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PubMed1993

MRI gradient waveform design by numerical optimization.

This manuscript describes a method of gradient waveform design by nonlinear constrained optimization. Methods of formulation and solution of the waveform optimization problem are briefly described for minimization of root mean squared current and minimization of waveform moments. Waveforms generated using these objectives are presented and compared with those obtained with other objectives. The method uses waveforms which are defined as a set of discrete amplitudes in order to remove artificial constraints on waveform shape imposed by "multilobe" designs. These point-to-point amplitudes are the parameters determined in the optimization procedure which includes knowledge of the specific imaging conditions and the specific gradient hardware system. Some beneficial results of this design approach are: a) physically realizable waveforms which optimally achieve specific imaging and motion artifact reduction goals, b) waveforms which are guaranteed to be optimal with respect to one of several possible objective, c) less reliance on the experience of the designer, and d) a potential reduction in waveform design time.

Humans↗

PubMed2001

Optimization of solvation models for predicting the structure of surface loops in proteins.

A novel procedure for optimizing the atomic solvation parameters (ASPs) sigma(i) developed recently for cyclic peptides is extended to surface loops in proteins. The loop is free to move, whereas the protein template is held fixed in its X-ray structure. The energy is E(tot) = E(FF)(epsilon = nr) + summation operator sigma(i)A(i), where E(FF)(epsilon = nr) is the force-field energy of the loop-loop and loop-template interactions, epsilon = nr is a distance-dependent dielectric constant, and n is an additional parameter to be optimized. A(i) is the solvent-accessible surface area of atom i. The optimal sigma(i) and n are those for which the loop structure with the global minimum of E(tot)(n, sigma(i)) becomes the experimental X-ray structure. Thus, the ASPs depend on the force field and are optimized in the protein environment, unlike commonly used ASPs such as those of Wesson and Eisenberg (Protein Sci 1992;1:227-235). The latter are based on the free energy of transfer of small molecules from the gas phase to water and have been traditionally combined with various force fields without further calibration. We found that for loops the all-atom AMBER force field performed better than OPLS and CHARMM22. Two sets of ASPs [based on AMBER (n = 2)], optimized independently for loops 64-71 and 89-97 of ribonuclease A, were similar and thus enabled the definition of a best-fit set. All these ASPs were negative (hydrophilic), including those for carbon. Very good (i.e., small) root-mean-square-deviation values from the X-ray loop structure were obtained with the three sets of ASPs, suggesting that the best-fit set would be transferable to loops in other proteins as well. The structure of loop 13-24 is relatively stretched and was insensitive to the effect of the ASPs.

Hydrogen↗

PubMed1994

Spatial optimization of electrostatic interactions between the ionized groups in globular proteins.

A model approach is suggested to estimate the degree of spatial optimization of the electrostatic interactions in protein molecules. The method is tested on a set of 44 globular proteins, representative of the available crystallographic data. The theoretical model is based on macroscopic computation of the contribution of charge-charge interactions to the electrostatic term of the free energy for the native proteins and for a big number of virtual structures with randomly distributed on protein surface charge constellations (generated by a Monte-Carlo technique). The statistical probability of occurrence of random structures with electrostatic energies lower than the energy of the native protein is suggested as a criterion for spatial optimization of the electrostatic interactions. The results support the hypothesis that the folding process optimizes the stabilizing effect of electrostatic interactions, but to very different degree for different proteins. A parallel analysis of ion pairs shows that the optimization of the electrostatic term in globular proteins has increasingly gone in the direction of rejecting the repulsive short contacts between charges of equal sign than of creating of more salt bridges (in comparison with the statistically expected number of short-range ion pairs in the simulated random structures). It is observed that the decrease in the spatial optimization of the electrostatic interactions is usually compensated for by an appearance of disulfide bridges in the covalent structure of the examined proteins.

Alcohol Dehydrogenase↗

PubMed1994

An optimal three-stage design for phase II clinical trials.

