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PubMed2000

A direct optimization approach to hidden Markov modeling for single channel kinetics.

Hidden Markov modeling (HMM) provides an effective approach for modeling single channel kinetics. Standard HMM is based on Baum's reestimation. As applied to single channel currents, the algorithm has the inability to optimize the rate constants directly. We present here an alternative approach by considering the problem as a general optimization problem. The quasi-Newton method is used for searching the likelihood surface. The analytical derivatives of the likelihood function are derived, thereby maximizing the efficiency of the optimization. Because the rate constants are optimized directly, the approach has advantages such as the allowance for model constraints and the ability to simultaneously fit multiple data sets obtained at different experimental conditions. Numerical examples are presented to illustrate the performance of the algorithm. Comparisons with Baum's reestimation suggest that the approach has a superior convergence speed when the likelihood surface is poorly defined due to, for example, a low signal-to-noise ratio or the aggregation of multiple states having identical conductances.

Algorithms↗

PubMed2004

An optimal structure-discriminative amino acid index for protein fold recognition.

Identifying the fold class of a protein sequence of unknown structure is a fundamental problem in modern biology. We apply a supervised learning algorithm to the classification of protein sequences with low sequence identity from a library of 174 structural classes created with the Combinatorial Extension structural alignment methodology. A class of rules is considered that assigns test sequences to structural classes based on the closest match of an amino acid index profile of the test sequence to a profile centroid for each class. A mathematical optimization procedure is applied to determine an amino acid index of maximal structural discriminatory power by maximizing the ratio of between-class to within-class profile variation. The optimal index is computed as the solution to a generalized eigenvalue problem, and its performance for fold classification is compared to that of other published indices. The optimal index has significantly more structural discriminatory power than all currently known indices, including average surrounding hydrophobicity, which it most closely resembles. It demonstrates >70% classification accuracy over all folds and nearly 100% accuracy on several folds with distinctive conserved structural features. Finally, there is a compelling universality to the optimal index in that it does not appear to depend strongly on the specific structural classes used in its computation.

Algorithms↗

PubMed2002

On-line identification and optimization of feed rate profiles for high productivity fed-batch culture of hybridoma cells using genetic algorithms.

In this paper, an on-line identification and optimization method based on genetic algorithms (GAs) has been used to optimize the productivity of a seventh-order nonlinear model of fed-batch culture of hybridoma cells. The parameters of the seventh-order nonlinear model are assumed to be unknown. The intention of this paper is to use GAs for (1) identifying the parameters of a seventh-order nonlinear model of fed-batch culture of hybridoma cells, and (2) determining the best feed rate control profiles for glucose and glutamine. The final level of monoclonal antibodies obtained by this method is then compared with the case where all the parameters are assumed to be known. It is found that the final level of monoclonal antibodies obtained by the on-line identification and optimization method is only about 3% less than the final level of monoclonal antibodies obtained by the case where all the parameters are assumed to be known. GAs proved to be a good alternative method for solving on-line identification and optimization problems.

Algorithms↗

PubMed2005

Online optimization of fuzzy-PID control of a thermal process.

A constrained optimization of a simple fuzzy-PID (PID-proportional integral derivative) system is designed for the online improvement of PID control performance during productive control runs. The cost function design yields a desirable balance between rise time, setpoint overshoot, and settling time to the setpoint. The constraints determined by simulation yield control performance no worse than the existing control performance during online optimization. The optimized fuzzy-PID system is compared to a similarly optimized PID controller and a benchmark model predictive controller.

Journal Article↗

PubMed2006

Nominal and robust stability regions of optimization-based PID controllers.

In recent decades, several optimization-based methods have been developed for the proportional-integral-derivative (PID) controller design, and the common feature of these methods is that the controller has only one adjustable parameter. To keep the closed-loop systems stable is an essential requirement for the optimization-based PID controllers. In almost all these methods, however, no exact stability region for the single adjustable parameter was sketched. In this paper, using the proposed analytical procedure based on the dual-locus diagram technique, explicit stability regions of the optimization-based PID controllers are derived for stable, integrating, and unstable processes with time delay in the nominal and perturbed cases, respectively. It is revealed that the proposed analytical procedure is effective for the determination of the nominal and robust stability regions and it offers simplicity and ease of mathematical calculations over other available stability analysis methods. The results in this paper provide some insight into the tuning of the optimization-based PID controllers.

