Hybrid Global Optimization Algorithms for Protein Structure Prediction: Alternating Hybrids

Hybrid global optimization methods attempt to combine the beneficial features of two or more algorithms, and can be powerful methods for solving challenging nonconvex optimization problems. In this paper, novel classes of hybrid global optimization methods, termed alternating hybrids, are introduced for application as a tool in treating the peptide and protein structure prediction problems. In particular, these new optimization methods take the form of hybrids between a deterministic global optimization algorithm, the αBB, and a stochastically based method, conformational space annealing (CSA). The αBB method, as a theoretically proven global optimization approach, exhibits consistency, as it guarantees convergence to the global minimum for twice-continuously differentiable constrained nonlinear programming problems, but can benefit from computationally related enhancements. On the other hand, the independent CSA algorithm is highly efficient, though the method lacks theoretical guarantees of convergence. Furthermore, both the αBB method and the CSA method are found to identify ensembles of low-energy conformers, an important feature for determining the true free energy minimum of the system. The proposed hybrid methods combine the desirable features of efficiency and consistency, thus enabling the accurate prediction of the structures of larger peptides. Computational studies for met-enkephalin and melittin, employing sequential and parallel computing frameworks, demonstrate the promise for these proposed hybrid methods.     

Estimating individualized treatment rules with risk constraint

Individualized treatment rules (ITRs) recommend treatments based on patient-specific characteristics in order to maximize the expected clinical outcome. At the same time, the risks caused by various adverse events cannot be ignored. In this paper, we propose a method to estimate an optimal ITR that maximizes clinical benefit while having the overall risk controlled at a desired level. Our method works for a general setting of multi-category treatment. The proposed procedure employs two shifted ramp losses to approximate the 0-1 loss in the objective function and constraint, respectively, and transforms the estimation problem into a difference of convex functions (DC) programming problem. A relaxed DC algorithm is used to solve the nonconvex constrained optimization problem. Simulations and a real data example are used to demonstrate the finite sample performance of the proposed method.     

Improving metabolic flux estimation via evolutionary optimization for convex solution space

MOTIVATION: Flux estimation by using (13) C-labeling pattern information of metabolites is currently the only method that can give accurate, detailed quantification of all intracellular fluxes in the central metabolism of a microorganism. In essence, it corresponds to a constrained optimization problem which minimizes a weighted distance between measured and simulated results. Characteristics, such as existence of multiple local minima, non-linear and non-differentiable make this problem a special difficulty. RESULTS: In the present work, we propose an evolutionary-based global optimization algorithm taking advantage of the convex feature of the problem's solution space. Based on the characteristics of convex spaces, specialized initial population and evolutionary operators are designed to solve (13)C-based metabolic flux estimation problem robustly and efficiently. The algorithm was applied to estimate the central metabolic fluxes in Escherichia coli and compared with conventional optimization technique. Experimental results illustrated that our algorithm is capable of achieving fast convergence to good near-optima and maintaining the robust nature of evolutionary algorithms at the same time. AVAILABILITY: Available from the authors upon request.     

Dynamic optimization of bioprocesses: efficient and robust numerical strategies

The dynamic optimization (open loop optimal control) of non-linear bioprocesses is considered in this contribution. These processes can be described by sets of non-linear differential and algebraic equations (DAEs), usually subject to constraints in the state and control variables. A review of the available solution techniques for this class of problems is presented, highlighting the numerical difficulties arising from the non-linear, constrained and often discontinuous nature of these systems. In order to surmount these difficulties, we present several alternative stochastic and hybrid techniques based on the control vector parameterization (CVP) approach. The CVP approach is a direct method which transforms the original problem into a non-linear programming (NLP) problem, which must be solved by a suitable (efficient and robust) solver. In particular, a hybrid technique uses a first global optimization phase followed by a fast second phase based on a local deterministic method, so it can handle the nonconvexity of many of these NLPs. The efficiency and robustness of these techniques is illustrated by solving several challenging case studies regarding the optimal control of fed-batch bioreactors and other bioprocesses. In order to fairly evaluate their advantages, a careful and critical comparison with several other direct approaches is provided. The results indicate that the two-phase hybrid approach presents the best compromise between robustness and efficiency.     

