Sampling and efficiency of metric matrix distance geometry: A novel partial metrization algorithm

Summary In this paper, we present a reassessment of the sampling properties of the metric matrix distance geometry algorithm, which is in wide-spread use in the determination of three-dimensional structures from nuclear magnetic resonance (NMR) data. To this end, we compare the conformational space sampled by structures generated with a variety of metric matrix distance geometry protocols. As test systems we use an unconstrained polypeptide, and a small protein (rabbit neutrophil defensin peptide 5) for which only few tertiary distances had been derived from the NMR data, allowing several possible folds of the polypeptide chain. A process called metrization in the preparation of a trial distance matrix has a very large effect on the sampling properties of the algorithm. It is shown that, depending on the metrization protocol used, metric matrix distance geometry can have very good sampling properties'indeed, both for the unconstrained model system and the NMR-structure case. We show that the sampling properties are to a great degree determined by the way in which the first few distances are chosen within their bounds. Further, we present a new protocol (partial metrization) that is computationally more efficient but has the same excellent sampling properties. This novel protocol has been implemented in an expanded new release of the program X-PLOR with distance geometry capabilities.     

Extensive distance geometry calculations with different NOE calibrations: New criteria for structure selection applied to Sandostatin and BPTI

Summary To generate structures efficiently, a version of the distance geometry program DIANA for a parallel computer was developed, new objective criteria for the selection of NMR solution structures are presented, and the influence of using different calibrations of NOE intensities on the final structures are described. The methods are applied to the structure determination of Sandostatin, a disulfide-bridge octapeptide, and to model calculations of BPTI. On an Alliant FX2800 computer using 10 processors in parallel, the calculations were done 9.2 times faster than with a single processor. Up to 7000 Sandostatin structures were calculated with distance and angular constraints. The procedure for selecting acceptable structures is based on the maximum values of pairwise RMSDs between structures. Suitable target function cut-offs are defined independent of the number of starting structures. The method allowed for an objective comparison of three groups of Sandostatin structures that were calculated from different sets of upper distance constraints which were derived from the same NOE intensity data using three empirical calibration curves. The number of converged structures and the target function values differed significantly among the three groups, but the structures were qualitatively and quantitatively very similar. The conformation is well determined in the cyclic region Cys²–Cys⁷ and adopts a -turn centered at d-Trp⁴–Lys⁵. The criteria for structure selection were further tested with BPTI. Results obtained from sets of structures calculated with and without using the REDAC strategy are consistent and suggest that the structure selection method is objective and generally applicable.     

Modelling zinc-binding proteins with GADGET: genetic algorithm and distance geometry for exploring topology

A novel combination of optimization methods (Genetic Algorithm with Distance Geometry) has been developed and shown to find near-optimal solutions to a set of imposed structural constraints. With this modelling tool (GADGET), the fold-space of a variety of small zinc-binding proteins was investigated under the constraints required to form a zinc-binding site (or pair of sites). Analysis of the results concentrated on the ring-finger domain as the "classic" zinc-finger domains were too constrained to provide much topological variety, whilst the TFIIH domain (which has large unstructured loops) did not behave well. The intermediate ring-finger domain, however, was found to adopt a variety of different folds, many of which had near-optimal scores under the fitness function employed in GADGET (forming good secondary structures and zinc-coordination). Although the native fold was dominant amongst the solutions, the discovery of good alternate folds shows that even the eight residues constrained to form two zinc-binding sites was not sufficient to uniquely determine the native fold. Despite this, the fold-space of 48 theoretically possible folds was greatly reduced with just six topologies found in significant numbers.     

Intrinsic nature of the three-dimensional structure of proteins as determined by distance geometry with good sampling properties

Summary A protocol for distance geometry calculation is shown to have excellent sampling properties in the determination of three-dimensional structures of proteins from nuclear magnetic resonance (NMR) data. This protocol uses a simulated annealing optimization employing mass-weighted molecular dynamics in four-dimensional space (Havel, T.F. (1991) Prog. Biophys. Mol. Biol., 56, 43–78). It attains an extremely large radius of convergence, allowing a random coil conformation to be used as the initial estimate for the succeeding optimization process. Computations are performed with four systems of simulated distance data as tests of the protocol, using an unconstrained l-alanine 30mer and three different types of proteins, bovine pancreatic trypsin inhibitor, the -amylase inhibitor Tendamistat, and the N-terminal domain of the 434-repressor. The test of the unconstrained polypeptide confirms that the sampled conformational space is that of the statistical random coil. In the larger and more complicated systems of the three proteins, the protocol gives complete convergence of the optimization without any trace of initial structure dependence. As a result of an exhaustive conformational sampling by the protocol, the intrinsic nature of the structures generated with distance restraints derived from NMR data has been revealed. When the sampled structures are compared with the corresponding X-ray structures, we find that the averages of the sampled structures always show a certain pattern of discrepancy from the X-ray structure. This discrepancy is due to the short distance nature of the distance restraints, and correlates with the characteristic shape of the protein molecule.Abbreviations r.m.s.d. root-mean-square deviation - MD molecular dynamics - NMR nuclear magnetic resonance - NOE nuclear Overhauser enhancement - BPTI bovine pancreatic trypsin inhibitor     