Algorithms↗

PubMed2000

A model of bone adaptation as an optimization process.

The internal bone adaptation of the proximal femur is considered. A three-dimensional finite element model of the proximal femur is used. The bone remodeling in this work is numerically described by an evolutionary remodeling scheme with anisotropic material parameters and time-dependent loading. The memory of past loading is included in the model to account for the delay in the bone response from the load changes. The remodeling rate equation is derived from the structural optimization task of maximizing the stiffness in each time step. Additional information can be extracted from the optimization process; the remodeling equilibrium parameter where no apposition or resorption takes place, is defined as the element optimality conditions and the optimal design is used as an initial design for the onset of the remodeling simulation. Two examples of bone adaptation resulting from load changes are given, and the irreversible nature of the model is illustrated.

Adaptation, Physiological↗

PubMed2002

Hierarchical genetic algorithm versus static optimization-investigation of elbow flexion and extension movements.

The applicability of static optimization (and, respectively, frequently used objective functions) for prediction of individual muscle forces for dynamic conditions has often been discussed. Some of the problems are whether time-independent objective functions are suitable, and how to incorporate muscle physiology in models. The present paper deals with a twofold task: (1) implementation of hierarchical genetic algorithm (HGA) based on the properties of the motor units (MUs) twitches, and using multi-objective, time-dependent optimization functions; and (2) comparison of the results of the HGA application with those obtained through static optimization with a criterion "minimum of a weighted sum of the muscle forces raised to the power of n". HGA and its software implementation are presented. The moments of neural stimulation of all MUs are design variables coding the problem in the terms of HGA. The main idea is in using genetic operations to find these moments, so that the sum of MUs twitches satisfies the imposed goals (required joint moments, minimal sum of muscle forces, etc.). Elbow flexion and extension movements with different velocities are considered as proper illustration. It is supposed that they are performed by two extensor muscles and three flexor muscles. The results show that HGA is a suitable means for precise investigation of motor control. Many experimentally observed phenomena (such as antagonistic co-contraction, three-phasic behavior of the muscles during fast movements) can find their explanation by the properties of the MUs twitches. Static optimization is also able to predict three-phasic behavior and could be used as practicable and computationally inexpensive method for total estimation of the muscle forces.

Action Potentials↗

PubMed1997

Forces of individual cat ankle extensor muscles during locomotion predicted using static optimization.

In order to test the principles of the control of synergistic muscles that were proposed in the literature, forces of cat soleus (SO), gastrocnemius (GA), and plantaris (PL) measured during locomotion were compared with the corresponding forces predicted using different optimization criteria. Forces of cat SO, GA, and PL, and the corresponding cat kinematics were recorded simultaneously using E-shaped force transducers and high-speed video, respectively. Measurements were obtained from three cats walking and trotting on a treadmill at five nominal speeds ranging from 0.4 to 1.8 m s-1. Muscle forces were predicted using static optimization and a musculoskeletal model of the cat hindlimb consisting of three segments (foot, shank, and thigh) and three muscles (SO, GA, and PL). Six optimization criteria which had been proposed in the literature were tested. Linear criteria based on the principles of minimum muscle force and stress predicted forces during the stance phase with an average normalized error of 59-322%. Three other criteria--minimization of the sum of the relative muscle forces squared, minimization of the sum of the muscle stresses cubed, and minimization of the upper bound for all of the muscle stresses-showed a better performance: (i) the average error was 43-119% and (ii) the correlation coefficient calculated between the predicted and actual forces exceeded 0.9 for all three muscles. A criterion that was based on the principle of minimum fatigue and accounted for the percentage of slow-twitch fibers in the muscles, had the lowest average error (26-52%). The high correlation (0.97-0.99) between the measured forces and forces predicted by using the minimum fatigue criterion suggested that force sharing among SO, GA, and PL during cat locomotion may be the same for a given set of joint moments and muscle moment arms. It was concluded that static optimization with the appropriate criterion can predict muscle forces adequately for specific movement conditions.

Animals↗

PubMed2000

Optimization of ion-exchange displacement separations. I. Validation of an iterative scheme and its use as a methods development tool.

