Thermodynamic calculations in biological systems

The ability to compute intra- and inter-molecular interactions provides the opportunity to gain a deeper understanding of previously intractable problems in biochemistry and biophysics. This review presents three examples in which molecular dynamics calculations were used to gain insight into the atomic detail underlying important experimental observations. The three examples are the following: (1) Entropic contribution to rate acceleration that results from conformational constraints imposed on the reactants; (2) Mechanism of force unfolding of a small protein molecule by the application of a force that separates its N- and C-terminals; and (3) Loss of translational entropy experienced by small molecules when they bind to proteins.     

Thermodynamic calculations for biochemical transport and reaction processes in metabolic networks

Thermodynamic analysis of metabolic networks has recently generated increasing interest for its ability to add constraints on metabolic network operation, and to combine metabolic fluxes and metabolite measurements in a mechanistic manner. Concepts for the calculation of the change in Gibbs energy of biochemical reactions have long been established. However, a concept for incorporation of cross-membrane transport in these calculations is still missing, although the theory for calculating thermodynamic properties of transport processes is long known. Here, we have developed two equivalent equations to calculate the change in Gibbs energy of combined transport and reaction processes based on two different ways of treating biochemical thermodynamics. We illustrate the need for these equations by showing that in some cases there is a significant difference between the proposed correct calculation and using an approximative method. With the developed equations, thermodynamic analysis of metabolic networks spanning over multiple physical compartments can now be correctly described.     

Study of statistical correlations in DNA sequences

Here we present a study of statistical correlations among different positions in DNA sequences and their implications by directly using the autocorrelation function. Such an analysis is possible now because of the availability of large sequences or even complete genomes of many organisms. After describing the way in which the autocorrelation function can be applied to DNA-sequence analysis, we show that long-range correlations, implying scale independence, appear in several bacterial genomes as well as in long human chromosome contigs. The source for such correlations in bacteria, which may extend up to 60 kb in Bacillus subtilis, may be related to massive lateral transfer of compositionally biased genes from other genomes. In the human genome, correlations extend for more than five decades and may be related to the evolution of the ’neogenome’, a modern evolutionary acquisition composed by GC-rich isochores displaying long-range correlations and scale invariance.     

A strategy to optimize the oligo-probes for microarray-based detection of viruses

DNA microarrays have been acknowledged to represent a promising approach for the detection of viral pathogens. However, the probes designed for current arrays could cover only part of the given viral variants, that could result in false-negative or ambiguous data. If all the variants are to be covered, the requirement for more probes would render much higher spot density and thus higher cost of the arrays. Here we have developed a new strategy for oligonucleotide probe design. Using type I human immunodeficiency virus (HIV-1) tat gene as an example, we designed the array probes and validated the optimized parameters in silico. Results show that the oligo number is significantly reduced comparing with the existing methods, while specificity and hybridization efficiency remain intact. The adoption of this method in reducing the oligo numbers could increase the detection capacity for DNA microarrays, and would significantly lower the manufacturing cost for making array chips. These authors contribute equally to the work.     

On statistical energy functions for biomolecular modeling and design

Statistical energy functions are general models about atomic or residue-level interactions in biomolecules, derived from existing experimental data. They provide quantitative foundations for structural modeling as well as for structure-based protein sequence design. Statistical energy functions can be derived computationally either based on statistical distributions or based on variational assumptions. We present overviews on the theoretical assumptions underlying the various types of approaches. Theoretical considerations underlying important pragmatic choices are discussed.     

One- and two-body decomposable Poisson-Boltzmann methods for protein design calculations

Successfully modeling electrostatic interactions is one of the key factors required for the computational design of proteins with desired physical, chemical, and biological properties. In this paper, we present formulations of the finite difference Poisson-Boltzmann (FDPB) model that are pairwise decomposable by side chain. These methods use reduced representations of the protein structure based on the backbone and one or two side chains in order to approximate the dielectric environment in and around the protein. For the desolvation of polar side chains, the two-body model has a 0.64 kcal/mol RMSD compared to FDPB calculations performed using the full representation of the protein structure. Screened Coulombic interaction energies between side chains are approximated with an RMSD of 0.13 kcal/mol. The methods presented here are compatible with the computational demands of protein design calculations and produce energies that are very similar to the results of traditional FDPB calculations.     