Evaluation of a particle swarm algorithm for biomechanical optimization

Optimization is frequently employed in biomechanics research to solve system identification problems, predict human movement, or estimate muscle or other internal forces that cannot be measured directly. Unfortunately, biomechanical optimization problems often possess multiple local minima, making it difficult to find the best solution. Furthermore, convergence in gradient-based algorithms can be affected by scaling to account for design variables with different length scales or units. In this study we evaluate a recently-developed version of the particle swarm optimization (PSO) algorithm to address these problems. The algorithm's global search capabilities were investigated using a suite of difficult analytical test problems, while its scale-independent nature was proven mathematically and verified using a biomechanical test problem. For comparison, all test problems were also solved with three off-the-shelf optimization algorithms--a global genetic algorithm (GA) and multistart gradient-based sequential quadratic programming (SQP) and quasi-Newton (BFGS) algorithms. For the analytical test problems, only the PSO algorithm was successful on the majority of the problems. When compared to previously published results for the same problems, PSO was more robust than a global simulated annealing algorithm but less robust than a different, more complex genetic algorithm. For the biomechanical test problem, only the PSO algorithm was insensitive to design variable scaling, with the GA algorithm being mildly sensitive and the SQP and BFGS algorithms being highly sensitive. The proposed PSO algorithm provides a new off-the-shelf global optimization option for difficult biomechanical problems, especially those utilizing design variables with different length scales or units.     

On the adaptive partition approach to the detection of multiple change-points

With an adaptive partition procedure, we can partition a "time course" into consecutive non-overlapped intervals such that the population means/proportions of the observations in two adjacent intervals are significantly different at a given level . However, the widely used recursive combination or partition procedures do not guarantee a global optimization. We propose a modified dynamic programming algorithm to achieve a global optimization. Our method can provide consistent estimation results. In a comprehensive simulation study, our method shows an improved performance when it is compared to the recursive combination/partition procedures. In practice, can be determined based on a cross-validation procedure. As an application, we consider the well-known Pima Indian Diabetes data. We explore the relationship among the diabetes risk and several important variables including the plasma glucose concentration, body mass index and age.     

Gene regulatory network modeling via global optimization of high-order dynamic Bayesian network

ABSTRACT: BACKGROUND: Dynamic Bayesian network (DBN) is among the mainstream approaches for modeling various biological networks, including the gene regulatory network (GRN). Most current methods for learning DBN employ either local search such as hill-climbing, or a meta stochastic global optimization framework such as genetic algorithm or simulated annealing, which are only able to locate sub-optimal solutions. Further, current DBN applications have essentially been limited to small sized networks. RESULTS: To overcome the above difficulties, we introduce here a deterministic global optimization based DBN approach for reverse engineering genetic networks from time course gene expression data. For such DBN models that consist only of inter time slice arcs, we show that there exists a polynomial time algorithm for learning the globally optimal network structure. The proposed approach, named GlobalMIT+, employs the recently proposed information theoretic scoring metric named mutual information test (MIT). GlobalMIT+ is able to learn high-order time delayed genetic interactions, which are common to most biological systems. Evaluation of the approach using both synthetic and real data sets, including a 733 cyanobacterial gene expression data set, shows significantly improved performance over other techniques. CONCLUSIONS: Our studies demonstrate that deterministic global optimization approaches can infer large scale genetic networks.     

A stochastic online algorithm for unloading boxes from a conveyor line

This article discusses the problem of unloading a sequence of boxes from a single conveyor line with a minimum number of moves. The problem under study is efficiently solvable with dynamic programming if the complete sequence of boxes is known in advance. In practice, however, the problem typically occurs in a real-time setting where the boxes are simultaneously placed on and picked from the conveyor line. Moreover, a large part of the sequence is often not visible. As a result, only a part of the sequence is known when deciding which boxes to move next. We develop an online algorithm that evaluates the quality of each possible move with a scenario-based stochastic method. Two versions of the algorithm are analyzed: in one version, the quality of each scenario is measured with an exact method, while a heuristic technique is applied in the second version. We evaluate the performance of the proposed algorithms using extensive computational experiments and establish a simple policy for determining which version to choose for specific problems. Numerical results show that the proposed approach consistently provides high-quality results, and compares favorably with the best known deterministic online algorithms. Indeed, the new approach typically provides results with relative gaps of 1–5% to the optimum, which is about 20–80% lower than those obtained with the best deterministic approach.     

Designing patterns for profile HMM search

MOTIVATION: Profile HMMs are a powerful tool for modeling conserved motifs in proteins. These models are widely used by search tools to classify new protein sequences into families based on domain architecture. However, the proliferation of known motifs and new proteomic sequence data poses a computational challenge for search, requiring days of CPU time to annotate an organism's proteome. RESULTS: We use PROSITE-like patterns as a filter to speed up the comparison between protein sequence and profile HMM. A set of patterns is designed starting from the HMM, and only sequences matching one of these patterns are compared to the HMM by full dynamic programming. We give an algorithm to design patterns with maximal sensitivity subject to a bound on the false positive rate. Experiments show that our patterns typically retain at least 90% of the sensitivity of the source HMM while accelerating search by an order of magnitude. AVAILABILITY: Contact the first author at the address below.     