A phase II clinical trial in cancer therapeutics is usually a single-arm study to determine whether an experimental treatment (E) holds sufficient promise to warrant further testing. When the criterion of treatment efficacy is a binary endpoint (response/no response) with probability of response p, we propose a three-stage optimal design for testing H0: p < or = p0 versus H1: p > or = p1, where p1 and p0 are response rates such that E does or does not merit further testing at given levels of statistical significance (alpha) and power (1--beta). The proposed design is essentially a combination of earlier proposals by Gehan and Simon. The design stops with rejection of H1 at stage 1 when there is an initial moderately long run of consecutive treatment failures; otherwise there is continuation to stage 2 and (possibly) stage 3 which have decision rules analogous to those in stages 1 and 2 of Simon's design. Thus, rejection of H1 is possible at any stage, but acceptance only at the final stage. The design is optimal in the sense that expected sample size is minimized when p = p0, subject to the practical constraint that the minimum stage 1 sample size is at least 5. The proposed design has greatest utility when the true response rate of E is small, it is desirable to stop early if there is a moderately long run of early treatment failures, and it is practical to implement a three-stage design. Compared to Simon's optimal two-stage design, the optimal three-stage design has the following features: stage 1 is the same size or smaller and has the possibility of stopping earlier when 0 successes are observed; the expected sample size under the null hypothesis is smaller; stages 1 and 2 generally have more patients than stage 1 of the two-stage design, but a higher probability of early termination under H0; and the total sample size and criteria for rejection of H1 at stage 3 are similar to the corresponding values at the end of stage 2 in the two-stage optimal design.

Clinical Trials, Phase II as Topic↗

PubMed1995

Optimization of calcium phosphate transfection for bovine chromaffin cells: relationship to calcium phosphate precipitate formation.

Optimal conditions for formation of calcium phosphate-DNA precipitates and for chromaffin cell transfection by the calcium phosphate method were examined. A relationship was observed between turbidity of calcium phosphate solutions and the ability of calcium phosphate-DNA mixtures to give efficient transfection of bovine chromaffin cells. Under optimal conditions up to 35% of chromaffin cells in cultures transfected with plasmid DNA encoding human proenkephalin or Escherichia coli beta-galactosidase expressed the respective proteins. Important factors for transfection were the pH (6.95) and buffer employed for calcium phosphate-DNA precipitate formation, the amount and type of DNA, and the absence of serum in the cultures. Additionally, phosphate and calcium concentrations in the culture medium during incubation of cells with DNA are critical. Optimal conditions for transfection of chromaffin cells were also useful for transfection of clonal BSC-40 cells, an African green monkey kidney cell line. These results suggest that the optimal conditions described here for chromaffin cells may have broad applicability to other cell types. In addition, the results suggest that it is possible to optimize the solutions used for transfection conditions by monitoring calcium phosphate formation.

Adrenal Medulla↗

PubMed1993

Optimalization of southwestern technique for detection of binding of Epstein-Barr virus nuclear antigen 1 to origin of replication.

An optimized protocol of Southwestern analysis for detection of Epstein-Barr virus (EBV) nuclear antigen 1 (EBNA-1) binding to the origin of viral replication (oriP) was described. The unique feature of this optimized protocol includes the restoration of the denatured proteins to native conformation after SDS-polyacrylamide gel electrophoresis and blocking of nonspecific and low-affinity binding sites prior to DNA binding. The parameters and conditions that may affect the specific interaction of EBNA-1 to oriP DNA were then determined. The specific binding was affected by divalent cations (MgCl2) and ionic strength; the optimal concentrations of MgCl2 and NaCl were observed at 10 and 300 mM, respectively. The various buffer systems and pH values tested had no apparent effect on EBNA-1 binding. Under the optimal conditions, a single protein of 68 Kd was detected and the bindings of other nonspecific, low-affinity DNA-binding proteins were abolished. The authenticity and specificity of 68 Kd protein as EBNA-1 were determined by reaction with antibody specific for EBNA-1 and competition assay with specific DNA sequence. After optimization this technique can be a powerful and yet simple means of studying protein-DNA interactions and their roles in gene expression.

Antigens, Viral↗

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

Optimizing drug regimens in cancer chemotherapy by an efficacy-toxicity mathematical model.

In cancer chemotherapy, it is important to design treatment strategies that ensure a desired rate of tumor cell kill without unacceptable toxicity. To optimize treatment, we used a mathematical model describing the pharmacokinetics of anticancer drugs, antitumor efficacy, and drug toxicity. This model was associated with constraints on the allowed plasma concentrations, drug exposure, and leukopenia. Given a schedule of drug administrations, the mathematical model optimized the drug doses that can minimize the tumor burden while limiting toxicity at the level of the white blood cells. The main result is that the optimal drug administration is an initial high-dose chemotherapy up to saturation of constraints associated with normal cell toxicity and a maintenance continuous infusion at a moderate rate. Data related to etoposide investigations were used in a feasibility study. Simulations with the optimized protocol showed better performances than usual clinical protocols. Model-based optimal drug doses provide for greater cytoreduction, while limiting the risk of unacceptable toxicity.