Displacement chromatography has been demonstrated to be a powerful, high-resolution preparative tool. The performance of displacement systems can be affected by a variety of factors such as the feed load, flow-rate, initial salt concentration and the displacer partition ratio. Thus, the optimization of displacement separations is a uniquely challenging problem. In this manuscript, an iterative optimization scheme has been presented whereby one can identify the optimum operating conditions for displacement separations at a given level of loading on a given resin material. The solid film linear driving force model has been employed in concert with the Steric Mass Action formalism of ion-exchange chromatography to describe the chromatographic behavior in these systems. Simple pulse techniques have been employed to estimate the transport parameters. The iterative scheme has been validated using a rigorous Feasible Sequential Quadratic Programming algorithm. Finally, the utility of the iterative optimization scheme as a methods development tool for displacement separations has been demonstrated for a difficult separation. The results indicate that the use of the optimization scheme leads to significantly better performance than standard rules of thumb.

Algorithms↗

PubMed1988

Selection of high-performance liquid chromatographic methods in pharmaceutical analysis. II. Optimization for selectivity in normal-phase systems.

Optimization of selectivity in normal-phase chromatography was studied. Using the same optimization criteria (Rs,min, Dmin, Rsb and Rsa) as in Part I the possible combination of "solvent strength" optimization by variation of the percentage of polar modifier in the less polar mobile phase and "solvent type" optimization by measuring the solvent selectivity of chloroform, acetonitrile, tetrahydrofuran and dioxane was examined. From the results it can be concluded that by replacement of medium-polarity solvents (chloroform, acetonitrile, tetrahydrofuran and dioxane) in the mobile phase, the selectivity of the separation can be significantly improved as the elution order is a function of solvent type belonging to Class P. In the separation of a steroid mixture dioxane provides the best properties for improving band spacing.

Chromatography, High Pressure Liquid↗

PubMed2001

Optimization and application of high-resolution gas chromatography with ion trap tandem mass spectrometry to the determination of polychlorinated biphenyls in atmospheric aerosols.

Optimization of the Finnigan GCQ ion trap mass spectrometry (ITMS) system and a clean-up procedure were carried out in order to apply high-resolution gas chromatography-tandem mass spectrometry for the analysis of polychlorinated biphenyls (PCBs) in aerosols. Six ITMS operating parameters, including isolation time, excitation voltage, excitation time, "q" value, ion source temperature and electron energy were adjusted in order to optimize the instrument analytical performance. The adjustment of all parameters substantially increased the sensitivity of ITMS in the MS-MS mode. Changes in isolation time did not particularly affect ITMS sensitivity while ion source temperature had the strongest influence. After optimization, a limit of detection of 600 fg/microl with S/N varying from 8 up to 91 was achieved. The application of the optimized ITMS parameters conjointly with the developed clean-up procedure resulted in method detection limits of 10-20 fg/m3 for the determination of PCBs, in the particulate and gas phase of the atmospheric aerosol of background areas in the Eastern Mediterranean and Sweden.

Aerosols↗

PubMed1990

Simultaneous optimization of variables influencing selectivity and elution strength in micellar liquid chromatography. Effect of organic modifier and micelle concentration.

Previously, the simultaneous enhancement of separation selectivity with elution strength was reported in micellar liquid chromatography (MLC) using the hybrid eluents of water-organic solvent-micelles. The practical implication of this phenomenon is that better separations can be achieved in shorter analysis times by using the hybrid eluents. Since both micelle concentration and volume fraction of organic modifier influence selectivity and solvent strength, only an investigation of the effects of a simultaneous variation of these parameters will disclose the full separation capability of the method, i.e. the commonly used sequential solvent optimization approach of adjusting the solvent strength first and then improving selectivity in reversed-phase liquid chromatography is inefficient for the case of MLC with the hybrid eluents. This is illustrated in this paper with two examples: the optimization of the selectivity in the separation of a mixture of phenols and the optimization of a resolution-based criterion determined for the separation of a number of amino acids and small peptides. The large number of variables involved in the separation process in MLC necessitates a structured approach in the development of practical applications of this technique. A regular change in retention behavior is observed with the variation of the surfactant concentration and the concentration of organic modifier, which enables a successful prediction of retention times. Consequently interpretive optimization strategies such as the interative regression method are applicable.