Optimization algorithm performance in determining optimal controls in human movement analyses

The objective of this study was to evaluate the performance of different multivariate optimization algorithms by solving a "tracking" problem using a forward dynamic model of pedaling. The tracking problem was defined as solving for the muscle controls (muscle stimulation onset, offset, and magnitude) that minimized the error between experimentally collected kinetic and kinematic data and the simulation results of pedaling at 90 rpm and 250 W. Three different algorithms were evaluated: a downhill simplex method, a gradient-based sequential quadratic programming algorithm, and a simulated annealing global optimization routine. The results showed that the simulated annealing algorithm performed for superior to the conventional routines by converging more rapidly and avoiding local minima.     

ConvAn: a convergence analyzing tool for optimization of biochemical networks

Dynamic models of biochemical networks usually are described as a system of nonlinear differential equations. In case of optimization of models for purpose of parameter estimation or design of new properties mainly numerical methods are used. That causes problems of optimization predictability as most of numerical optimization methods have stochastic properties and the convergence of the objective function to the global optimum is hardly predictable. Determination of suitable optimization method and necessary duration of optimization becomes critical in case of evaluation of high number of combinations of adjustable parameters or in case of large dynamic models. This task is complex due to variety of optimization methods, software tools and nonlinearity features of models in different parameter spaces. A software tool ConvAn is developed to analyze statistical properties of convergence dynamics for optimization runs with particular optimization method, model, software tool, set of optimization method parameters and number of adjustable parameters of the model. The convergence curves can be normalized automatically to enable comparison of different methods and models in the same scale. By the help of the biochemistry adapted graphical user interface of ConvAn it is possible to compare different optimization methods in terms of ability to find the global optima or values close to that as well as the necessary computational time to reach them. It is possible to estimate the optimization performance for different number of adjustable parameters. The functionality of ConvAn enables statistical assessment of necessary optimization time depending on the necessary optimization accuracy. Optimization methods, which are not suitable for a particular optimization task, can be rejected if they have poor repeatability or convergence properties. The software ConvAn is freely available on www.biosystems.lv/convan.     

Non Linear Programming (NLP) Formulation for Quantitative Modeling of Protein Signal Transduction Pathways

Modeling of signal transduction pathways plays a major role in understanding cells'' function and predicting cellular response. Mathematical formalisms based on a logic formalism are relatively simple but can describe how signals propagate from one protein to the next and have led to the construction of models that simulate the cells response to environmental or other perturbations. Constrained fuzzy logic was recently introduced to train models to cell specific data to result in quantitative pathway models of the specific cellular behavior. There are two major issues in this pathway optimization: i) excessive CPU time requirements and ii) loosely constrained optimization problem due to lack of data with respect to large signaling pathways. Herein, we address both issues: the former by reformulating the pathway optimization as a regular nonlinear optimization problem; and the latter by enhanced algorithms to pre/post-process the signaling network to remove parts that cannot be identified given the experimental conditions. As a case study, we tackle the construction of cell type specific pathways in normal and transformed hepatocytes using medium and large-scale functional phosphoproteomic datasets. The proposed Non Linear Programming (NLP) formulation allows for fast optimization of signaling topologies by combining the versatile nature of logic modeling with state of the art optimization algorithms.     

Branch-and-terminate: a combinatorial optimization algorithm for protein design.

BACKGROUND: Several deterministic and stochastic combinatorial optimization algorithms have been applied to computational protein design and homology modeling. As structural targets increase in size, however, it has become necessary to find more powerful methods to address the increased combinatorial complexity. RESULTS: We present a new deterministic combinatorial search algorithm called 'Branch-and-Terminate' (B&T), which is derived from the Branch-and-Bound search method. The B&T approach is based on the construction of an efficient but very restrictive bounding expression, which is used for the search of a combinatorial tree representing the protein system. The bounding expression is used both to determine the optimal organization of the tree and to perform a highly effective pruning procedure named 'termination'. For some calculations, the B&T method rivals the current deterministic standard, dead-end elimination (DEE), sometimes finding the solution up to 21 times faster. A more significant feature of the B&T algorithm is that it can provide an efficient way to complete the optimization of problems that have been partially reduced by a DEE algorithm. CONCLUSIONS: The B&T algorithm is an effective optimization algorithm when used alone. Moreover, it can increase the problem size limit of amino acid sidechain placement calculations, such as protein design, by completing DEE optimizations that reach a point at which the DEE criteria become inefficient. Together the two algorithms make it possible to find solutions to problems that are intractable by either algorithm alone.     

Constrained global optimization for estimating molecular structure from atomic distances.

