for this test was 1.87. All the high resolution structures (training and testing) used for this work are available online and can be downloaded from http://titan.princeton.edu/HRDecoys.

Algorithms↗
PubMed1992

Fast structure alignment for protein databank searching.

A fast method is described for searching and analyzing the protein structure databank. It uses secondary structure followed by residue matching to compare protein structures and is developed from a previous structural alignment method based on dynamic programming. Linear representations of secondary structures are derived and their features compared to identify equivalent elements in two proteins. The secondary structure alignment then constrains the residue alignment, which compares only residues within aligned secondary structures and with similar buried areas and torsional angles. The initial secondary structure alignment improves accuracy and provides a means of filtering out unrelated proteins before the slower residue alignment stage. It is possible to search or sort the protein structure databank very quickly using just secondary structure comparisons. A search through 720 structures with a probe protein of 10 secondary structures required 1.7 CPU hours on a Sun 4/280. Alternatively, combined secondary structure and residue alignments, with a cutoff on the secondary structure score to remove pairs of unrelated proteins from further analysis, took 10.1 CPU hours. The method was applied in searches on different classes of proteins and to cluster a subset of the databank into structurally related groups. Relationships were consistent with known families of protein structure.

Amino Acid Sequence↗
PubMed2005

Improved estimation of controlled direct effects in the presence of unmeasured confounding of intermediate variables.

Adjusting for a causal intermediate is a common analytic strategy for estimating an average causal direct effect (ACDE). The ACDE is the component of the total exposure effect that is not relayed through the specified intermediate. Even if the total effect is unconfounded, the usual ACDE estimate may be biased when an unmeasured variable affects the intermediate and outcome variables. Using linear programming optimization to compute non-parametric bounds, we develop new ACDE estimators for binary measured variables in this causal structure, and use root mean square confounding bias (RMSB) to compare their performance with the usual stratified estimator in simulated distributions of target populations comprised of the 64 possible potential response types as well as distributions of target populations restricted to subsets of 18 or 12 potential response types defined by monotonicity or no-interactions assumptions of unit-level causal effects. We also consider target population distributions conditioned on fixed outcome risk among the unexposed, or fixed true ACDE in one stratum of the intermediate. Results show that a midpoint estimator constructed from the optimization bounds has consistently lower RMSB than the usual stratified estimator both unconditionally and conditioned on any risk in the unexposed. When conditioning on true ACDE, this midpoint estimator performs more poorly only when conditioned on an extreme true ACDE in one stratum of the intermediate, yet outperforms the stratified estimator in the other stratum when interaction is permitted. An alternate 'limit-modified crude' estimator can never perform less favourably than the stratified estimator, and often has lower RMSB.

Bias↗
PubMed2007

Induced smoothing for rank regression with censored survival times.

Adaptions of weighted rank regression to the accelerated failure time model for censored survival data have been successful in yielding asymptotically normal estimates and flexible weighting schemes to increase statistical efficiencies. However, for only one simple weighting scheme, Gehan or Wilcoxon weights, are estimating equations guaranteed to be monotone in parameter components, and even in this case are step functions, requiring the equivalent of linear programming for computation. The lack of smoothness makes standard error or covariance matrix estimation even more difficult. An induced smoothing technique overcame these difficulties in various problems involving monotone but pure jump estimating equations, including conventional rank regression. The present paper applies induced smoothing to the Gehan-Wilcoxon weighted rank regression for the accelerated failure time model, for the more difficult case of survival time data subject to censoring, where the inapplicability of permutation arguments necessitates a new method of estimating null variance of estimating functions. Smooth monotone parameter estimation and rapid, reliable standard error or covariance matrix estimation is obtained.

Data Interpretation, Statistical↗
PubMed2007

A new estimation method for the semiparametric accelerated failure time mixture cure model.

The proportional hazard (PH) mixture cure model and the accelerated failure time (AFT) mixture cure model are usually used in analysing failure time data with long-term survivors. However, the semiparametric AFT mixture cure model has attracted less attention than the semiparametric PH mixture cure model because of the complexity of its estimation method. In this paper, we propose a new estimation method for the semiparametric AFT mixture cure model. This method employs the EM algorithm and the rank estimator of the AFT model to estimate the parameters of interest. The M-step in the EM algorithm, which incorporates the rank-like estimating equation, can be carried out easily using the linear programming method. To evaluate the performance of the proposed method, we conduct a simulation study. The results of the simulation study demonstrate that the proposed method performs better than the existing estimation method and the semiparametric AFT mixture cure model improves the identifiability of the parameters in comparison to the parametric AFT mixture cure model. To illustrate, we apply the model and the proposed method to a data set of failure times from bone marrow transplant patients.