Selection for environmental variation: a statistical analysis and power calculations to detect response

Data from uterine capacity in rabbits (litter size) were analyzed to determine whether the environmental variance was partly genetically determined. The fit of a classical homogeneous variance mixed linear (HOM) model and that of a genetically structured heterogeneous variance mixed linear (HET) model were compared. Various methods to assess the quality of fit favor the HET model. The posterior mean (95% posterior interval) of the additive genetic variance affecting the environmental variance was 0.16 (0.10; 0.25) and the corresponding number for the coefficient of correlation between genes affecting mean and variance was -0.74 (-0.90;-0.52). It is argued that stronger support for the HET model than that derived from statistical analysis of data would be provided by a successful selection experiment designed to modify the environmental variance. A simple selection criterion is suggested (average squared deviation from the mean of repeated records within individuals) and its predicted response and variance under the HET model are derived. This is used to determine the appropriate size and length of a selection experiment designed to change the environmental variance. Results from the analytical expressions are compared with those obtained using simulation. There is good agreement provided selection intensity is not intense.     

Thermodynamic criteria for high hit rate antisense oligonucleotide design

Antisense oligonucleotides are used for therapeutic applications and in functional genomic studies. In practice, however, many of the oligonucleotides complementary to an mRNA have little or no antisense activity. Theoretical strategies to improve the ‘hit rate’ in antisense screens will reduce the cost of discovery and may lead to identification of antisense oligonucleotides with increased potency. Statistical analysis performed on data collected from more than 1000 experiments with phosphorothioate-modified oligonucleotides revealed that the oligo-probes, which form stable duplexes with RNA (ΔG^o₃₇ ≤ –30 kcal/mol) and have small self-interaction potential, are more frequently efficient than molecules that form less stable oligonucleotide–RNA hybrids or more stable self-structures. To achieve optimal statistical preference, the values for self-interaction should be (ΔG^o₃₇) ≥ –8 kcal/mol for inter-oligonucleotide pairing and (ΔG^o₃₇) ≥ –1.1 kcal/mol for intra-molecular pairing. Selection of oligonucleotides with these thermodynamic values in the analyzed experiments would have increased the ‘hit rate’ by as much as 6-fold.     

An overview of statistical approaches for adaptive designs and design modifications

With adaptive design methods for clinical trials, design elements such as sample size or further interim sample sizes may be changed during the course of the trial depending on all previously collected data. The focus of the overview is on group sequential approaches where the types of adaptations need not be specified in advance. An overview of the different statistical approaches for adaptive design methods proposed in the literature is given, relations between these methods are described and some perspectives of application and for future research are discussed.     

Thermodynamic cycle analysis and inhibitor design against beta-lactamase

Beta-lactamases are the most widespread resistance mechanism to beta-lactam antibiotics, such as the penicillins and cephalosporins. Transition-state analogues that bind to the enzymes with nanomolar affinities have been introduced in an effort to reverse the resistance conferred by these enzymes. To understand the origins of this affinity, and to guide design of future inhibitors, double-mutant thermodynamic cycle experiments were undertaken. An unexpected hydrogen bond between the nonconserved Asn289 and a key inhibitor carboxylate was observed in the X-ray crystal structure of a 1 nM inhibitor (compound 1) in complex with AmpC beta-lactamase. To investigate the energy of this hydrogen bond, the mutant enzyme N289A was made, as was an analogue of 1 that lacked the carboxylate (compound 2). The differential affinity of the four different protein and analogue complexes indicates that the carboxylate-amide hydrogen bond contributes 1.7 kcal/mol to overall binding affinity. Synthesis of an analogue of 1 where the carboxylate was replaced with an aldehyde led to an inhibitor that lost all this hydrogen bond energy, consistent with the importance of the ionic nature of this hydrogen bond. To investigate the structural bases of these energies, X-ray crystal structures of N289A/1 and N289A/2 were determined to 1.49 and 1.39 A, respectively. These structures suggest that no significant rearrangement occurs in the mutant versus the wild-type complexes with both compounds. The mutant enzymes L119A and L293A were made to investigate the interaction between a phenyl ring in 1 and these residues. Whereas deletion of the phenyl itself diminishes affinity by 5-fold, the double-mutant cycles suggest that this energy does not come through interaction with the leucines, despite the close contact in the structure. The energies of these interactions provide key information for the design of improved inhibitors against beta-lactamases. The high magnitude of the ion-dipole interaction between Asn289 and the carboxylate of 1 is consistent with the idea that ionic interactions can provide significant net affinity in inhibitor complexes.     