Finding optimal three-dimensional molecular configurations based on a limited amount of experimental and/or theoretical data requires efficient nonlinear optimization algorithms. Optimization methods must be able to find atomic configurations that are close to the absolute, or global, minimum error and also satisfy known physical constraints such as minimum separation distances between atoms (based on van der Waals interactions). The most difficult obstacles in these types of problems are that 1) using a limited amount of input data leads to many possible local optima and 2) introducing physical constraints, such as minimum separation distances, helps to limit the search space but often makes convergence to a global minimum more difficult. We introduce a constrained global optimization algorithm that is robust and efficient in yielding near-optimal three-dimensional configurations that are guaranteed to satisfy known separation constraints. The algorithm uses an atom-based approach that reduces the dimensionality and allows for tractable enforcement of constraints while maintaining good global convergence properties. We evaluate the new optimization algorithm using synthetic data from the yeast phenylalanine tRNA and several proteins, all with known crystal structure taken from the Protein Data Bank. We compare the results to commonly applied optimization methods, such as distance geometry, simulated annealing, continuation, and smoothing. We show that compared to other optimization approaches, our algorithm is able combine sparse input data with physical constraints in an efficient manner to yield structures with lower root mean squared deviation.     

Chaotic Artificial Bee Colony algorithm: A new approach to the problem of minimization of energy of the 3D protein structure

Prediction of the three-dimensional structure of a protein from its amino acid sequence can be considered as a global optimization problem. In this paper, the Chaotic Artificial Bee Colony (CABC) algorithm was introduced and applied to 3D protein structure prediction. Based on the 3D off-lattice AB model, the CABC algorithm combines global search and local search of the Artificial Bee Colony (ABC) algorithm with the chaotic search algorithm to avoid the problem of premature convergence and easily trapping the local optimum solution. The experiments carried out with the popular Fibonacci sequences demonstrate that the proposed algorithm provides an effective and high-performance method for protein structure prediction.     

A novel ensemble-based scoring and search algorithm for protein redesign and its application to modify the substrate specificity of the gramicidin synthetase a phenylalanine adenylation enzyme.

Realization of novel molecular function requires the ability to alter molecular complex formation. Enzymatic function can be altered by changing enzyme-substrate interactions via modification of an enzyme's active site. A redesigned enzyme may either perform a novel reaction on its native substrates or its native reaction on novel substrates. A number of computational approaches have been developed to address the combinatorial nature of the protein redesign problem. These approaches typically search for the global minimum energy conformation among an exponential number of protein conformations. We present a novel algorithm for protein redesign, which combines a statistical mechanics-derived ensemble-based approach to computing the binding constant with the speed and completeness of a branch-and-bound pruning algorithm. In addition, we developed an efficient deterministic approximation algorithm, capable of approximating our scoring function to arbitrary precision. In practice, the approximation algorithm decreases the execution time of the mutation search by a factor of ten. To test our method, we examined the Phe-specific adenylation domain of the nonribosomal peptide synthetase gramicidin synthetase A (GrsA-PheA). Ensemble scoring, using a rotameric approximation to the partition functions of the bound and unbound states for GrsA-PheA, is first used to predict binding of the wildtype protein and a previously described mutant (selective for leucine), and second, to switch the enzyme specificity toward leucine, using two novel active site sequences computationally predicted by searching through the space of possible active site mutations. The top scoring in silico mutants were created in the wetlab and dissociation/binding constants were determined by fluorescence quenching. These tested mutations exhibit the desired change in specificity from Phe to Leu. Our ensemble-based algorithm, which flexibly models both protein and ligand using rotamer-based partition functions, has application in enzyme redesign, the prediction of protein-ligand binding, and computer-aided drug design.     

Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems

Background  

We consider the problem of parameter estimation (model calibration) in nonlinear dynamic models of biological systems. Due to the frequent ill-conditioning and multi-modality of many of these problems, traditional local methods usually fail (unless initialized with very good guesses of the parameter vector). In order to surmount these difficulties, global optimization (GO) methods have been suggested as robust alternatives. Currently, deterministic GO methods can not solve problems of realistic size within this class in reasonable computation times. In contrast, certain types of stochastic GO methods have shown promising results, although the computational cost remains large. Rodriguez-Fernandez and coworkers have presented hybrid stochastic-deterministic GO methods which could reduce computation time by one order of magnitude while guaranteeing robustness. Our goal here was to further reduce the computational effort without loosing robustness.     

Optimization of feed rate profile for the monoclonal antibody production

The optimal control algorithm to calculate the optimal feed rate profile of nutrient solution containing two limiting nutrients was proposed. Different from other conventional optimization methods, the proposed algorithm calculated the optimal control profiles for different initial and feed conditions. The singular optimal control algorithm, dynamic programming, and nonsingular transformation algorithm were used for the optimization of simple problems of the 4th order and the performances were compared. With the proposed transformation algorithm, the final MAb concentration increased and the CPU time decreased. For the different initial glucose and glutamine conditions, the optimal control profiles were calculated with the proposed transformation algorithm. As the initial glutamine concentration increased, the final MAb concentration also increased due to the cell viability increase. This was also applied to the different feed compositions. When the glutamine concentration was increased in the feed stream, the final MAb concentration also increased.