Algorithms↗
PubMed2002

Modelling, steady state analysis and optimization of the catalytic efficiency of the triosephosphate isomerase.

In the present work we have modelled and optimized the reaction mechanism of the triose phosphate isomerase (TIM) enzyme (E.C. 5.3.1.1). For this purpose we have used an approach that combines the S-system representation within the power law formalism and linear programming techniques. By this means we have explored those rate constants whose alterations are likely to improve the catalytic efficiency of the enzyme and investigated the available room for optimization in different metabolic conditions. The role and plausibility of the different types of mutations on the evolution of this enzyme have also been considered. Steady state sensitivity analysis was carried out and a new set of aggregated logarithmic gains was defined in order to quantify the responses of the system to changes in groups of rate constants that could be explained in terms of mutations affecting the catalytic properties of the enzyme. Evaluation of these logarithmic gains at different levels of saturation and disequilibrium ratios enabled us to reach conclusions about the meaning and role of the diffusion limitation terms. The catalytic efficiency of the monoenzymatic system was optimized through changes in the kinetic rate constants within different sets of restrictions ranging from thermodynamic or kinetic to evolutionary ones. Results showed that, at very different conditions, there is still room for improvement in the TIM enzyme. Thus, in a wide range of metabolically significant values of the disequilibrium ratio there is a minimal variation in the optimal profile that yields 2.1 times the velocity of the basal states. Though most of this increase is accounted for by the increase of the second order constants (that could have already reached a theoretical maximum) significant increases (20%) in catalytic efficiencies are obtained by changes of the internal steps only. Besides these new findings our optimization approach has been able to reproduce results obtained with other approaches.

Catalysis↗
PubMed2000

Metabolic flux analysis in Streptomyces coelicolor under various nutrient limitations.

Metabolic flux analysis was applied to Streptomyces coelicolor continuous culture data obtained under nitrogen, phosphate, sulfate, and potassium limitations. The metabolic reaction network involved more than 200 reactions describing the major pathways as well as the secondary metabolism for the production of actinorhodin and excretion of certain metabolites. Linear programming was used for the optimization of specific growth rates and energy requirements. Two types of specific growth rates, stoichiometric and theoretical, were defined, maximized, and compared in order to investigate the microbial potential. Potassium limitation led to the largest and nitrogen limitation to the smallest difference between the stoichiometric and theoretical specific growth rates. Although the value of the maximum theoretical specific growth rate was close to that of the experimental specific growth rate with potassium limitation, this difference was the largest in the case of nitrogen limitation. Energy requirements during different nutrient limitations were also investigated. The model indicated that although the highest actinorhodin production rate was with nitrogen limitation, this was accompanied with the undesired excretion of certain metabolites.

Culture Media↗
PubMed2001

A MILP-based flux alternative generation and NMR experimental design strategy for metabolic engineering.

A mixed-integer linear program (MILP) is described that can enumerate all the ways fluxes can distribute in a metabolic network while still satisfying the same constraints and objective function. The multiple solutions can be used to (1) generate alternative flux scenarios that can account for limited experimental observations, (2) forecast the potential responses to mutation (e.g., new reaction pathways may be used), and (3) (as illustrated) design (13)C NMR experiments such that different potential flux patterns in a mutant can be distinguished. The experimental design is enabled by using the MILP results as an input to an isotopomer mapping matrices (IMM)-based program, which accounts for the network circulation of (13)C from a precursor such as glucose. The IMM-based program can interface to common plotting programs with the result that the user is provided with predicted NMR spectra that are complete with splittings and Lorentzian line-shape features. The example considered is the trafficking of carbon in an Escherichia coli mutant, which has pyruvate kinase activity deleted for the purpose of eliminating acetate production. Similar yields and extracellular measurements would be manifested by the flux alternatives. The MILP-IMM results suggest how NMR experiments can be designed such that the spectra of glutamate for two flux distribution scenarios differ significantly.

Algorithms↗
PubMed1998

Resource-Allocation Strategies: A Verbal Protocol Analysis.

The current study examined the strategies used by people to solve resource-allocation problems. Verbal protocols were recorded as participants provided meal choices for seven consecutive days with limited resources available to spend on meals and with daily constraints imposed on meal consumption. None of the participants incorporated the established mathematical procedures (i.e., Linear Programming) to arrive at the optimum number of meals possible in a week. However, the strategies they did use enabled them to achieve meal totals on average at 94% of this optimal amount. A few participants attempted to first solve the maximum meals possible in a week before scheduling this solution across the seven days (solve-and-schedule strategy), but the majority of participants simply selected meals on a day-to-day basis while checking resource availability each day to allow for full resource consumption (consume-and-check strategy). The findings of this study provide a preliminary step toward understanding how people make intuitive resource-allocation decisions. Copyright 1998 Academic Press.