Antineoplastic Agents↗

PubMed2002

Can serum CA-125 levels predict the optimal primary cytoreduction in patients with advanced ovarian carcinoma?

OBJECTIVE: The aim of this study was to investigate the predictive value of serum CA-125 levels to ability of optimal primary cytoreduction in patients with advanced epithelial ovarian carcinoma. METHODS: Preoperative serum CA-125 levels were determined by a commercial enzyme immunoassay kit in a series of 92 patients with stage IIIC epithelial ovarian carcinoma. The abilities of various cutoff value of CA-125 to predict suboptimal cytoreductive surgery were determined. A receiver operating characteristic curve was used to find the most clinically useful CA-125 cutoff value. RESULTS: Optimal cytoreduction was obtained in 48 patients (52%) using the diameter of the largest residual tumor nodule less than 1 cm. Receiver operating characteristic curve showed that the most clinically suitable CA-125 cutoff value was 500 U/ml. Forty-seven patients (51%) had preoperative serum CA-125 levels below 500 U/ml. Of these patients, optimal cytoreductive surgery was performed in 36 (77%). Of the 45 patients with serum CA-125 levels greater than 500 U/ml, optimal cytoreductive surgery was achieved in 12 (27%). True- and false-positive rates were 73 and 23%, respectively. CONCLUSIONS: Although our results showed that preoperative serum CA-125 levels might predict the optimal resectable patients, larger prospective studies are needed to prove its predictivity. Gynecologic oncologists should evaluate the sum of all criteria until more data are available.

CA-125 Antigen↗

PubMed1999

Humanization of a murine monoclonal antibody by simultaneous optimization of framework and CDR residues.

Optimal protein function often depends on co-operative interactions between amino acid residues distant in the protein primary sequence yet spatially near one another following protein folding. For example, antibody affinity is influenced by interactions of framework residues with complementarity-determining region (CDR) residues. However, despite the abundance of antibody structural information and computational tools the humanization of rodent antibodies for clinical use often results in a significant loss of affinity. To date, antibody engineering efforts have focused either on optimizing CDR residues involved in antigen binding or on optimizing antibody framework residues that serve critical roles in preserving the conformation of CDRs. In the present study a new approach which permits the rapid identification of co-operatively interacting framework and CDR residues was used to simultaneously humanize and optimize a murine antibody directed against CD40. Specifically, a combinatorial library that examined eight potentially important framework positions concomitantly with focused CDR libraries consisting of variants containing random single amino acid mutations in the third CDR of the heavy and light chains was expressed. Multiple anti-CD40 Fab variants containing as few as one murine framework residue and displaying up to approximately 500-fold higher affinity than the initial chimeric Fab were identified. The higher affinity humanized variants demonstrated a co-operative interaction between light chain framework residue Y49 and heavy chain CDR3 residue R/K101 (coupling energy, DeltaGI=0.9 kcal/mol). Screening of combinatorial framework-CDR libraries permits identification of monoclonal antibodies (mAb) with structures optimized for function, including instances in which the antigen induces conformational changes in the mAb. Moreover, the enhanced humanized variants contain fewer murine framework residues and could not be identified by sequential in vitro humanization and affinity muturation strategies. This approach to identifying co-operatively interacting residues is not restricted to antibody-antigen interactions and consequently, may be used broadly to gain insight into protein structure-function relationships, including proteins that serve as catalysts.

Amino Acid Sequence↗

PubMed1996

Optimization of Transverse Gradient Coils with Coaxial Return Paths by Simulated Annealing

Coils with coaxial return paths are used to generate transverse magnetic field gradients. This paper describes optimization of such coils by the method of simulated annealing, a method known to be able to find the global minimum of a function. The adaptive simulated annealing (ASA) program has been analyzed and applied to optimization of a family of coils with 8-16 building blocks, each carrying equal current. Positions of the blocks along the longitudinal axis of the coils were optimized. A new subclass of coils is proposed; the diameter of return paths of this subclass of coils is not fixed but may be varied. The new coils provide greater gradient uniformity than those for which only positions of the blocks are optimized. All optimized coils should find applications in high-precision and high-resolution imaging and spectroscopic experiments.

Journal Article↗

PubMed1997

Does Escherichia coli optimize the economics of the translation process?