1-Propanol↗

PubMed2002

Prediction of chromatographic retention, pKa values and optimization of the separation of polyphenolic acids in strawberries.

Polyphenolic acids are a complex group of compounds that have attracted enormous attention in the last few years because of their biological properties. In this work, the proportion of organic modifier and the pH of acetonitrile-water mixtures used as mobile phases were optimized in order to separate a series of polyphenolic compounds. The linear solvation energy relationship formalism based on the single solvent polarity parameter, E(T)N was used to predict their chromatographic behavior as a function of the percentage of acetonitrile in the eluent. Moreover, the correlation established between retention and the pH of the aqueous-organic mobile phase was used to optimize the pH of the mobile phase. The optimized mobile phase is composed of acetonitrile and formic acid buffer adjusted to pH 4.25, with 12% (v/v) acetonitrile. Also, the pKa values of polyphenolic acids in acetonitrile-water mixtures were determined using chromatographic data, and in order to validate the optimized conditions, a series of polyphenolic compounds was studied in strawberries.

Fruit↗

PubMed2003

Multiobjective optimization of simulated moving bed and Varicol processes using a genetic algorithm.

The size of the packing material, the total number of columns and the total feed concentration have significant impacts on the economics of a preparative chromatographic separation, through their effects on column pressure drop, column efficiency and thermodynamics. In this work, the role of these parameters on the performances of a simulated moving bed and a Varicol process is investigated on a chiral separation system from literature, using an equilibrium stage model. A multiple objective optimization technique based on a genetic algorithm is adopted, which allows to maximize simultaneously the purity of the extract and productivity of the unit. In this way, it is possible to optimize and compare the performances of both processes in a wide range of parameter values, so as to assess their relative potential under equally optimized conditions. The optimization results, i.e. the so-called Pareto sets, have been discussed in the frame of equilibrium theory and the roles of these three parameters have been clarified.

Algorithms↗

PubMed2003

Optimization of microwave-assisted extraction and supercritical fluid extraction of carbamate pesticides in soil by experimental design methodology.

Orthogonal array design (OAD) was applied for the first time to optimize microwave-assisted extraction (MAE) and supercritical fluid extraction (SFE) conditions for the analysis of four carbamates (propoxur, propham, methiocarb, chlorpropham) from soil. The theory and methodology of a new OA16 (4(4)) matrix derived from a OA16 (2(15)) matrix were developed during the MAE optimization. An analysis of variance technique was employed as the data analysis strategy in this study. Determinations of analytes were completed using high-performance liquid chromatography (HPLC) with UV detection. Four carbamates were successfully extracted from soil with recoveries ranging from 85 to 105% with good reproducibility (approximately 4.9% RSD) under the optimum MAE conditions: 30 ml methanol, 80 degrees C extraction temperature, and 6-min microwave heating. An OA8 (2(7)) matrix was employed for the SFE optimization. The average recoveries and RSD of the analytes from spiked soil by SFE were 92 and 5.5%, respectively except for propham (66.3+/-7.9%), under the following conditions: heating for 30 min at 60 degrees C under supercritical CO2 at 300 kg/cm2 modified with 10% (v/v) methanol. The composition of the supercritical fluid was demonstrated to be a crucial factor in the extraction. The addition of a small volume (10%) of methanol to CO2 greatly enhanced the recoveries of carbamates. A comparison of MAE with SFE was also conducted. The results indicated that >85% average recoveries were obtained by both optimized extraction techniques, and slightly higher recoveries of three carbamates (propoxur, propham and methiocarb) were achieved using MAE. SFE showed slightly higher recovery for chlorpropham (93 vs. 87% for MAE). The effects of time-aged soil on the extraction of analytes were examined and the results obtained by both methods were also compared.

Carbamates↗

PubMed2003

Strategy for developing and optimizing liquid chromatography methods in pharmaceutical development using computer-assisted screening and Plackett-Burman experimental design.