Journal Article↗
PubMed1997

Identification of alkylpolyoxyethylene glycols in the residues after biodegradation of their mixtures by CGC and previous derivatization.

This study deals with the identification of individual n-alkylpolyoxyethylene glycols among the products of oxyethylenation of n-nonyl- and n-decylalcohol and with the identification of these compounds in the reaction mixture after their biodegradation. The individual glycols were identified by their retention indices for the column temperature programmed linearly, by the correlation of the retention indices with the number of oxyethylene groups in the molecule and by increments of retention indices for the incoming oxyethylene group or methylene group. The biodegradation process of oxyethylenation products of reaction of one mole of n-nonylalcohol and n-decylalcohol, respectively, with three moles of ethylene oxide was studied. n-Alkylpolyoxyethylene glycols in oxyethylenation products or their residues isolated from the aqueous solution after their biodegradation processes were derivatized into acetates, trifluoroacetates and trimethylsilyl derivatives before carrying out their identification and determination.

Acetates↗
PubMed2004

Short-term model of the production of construction aggregates in Taiwan based on artificial neural networks.

BACKGROUND: Taiwan's geography and limited stock of sandstone have caused sandstone resources to gradually decline to the point of exhaustion after long-term excavation. Moreover, the Taiwanese government has continuously increased the amount of land area near rivers that cannot be excavated to facilitate riverbed remediation and promote conservation of water resources. Accordingly, predicting and managing the annual production of construction aggregates in future construction projects, and dealing appropriately with some thorny problems, for instance, demand that excess supply, excessive excavation, unregulated excavation, and the consequent environmental damage, will significantly affect the efficient use of natural resources in a manner that accords with the national policy of Sustainable Development (SD). METHODS: . This study establishes an empirical model for forecasting the annual production of future construction aggregates using Artificial Neural Networks (ANN), based on 15 relevant socio-economic indicators, such as indicator of annual consumption of cement. A sensitivity analysis is then performed on these indicators. RESULTS AND DISCUSSION: This work applies ANN to estimate the annual production of construction aggregates; the estimates, the verification of the model and the sensitivity analysis are all acceptable. Furthermore, sensitivity analysis results indicate that the annual consumption of cement is the indicator that most strongly influences the production of construction aggregates, as well as whether construction waste can be recycled and steel structures can be used in buildings, helping to reduce the future production of construction aggregates in Taiwan. CONCLUSIONS: The elaborate prediction methodology presented in this study avoids some of the weaknesses or limitations of conventional linear statistics, linear programming or system dynamics. Additionally, the results not only provide a short-term prediction of the production of construction aggregates in Taiwan, but also provide a viable and flexible means of verifying quality certification of the production data of construction aggregates in the future by incorporating those relevant socio-economic indicators. RECOMMENDATIONS AND OUTLOOK: The continuity and quality of the database of relevant indicators used in this study should be closely scrutinized in order to ensure the SD means of exploiting resources.

Conservation of Natural Resources↗
PubMed2006

Genome-scale in silico aided metabolic analysis and flux comparisons of Escherichia coli to improve succinate production.

In the post-genome era, it is one challenge to understand the cellular metabolism at the systematic levels. Mathematical modeling of microorganisms and subsequent computer simulation are effective tools for systems biology. In this paper, based on the genome-scale Escherichia coli stoichiometric model iJR904, through the GAMS linear programming package, the in silico maximal succinate yield was estimated to be 1.714 mol/mol glucose. When another two constraints were added, the maximal succinate yield dropped to 1.60 mol/mol glucose. Further analysis substantiated the uniqueness of the flux distribution under such constraints. After comparisons with the metabolic flux analysis (MFA) results computed from the wet experimental data of the three kinds of E. coli, three potential improvement target sites, the glucose phosphotransferase transport system, the pyruvate carboxylase, and the glyoxylate shunt, were identified and selected for the genetic modifications. All the three genetic modified strains showed increased succinate yield. The final strain TUQ19/pQZ6 had a high yield of 1.29 mol succinate/mol glucose and high productivity. The success of the above experiments proved that this in silico optimal succinate production pathway is reasonable and practical. This method may also be used as a general strategy to help enhance the yields of other favorable metabolites in E. coli.