The codon translation rate is usually assumed to be proportional to the cellular concentration of the cognate tRNA, but synonymous codons sharing the same cognate tRNA may be translated at rather different rates. To account for the latter observation, we assume that the translation process is optimized in two respects: (i), the codon demand is optimized with respect to the supply of cognate tRNAs (composition of the tRNA pool); and (ii), for synonymous codons sharing the same cognate tRNA, the usage frequency of each codon correlates optimally with the stability of the codon-anticodon complex. These assumptions allow us to compute the relative rate constants of synonymous codons. Highly expressed genes, which produce 80-90% of the protein mass in the E. coli cell, appear to have selected codons which make an optimal use of the tRNA pool. Assuming the optimization criteria were valid, a list of codon translation times (in ms) were derived from available experimental data.

Codon, Terminator↗

PubMed1999

Shear stress distribution in arterial tree models, generated by constrained constructive optimization.

Models of arterial trees are generated by the algorithm of Constrained Constructive Optimization (CCO). Straight cylindrical, binary branching tubes are arranged in an optimized fashion so as to convey blood to the terminal sites of the tree, which are distributed over a predefined area, representing the tissue to be perfused. All terminal segments supply equal flows at a unique terminal pressure, and the radii of parent and daughter segments are related via a bifurcation law. The connective structure and geometry of the model are optimized according to a target function such as total intravascular volume. The shear rate between blood and the vessel walls is computed in each segment and a new method is presented for rescaling a given CCO tree to a desired value of shear rate in the root segment. The effect of viscosity varying with shear rate is evaluated and a new method is presented for rescaling a CCO-tree segment by segment to consistent values of radii and variable viscosity. Shear stress is evaluated for its deviation from being proportional to shear rate and then subjected to various types of analyses. Usually both, shear stress and its variability, are found to be larger in the smaller than in the larger segments of the CCO-model trees. However, it is shown how the shear-stress distribution can be reshuffled between small and large segments when rescaling a CCO tree to obey a different bifurcation law, while its whole geometry remains unchanged and all boundary conditions remain fulfilled. The selection of optimization target is found to drastically affect shear-stress variability within bifurcations, which reaches a distinct minimum if the model is optimized according to intravascular volume. Finally, a rank-analysis of shear stress within each bifurcation shows that only two out of six possible rank patterns actually occur: the parent segment always experiences medium shear stress while minimum shear stress resides mostly in the larger, less frequently in the smaller daughter.

Arteries↗

PubMed2001

Inducible defense against pathogens and parasites: optimal choice among multiple options.

Defense against pathogen, parasites and herbivores is often enhanced after their invasion into the host's body. Sometimes different options are adopted depending on the identity and the quantity of the pathogen, exemplified by the switch between Th1 and Th2 systems in mammalian immunity. In this paper, we study the optimal defense of the host when two alternative responses are available, which differ in the effectiveness of suppressing the growth of pathogen (parasite, or herbivore), the damage to the host caused by the defense response, and the magnitude of time delay before the defense response becomes fully effective. The optimal defense is the one that minimizes the sum of the damages caused by the pathogen and the cost due to defense activities. The damage by pathogens increases in proportion to the time integral of the pathogen abundance, and the cost is proportional to the defense activity. We can prove that a single globally optimal combination of defense options always exists and there is no other local optimum. Depending on the parameters, the optimal is to adopt only the early response, only the late response, or both responses. The defense response with a shorter time delay is more heavily used when the pathogen grows fast, the initial pathogen abundance is large, and the difference in time delay is long. We also study the host's optimal choice between constitutive and inducible defenses. In the constitutive defense, the response to pathogen attack works without delay, but it causes the cost even when the pathogen attack does not occur. We discuss mammalian immunity and the plant chemical defense from the model's viewpoint.

Animals↗

PubMed2001

Optimality under noise: higher memory strategies for the alternating prisoner's dilemma.