Habitat geometry, population viscosity and the rate of genetic drift

In all natural populations, individuals located close to one another tend to interact more than those further apart. The extent of population viscosity can have important implications for ecological and evolutionary processes. Here we develop a spatially explicit population model to examine how the rate of genetic drift depends upon both spatial population structure and habitat geometry. The results show that the time to fixation for a new and selectively neutral mutation is dramatically increased in viscous populations. Furthermore, in viscous populations the time to fixation depends critically on habitat geometry. Fixation time for populations of identical size increases markedly as landscape width decreases and length increases. We suggest that similar effects will also be important in metapopulations, with the spatial arrangement of subpopulations and their connectivity likely to determine the rate of drift. We argue that the recent increases in computer power should facilitate major advances in our understanding of evolutionary landscape ecology over the next few years, and suggest that the time is ripe for a unification of spatial population dynamics theory, landscape ecology and population genetics.     

Analysis of the evolution of the thrombin-inhibiting DNA aptamers using a genetic algorithm

We previously identified a thrombin-inhibiting DNA aptamer that was presumed to form a G-quartet structure with a duplex. To investigate the importance of the sequences in the duplex region and to obtain aptamers with higher inhibitory activities, we randomized the sequences of the duplex region of this aptamer and carried out selection based on inhibitory activity using a genetic algorithm. This method consisted of selection via an inhibition assay, crossover, and mutation in silico. After two cycles, we obtained ligands with greater inhibitory activities than that of the original aptamer. In addition, the duplex sequences were found to contribute to the inhibitory activities of aptamers.     

Comparison of distance matrices in studies of population structure and genetic microdifferentiation: quadratic assignment

Questions concerning the relative effects of various evolutionary forces in molding the genetic variability exhibited by groups of human populations have typically been investigated by comparing a variety of genetic and cultural/historical "distance" matrices. A major methodological difficulty has been the lack of formal testing procedures with which to assess the degree of confirmation or disconfirmation of an estimated measure of relationship between such matrices. In this paper, we examine a very flexible matrix combinatorial procedure which generates statistical significance levels for correlational measures of pattern similarity between distance matrices. A recent generalization of the basic procedure to the three-matrix case allows questions concerning which of two matrices best fits a third matrix to be formally tested. Applications of these hypothesis testing and inference procedures to two separate sets of genetic, geographic, and cultural distance matrices illustrates their potential for finally solving a long-standing problem in anthropological genetics.     

Genetic distance: probing the origin of a Papua New Guinea isolate

In an attempt to elucidate the origin of an isolated peripheral Highland, Papua New Guinea population (the Karimui), HLA, blood group and serum protein markers were investigated. Due to the paucity of published HLA marker data, genetic distances using non-HLA markers were constructed between populations surrounding the Karimui and compared in 3-dimensions by multidimensional scaling analysis. Genetically, the Karimui is most closely associated with Highland populations to the east and northeast. In a attempt to develop a more global view of relationships, distances constructed from HLA marker data between 2 close Highland populations, 2 Coastal Papua New Guinea populations and 4 Australian aborigine populations were compared. The Karimui associated most closely with the Highland populations and equidistantly and at opposite poles from both the Coastal Papuan and aborigine populations. A paradigm of the composition of the founder group and the early population dynamics is developed from genetic, linguistic and anthropologic data.     

Maximizing microbial degradation of perchlorate using a genetic algorithm: Media optimization

Microbial communities are under constant influence of physical and chemical components in ecosystems. Shifts in conditions such as pH, temperature or carbon source concentration can translate into shifts in overall ecosystem functioning. These conditions can be manipulated in a laboratory setup using evolutionary computation methods such as genetic algorithms (GAs). In work described here, a GA methodology was successfully applied to define sets of environmental conditions for microbial enrichments and pure cultures to achieve maximum rates of perchlorate degradation. Over the course of 11 generations of optimization using a GA, we saw a statistically significant 16.45 and 16.76-fold increases in average perchlorate degradation rates by Dechlorosoma sp. strain KJ and Dechloromonas sp. strain Miss R, respectively. For two bacterial consortia, Pl6 and Cw3, 5.79 and 5.75-fold increases in average perchlorate degradation were noted. Comparison of zero-order kinetic rate constants for environmental conditions in GA-determined first and last generations of all bacterial cultures additionally showed marked increases.     