We describe a three-step method development/optimization strategy for HPLC assay/impurity methods for pharmaceuticals, which include multiple-column/mobile phase screening using a system equipped with a column-switching device, further optimization of separation by using multiple organic modifiers in the mobile phase, and multiple-factor method optimization using Plackett-Burman experimental designs. In the first two steps, commercially available chromatography optimization software, DryLab, was used to perform computer simulations. This allows the method developer to evaluate each condition (one column/mobile phase combination) with retention data from two scouting gradient runs. This approach significantly reduces the number of runs in method development. After a satisfactory separation was obtained, we used a method optimization step with Plackett-Burman experimental designs. The purpose of the 16-injection set experiments was to evaluate nine method factors with regard to method precision, accuracy, sensitivity and specificity. The results provided logical justifications in selecting method parameters such as column temperature, detection wavelength, injection volume, and sample solvent, etc. In data analysis, instead of the traditional mathematical manipulations, we used the graphical methods to examine and present data by creating the so-called main effect plots. Because replicates of design points were not run, the data did not allow the testing of statistical significance. However, it provided visual presentations in a way that is easy to understand for the method developer and end user alike.

Chromatography, High Pressure Liquid↗

PubMed2000

Filter-feeding and cruising swimming speeds of basking sharks compared with optimal models: they filter-feed slower than predicted for their size.

Movements of six basking sharks (4.0-6.5 m total body length, L(T)) swimming at the surface were tracked and horizontal velocities determined. Sharks were tracked for between 1.8 and 55 min with between 4 and 21 mean speed determinations per shark track. The mean filter-feeding swimming speed was 0.85 m s(-1) (+/-0.05 S.E., n=49 determinations) compared to the non-feeding (cruising) mean speed of 1.08 m s(-1) (+/-0.03 S.E., n=21 determinations). Both absolute (m s(-1)) and specific (L s(-1)) swimming speeds during filter-feeding were significantly lower than when cruise swimming with the mouth closed, indicating basking sharks select speeds approximately 24% lower when engaged in filter-feeding. This reduction in speed during filter-feeding could be a behavioural response to avoid increased drag-induced energy costs associated with feeding at higher speeds. Non-feeding basking sharks (4 m L(T)) cruised at speeds close to, but slightly faster ( approximately 18%) than the optimum speed predicted by the Weihs (1977) [Weihs, D., 1977. Effects of size on the sustained swimming speeds of aquatic organisms. In: Pedley, T.J. (Ed.), Scale Effects in Animal Locomotion. Academic Press, London, pp. 333-338.] optimal cruising speed model. In contrast, filter-feeding basking sharks swam between 29 and 39% slower than the speed predicted by the Weihs and Webb (1983) [Weihs, D., Webb, P.W., 1983. Optimization of locomotion. In: Webb, P.W., Weihs, D. (Eds.), Fish Biomechanics. Praeger, New York, pp. 339-371.] optimal filter-feeding model. This significant under-estimation in observed feeding speed compared to model predictions was most likely accounted for by surface drag effects reducing optimum speeds of tracked sharks, together with inaccurate parameter estimates used in the general model to predict optimal speeds of basking sharks from body size extrapolations.

Journal Article↗

PubMed2003

An optimized homogeneous noncompetitive immunoassay based on the antigen-driven enzymatic complementation.

We describe an optimized noncompetitive and homogeneous immunoassay based on the antigen-dependent reassociation of antibody variable domains and beta-galactosidase (beta-gal) complementation (open sandwich enzymatic complementation immunoassay, OS-ECIA). The reassociation of two fusion proteins, an antibody heavy chain variable region fragment tethered to an N-terminal deletion mutant of beta-gal, V(H)Deltaalpha, and the light chain variable region fragment tethered to a C-terminal deletion mutant of beta-gal, V(L)Deltaomega, was monitored by the enzymatic complementation between the two. With the use of anti-hen egg lysozyme (HEL) antibody HyHEL10, an antigen-dependent enhancement in the enzymatic activity was clearly observed. To optimize the assay, the lengths of the linkers connecting the two domains of each fusion protein were varied, and the optimal pair V(H)(G(4)S)(2)Deltaalpha/V(L)(G(4)S)Deltaomega showed much improved antigen-responsive beta-gal activity. After various optimizations, almost 1000-fold improvement in sensitivity compared with that of our corresponding homogeneous open sandwich (OS) assays based on the energy transfer was observed, possibly due to lower V(H)/V(L) concentration and background heterodimer association.

Haptens↗