The Alternating Prisoner's Dilemma is a variant of the iterated Prisoner's Dilemma in which the players alternate in the roles of actor and recipient. We searched for strategies which are "optimal" in the Alternating Prisoner's Dilemma with noise (a non-zero probability that a player's decision will be transmitted incorrectly). In order to achieve success against a variety of other strategies, a strategy must be "self-cooperating" (able to achieve mutual cooperation with its clone), "C-exploiting" (able to exploit unconditional cooperators), and "D-unexploitable" (able to resist exploitation by defectors). It must also have high evolutionary "dominance", a general measure of evolutionary performance which considers both resistance to invasion and the ability to invade other strategies. A strategy which meets these optimality criteria can evolve cooperation by invading a population of defectors and establishing a stable cooperative society. Most of the strategies commonly discussed in the Alternating Prisoner's Dilemma literature are low-memory strategies such as Tit For Tat, Pavlov, and Firm But Fair, but none of these strategies can simultaneously meet all of the optimality criteria. However, we discovered a class of higher memory "Firm Pavlov" strategies, which not only meet our stringent optimality criteria, but also achieve remarkable success in round-robin tournaments and evolutionary interactions. These higher memory strategies are friendly enough to cooperate with their clone, pragmatic enough to exploit unconditional cooperators, and wary enough to resist exploitation by defectors: they are truly "optimal under noise" in the Alternating Prisoner's Dilemma.

Algorithms↗

PubMed2002

Detection versus estimation in event-related fMRI: choosing the optimal stimulus timing.

With the advent of event-related paradigms in functional MRI, there has been interest in finding the optimal stimulus timing, especially when the interstimulus interval is varied during the imaging run. Previous works have proposed stimulus timings to optimize either the estimation of the impulse response function (IRF) or the detection of signal changes. The purpose of this paper is to clarify that estimation and detection are fundamentally different goals and to determine the optimal stimulus timing and distribution with respect to both the accuracy of estimating the IRF and the power of detection assuming a particular hemodynamic model. Simulated stimulus distributions are varied systematically, from traditional blocked designs to rapidly varying event related designs. These simulations indicate that estimation of the hemodynamic impulse response function is optimized when stimuli are frequently alternated between task and control states, with shorter interstimulus intervals and stimulus durations, whereas the detection of activated areas is optimized by blocked designs. The stimulus timing for a given experiment should therefore be generated with the required detectability and estimation accuracy.

Cerebral Cortex↗

PubMed2000

Optimal Bayesian foraging policies and prey population dynamics-some comments on Rodriguez-Girones and Vasquez.

In this paper we show the density-dependent harvest rates of optimal Bayesian foragers exploiting prey occurring with clumped spatial distribution. Rodríguez-Gironés and Vásquez (1997) recently treated the issue, but they used a patch-leaving rule (current value assessment rule) that is not optimal for the case described here. An optimal Bayesian forager exploiting prey whose distribution follows the negative binomial distribution should leave a patch when the potential (and not instantaneous) gain rate in that patch equals the best long-term gain rate in the environment (potential value assessment rule). It follows that the instantaneous gain rate at which the patches are abandoned is an increasing function of the time spent searching in the patch. It also follows that the proportion of prey harvested in a patch is an increasing sigmoidal function of the number of prey initially present. In this paper we vary several parameters of the model to evaluate the effects on the forager's intake rate, the proportion of prey harvested per patch, and the prey's average mortality rate in the environment. In each case, we study an intake rate maximizing forager's optimal response to the parameter changes. For the potential value assessment rule we find that at a higher average prey density in the environment, a lower proportion of the prey is taken in a patch with a given initial prey density. The proportion of prey taken in a patch of a given prey density also decreases when the variance of the prey density distribution is increased and if the travel time between patches is reduced. We also evaluate the effect of using predation minimization, rather than rate maximization, as the currency. Then a higher proportion of the prey is taken for each given initial prey density. This is related to the assumption that traveling between patches is the most risky activity. Compared to the optimal potential value assessment rule, the current value assessment rule performs worse, in terms of long-term intake rate achieved. The difference in performance is amplified when prey density is high or highly aggregated. These results pertain to the foraging patch spatial scale and may have consequences for the spatial distribution of prey in the environment.

Animals↗

PubMed2005

Deformable registration of diffusion tensor MR images with explicit orientation optimization.

In this paper we present a novel deformable registration algorithm for diffusion tensor (DT) MR images that enables explicit analytic optimization of tensor reorientation. The optimization seeks a piecewise affine transformation that divides the image domain into uniform regions and transforms each of them affinely. The objective function captures both the image similarity and the smoothness of the transformation across region boundaries. The image similarity enables explicit orientation optimization by incorporating tensor reorientation, which is necessary for warping DT images. The objective function is formulated in a way that allows explicit implementation of analytic derivatives to drive fast and accurate optimization using the conjugate gradient method. The optimal transformation is hierarchically refined in a subdivision framework. A comparison with affine registration for inter-subject normalization of 8 subjects shows that our algorithm improves the alignment of manually segmented white matter structures (corpus callosum and cortio-spinal tracts).

Algorithms↗