Anaerobiosis↗
PubMed1997

RESEARCH: Optimizing the Mix of Strategies for Control of Vehicular Emissions

/ A number of strategies for the control of vehicular emissions are being considered by the Philippine government to address Metropolitan Manila's air quality problem. An analytical tool is needed for optimizing criteria pollutant reductions given the budgetary constraints. The simplest approach is to take costs and pollutant removals to be linear with each strategy's scale of activity, and this is readily solved as a linear programming problem. Another approach is to use a dynamic system of weights which shift with progressive improvements in pollutant emissions. The two approaches yield somewhat different results, suggesting the sensitivity of the solution to the assumed weights. The study also illustrates the importance of a sound methodology for evaluating priorities given to different air quality goals. One such methodology may involve a polling of expert panels and the public to gain insight into the relative importance given to competing emissions reduction goals. An informal polling of resource agency staff was conducted and discussed in this paper. The authors take the position that proper planning involves tracing intermediate steps to the final outcome and not just focusing on the latter.KEY WORDS: Vehicular emissions; Urban air quality; Emissions control; Optimization; Manila; Environmental systems analysis

Journal Article↗
PubMed2006

Quantification of retinal nerve fiber layer thickness reduction associated with a relative afferent pupillary defect.

BACKGROUND: A relative afferent pupillary defect (RAPD) is known to develop only when more than 25% of retinal ganglion cells are ablated in monkeys' eyes. However, there was no prior study to estimate biometrically the degree of retinal nerve fiber layer (RNFL) thickness reduction leading to the development of RAPD in live human eyes. The purpose of this study was to examine the correlation between the amount of RNFL thickness reduction and the depth of a clinically detectable RAPD in patients with unilateral optic atrophy. METHODS: Enrolled were 20 patients with optic atrophy of various etiologies. We quantified RAPD by performing the swinging flashlight test with log-scaled neutral density filters placed over the unaffected eye. Average RNFL thickness was measured by OCT3000 with the average RNFL thickness program. Linear regression analysis was used in assessing the relationship between RAPD and the ratio of affected to unaffected average RNFL thickness. RESULTS: The mean of average RNFL thickness was 95.6+/-17.3 microm in the unaffected eyes and 50.7+/-19.3 microm in the affected eyes (P<0.001). Regression analysis between RAPD and the ratio of affected to unaffected average RNFL thickness revealed a correlation coefficient R2=0.48 (P=0.0007). The regression line intersected the y-axis at 0.77. CONCLUSIONS: RAPD was not clinically detected until at least approximately 25% of the retinal nerve fibers were lost when compared with the unaffected eyes. Substantial retinal ganglion cell damage is required for the development of RAPD.

Adolescent↗
PubMed1985

Predicted pattern of human muscle activity during clenching derived from a computer assisted model: symmetric vertical bite forces.

A computer assisted three-dimensional model of the jaw, based on linear programming, is presented. The upper and lower attachments of the muscles of mastication have been measured on a single human skull and divided into thirteen independent units on each side--a total of 26 muscle elements. The direction (in three dimensions) and maximum forces that could be developed by each muscle element, the bite reaction and two joint reactions are included in the model. It is shown for symmetrical biting that a model which minimizes the sum of the muscle forces used to produce a given bite force activates muscles in a way which corresponds well with previous observations on human subjects. A model which minimizes the joint reactions behaves differently and is rejected. An analysis of the way the chosen model operates suggests that there are two types of jaw muscles, power muscles and control muscles. Power muscles (superficial masseter, medial pterygoid and some of temporalis) produce the bite force but tend to displace the condyle up or down the articular eminence. This displacement is prevented by control muscles (oblique temporalis and lateral pterygoid) which have very poor moment arms for generating usual bite forces, but are efficient for preventing condylar slide. The model incorporates the concept that muscles consist of elements which can contract independently. It predicts that those muscle elements with longer moment arms relative to the joint are the first to be activated and, as the bite force increases, a ripple of activity spreads into elements with shorter moment arms. In general, the model can be used to study the three-dimensional activity in any system of joints and muscles.

Bite Force↗
PubMed1987

Efficiency as a predictor of human jaw design in the sagittal plane.

The effects of changing the direction of the bite force and of the mandibular joint reaction have been studied with a mathematical model assisted by a computer using the technique of linear programming. We conclude the following: In the sagittal plane the long axes of lower molars are each tilted in the direction that most efficiently converts muscle force into work at the bite point rather than in the direction that would maximize static bite force. These genetically determined angles are referred to as the most 'work efficient' angles. Collectively they lead to the appearance of the curve of Spee associated with the postcanines. Given the most work efficient angle of the first molar, the model indicates for bite forces generated in this direction the joint reaction is least when tilted forward from the vertical at between 20 degrees and 30 degrees. The joint reaction is normal to the articular surface of the condyle which is itself tilted forward 20-30 degrees from the occlusal plane. We conclude the condyle and articular eminence are remodelled to the angle that minimizes the joint reaction. The direction of the bite force may be controlled via neuronal circuitry connecting mechanoreceptors of the periodontal ligament with motor nerves supplying the jaw-closing muscles. The height of the occlusal plane in the molar region has little effect on jaw efficiency.

Computer Simulation↗