Significant factors selection in the chemical and enzymatic hydrolysis of lignocellulosic residues by a genetic algorithm analysis and comparison with the standard Plackett-Burman methodology

A comparison between the classic Plackett-Burman design (PB) ANOVA analysis and a genetic algorithm (GA) approach to identify significant factors have been carried out. This comparison was made by applying both analyses to data obtained from the experimental results when optimizing both chemical and enzymatic hydrolysis of three lignocellulosic feedstocks (corn and wheat bran, and pine sawdust) by a PB experimental design. Depending on the kind of biomass and the hydrolysis being considered, different results were obtained. Interestingly, some interactions were found to be significant by the GA approach and allowed to identify significant factors, that otherwise, based only in the classic PB analysis, would have not been taken into account in a further optimization step. Improvements in the fitting of c.a. 80% were obtained when comparing the coefficient of determination (R2) computed for both methods.     

Study of the genetic code adaptability by means of a genetic algorithm

We used simulated evolution to study the adaptability level of the canonical genetic code. An adapted genetic algorithm (GA) searches for optimal hypothetical codes. Adaptability is measured as the average variation of the hydrophobicity that the encoded amino acids undergo when errors or mutations are present in the codons of the hypothetical codes. Different types of mutations and point mutation rates that depend on codon base number are considered in this study. Previous works have used statistical approaches based on randomly generated alternative codes or have used local search techniques to determine an optimum value. In this work, we emphasize what can be concluded from the use of simulated evolution considering the results of previous works. The GA provides more information about the difficulty of the evolution of codes, without contradicting previous studies using statistical or engineering approaches. The GA also shows that, within the coevolution theory, the third base clearly improves the adaptability of the current genetic code.     

Limited sampling of conformational space by the distance geometry algorithm: implications for structures generated from NMR data

Calculations with a metric matrix distance geometry algorithm were performed that show that the standard implementation of the algorithm generally samples a very limited region of conformational space. This problem is most severe when only a small amount of distance information is used as input for the algorithm. Control calculations were performed on linear peptides, disulfide-linked peptides, and a double-stranded DNA decamer where only distances defining the covalent structures of the molecules (as well as the hydrogen bonds for the base pairs in the DNA) were included as input. Since the distance geometry algorithm is commonly used to generate structures of biopolymers from distance data obtained from NMR experiments, simulations were performed on the small globular protein basic pancreatic trypsin inhibitor (BPTI) that mimic calculations performed with actual NMR data. The results on BPTI and on the control peptides indicate that the standard implementation of the algorithm has two main problems: first, that it generates extended structures; second, that it has a tendency to consistently produce similar structures instead of sampling all structures consistent with the input distance information. These results also show that use of a simple root-mean-square deviation for evaluating the quality of the structures generated from NMR data may not be generally appropriate. The main sources of these problems are identified, and our results indicate that the problems are not a fundamental property of the distance geometry algorithm but arise from the implementations presently used to generate structures from NMR data. Several possible methods for alleviating these problems are discussed.     

Protein refolding in silico with atom-based statistical potentials and conformational search using a simple genetic algorithm

A distance-dependent atom-pair potential that treats long range and local interactions separately has been developed and optimized to distinguish native protein structures from sets of incorrect or decoy structures. Atoms are divided into 30 types based on chemical properties and relative position in the amino acid side-chains. Several parameters affecting the calculation and evaluation of this statistical potential, such as the reference state, the bin width, cutoff distances between pairs, and the number of residues separating the atom pairs, are adjusted to achieve the best discrimination. The native structure has the lowest energy for 39 of the 40 sets of original ROSETTA decoys (1000 structures per set) and 23 of the 25 improved decoys (approximately 1900 structures per set). Combined with the orientation-dependent backbone hydrogen bonding potential used by ROSETTA and a statistical solvation potential based on the solvent exclusion model of Lazaridis & Karplus, this potential is used as a scoring function for conformational search based on a genetic algorithm method. After unfolding the native structure by changing every phi and psi angle by either +/-3, +/-5 or +/-7 degrees, five small proteins can be efficiently refolded, in some cases to within 0.5 A C(alpha) distance matrix error (DME) to the native state. Although no significant correlation is found between the total energy and structural similarity to the native state, a surprisingly strong correlation exists between the radius of gyration and the DME for low energy structures.     

The use of a genetic algorithm search for molecular mechanics (MM3)-based conformational analysis of oligosaccharides

We have implemented a system called glygal that can perform conformational searches on oligosaccharides using several different genetic algorithm (GA) search methods. The searches are performed in the torsion angle conformational space, considering both the primary glycosidic linkages as well as the pendant groups (C-5-C-6 and hydroxyl groups) where energy calculations are performed using the MM3(96) force field. The system includes a graphical user interface for setting calculation parameters and incorporates a 3D molecular viewer. The system was tested using dozens of structures and we present two case studies for two previously investigated O-specific oligosaccharides of the Shigella dysenteriae type 2 and 4. The results obtained using glygal show a significant reduction in the number of structures that need to be sampled in order to find the best conformation, as compared to filtered systematic search.     

Three-dimensional structure of a DNA hairpin in solution: two-dimensional NMR studies and distance geometry calculations on d(CGCGTTTTCGCG)

The three-dimensional structure of d(CGCGTTTTCGCG) in solution has been determined from proton NMR data by using distance geometry methods. The rate of dipolar cross-relaxation between protons close together in space is used to calculate distances between proton pairs within 5 A of each other; these distances are used as input to a distance geometry algorithm that embeds this distance matrix in three-dimensional space. The resulting refined structures that best agree with the input distances are all very similar to each other and show that the DNA sequence forms a hairpin in solution; the bases of the loop region are stacked, and the stem region forms a right-handed helix. The advantages and limitations of the technique, as well as the computer requirements of the algorithm, are discussed.     

Medium optimization for the production of the aroma compound 2-phenylethanol using a genetic algorithm

Using a genetic algorithm, 13 medium constituents and the temperature were varied to improve the bioconversion of -phenylalanine ( -phe) to 2-phenylethanol (2-PE) with Kluyveromyces marxianus CBS 600. Within four generations plus an additional temperature screening, corresponding to 98 parallel experiments altogether, a maximum 2-PE concentration of 5.6 g/l, equivalent to an increase of 87% compared to the non-optimized medium was obtained. The vitamin content of the medium had to be raised significantly.     

Efficient clustering in collaborative filtering recommender system: Hybrid method based on genetic algorithm and gravitational emulation local search algorithm

The ultimate goal of the Recommender System (RS) is to offer a proposal that is very close to the user's real opinion. Data clustering can be effective in increasing the accuracy of production proposals by the RS. In this paper, single-objective hybrid evolutionary approach is proposed for clustering items in the offline collaborative filtering RS. This method, after generating a population of randomized solutions, at each iteration, improves the population of solutions first by Genetic Algorithm (GA) and then by using the Gravitational Emulation Local Search (GELS) algorithm. Simulation results on standard datasets indicate that although the proposed hybrid meta-heuristic algorithm requires a relatively high run time, it can lead to more appropriate clustering of existing data and thus improvement of the Mean Absolute Error (MAE), Root Mean Square Error (RMSE) and Coverage criteria.     

Application of a clustering-based peak alignment algorithm to analyze various DNA fingerprinting data

DNA fingerprinting analysis such as amplified ribosomal DNA restriction analysis (ARDRA), repetitive extragenic palindromic PCR (rep-PCR), ribosomal intergenic spacer analysis (RISA), and denaturing gradient gel electrophoresis (DGGE) are frequently used in various fields of microbiology. The major difficulty in DNA fingerprinting data analysis is the alignment of multiple peak sets. We report here an R program for a clustering-based peak alignment algorithm, and its application to analyze various DNA fingerprinting data, such as ARDRA, rep-PCR, RISA, and DGGE data. The results obtained by our clustering algorithm and by BioNumerics software showed high similarity. Since several R packages have been established to statistically analyze various biological data, the distance matrix obtained by our R program can be used for subsequent statistical analyses, some of which were not previously performed but are useful in DNA fingerprinting studies.     

Dead reckoning in a small mammal: the evaluation of distance

When hoarding food under infra-red light, golden hamsters Mesocricetus auratus W. return fairly directly from a feeding place to their nest site by evaluating and updating internal signals that they have generated during the previous outward journey to the feeding place. To test more specifically the animals' capacity to evaluate the linear components of the outward journey, the subjects were led from their (cone-shaped) nest to a feeding place along a detour which comprised either 2 (experiment 1) or 5 (experiment 2) segments; adjoining segments were at right angles to each other. In these conditions, the subjects remained significantly oriented towards the nest and therefore were capable of assessing translations as well as rotations during the outward journey. In experiment 3, the nest was removed after the hamsters had started the direct outward journey to the feeding place and the hamsters were rotated during the food uptake. The animals were no longer oriented towards the starting point of their journey, but nonetheless covered, along a fairly straight path, the correct homing distance, and then changed over to a circular search path. These results confirm that mammals can derive the linear components of an outward journey from self-generated signals and therefore are able to judge the homing distance without relying on cues from the environment. For a number of detour outward journeys, our data yield an unexpectedly good fit to Müller and Wehner's (1988) model of dead reckoning in ants. However, this is no longer the case when the outward journey contains an initial loop which brings the subject back to the starting point. These findings are discussed in terms of the biological significance and limitations of an approximate form of path integration.