Information theory reveals large-scale synchronisation of statistical correlations in eukaryote genomes

We study short-range correlations in DNA sequences with methods from information theory and statistics. We find a persisting degree of identity between the correlation patterns of different chromosomes of a species. Except for the case of human and chimpanzee inter-species differences in this correlation pattern allow robust species distinction: in a clustering tree based upon the correlation curves on the level of individual chromosomes distinct clusters for the individual species are found. This capacity of distinguishing species persists, even when the length of the underlying sequences is drastically reduced. In comparison to the standard tool for studying symbol correlations in DNA sequences, namely the mutual information function, we find that an autoregressive model for higher order Markov processes significantly improves species distinction due to an implicit subtraction of random background.     

Guidelines for the design and statistical analysis of experiments using laboratory animals

For ethical and economic reasons, it is important to design animal experiments well, to analyze the data correctly, and to use the minimum number of animals necessary to achieve the scientific objectives---but not so few as to miss biologically important effects or require unnecessary repetition of experiments. Investigators are urged to consult a statistician at the design stage and are reminded that no experiment should ever be started without a clear idea of how the resulting data are to be analyzed. These guidelines are provided to help biomedical research workers perform their experiments efficiently and analyze their results so that they can extract all useful information from the resulting data. Among the topics discussed are the varying purposes of experiments (e.g., exploratory vs. confirmatory); the experimental unit; the necessity of recording full experimental details (e.g., species, sex, age, microbiological status, strain and source of animals, and husbandry conditions); assigning experimental units to treatments using randomization; other aspects of the experiment (e.g., timing of measurements); using formal experimental designs (e.g., completely randomized and randomized block); estimating the size of the experiment using power and sample size calculations; screening raw data for obvious errors; using the t-test or analysis of variance for parametric analysis; and effective design of graphical data.     

EDIBLE: experimental design and information calculations in phylogenetics

SUMMARY: Although evolutionary inference from molecular sequences is a statistical problem, little attention has been paid to questions of experimental design. A computer program, EDIBLE, has been developed to perform likelihood calculations based on Markov process models of nucleotide substitution allied with phylogenetic trees, and from these to compute Fisher information measures under different experimental designs. These calculations can be used to answer questions of optimal experimental design in molecular phylogenetics. AVAILABILITY: Source code (ANSI C), executables and documentation for EDIBLE are available from http://ng-dec1.gen.cam. ac.uk/info/index.htmland 'downstream' Web pages. CONTACT: N.Goldman@gen.cam.ac.uk     

Geometrical correlations useful for design of sequence-specific DNA narrow groove binding ligands

Isohelical geometry of sequence-specific DNA narrow groove binding ligands was analyzed in terms of H-bond donor/acceptor complementarity between the base pair atoms facing into the narrow groove and the corresponding H-bond donating atoms regularly disposed along the ligand molecule. Spatial correlations found in analytical form were applied to analysis of naturally occurring and hypothetical drug molecule structures. For the case of B-like isohelices the permitted values of the distance L0 between each two neighboring H-bond donating atoms of the ligand as well as the bending angle tau 0 of the line subsequently connecting these atoms were estimated as follows: L0 congruent to (5.0 +/- 0.4) A; tau 0 congruent to (26 +/- 2) degrees.     

The micronucleus test: statistical design and analysis.

Alternative statistical procedures are discussed which may be employed to compare the incidences among treatment groups of micronucleated polychromatic and normochromatic erythrocytes and their ratios. Comparison of incidences of micronucleated polychromatic erythrocytes using a sequential sampling strategy based on the negative binomial distribution is shown to require fewer animals for the same sensitivity of test than a similar procedure based on the binomial distribution. The sequential test is superior, both in power and number of animals required, to an alternative 1-stage test based on the same distribution. The procedure described permits the investigator to optimize the number of animals in each test group and the number of cells counted per animal to detect a predetermined increase in the incidence of micronucleated cells over that observed in the control population within chosen limits of type I and type II error. An alternative sequential approach based on the binomial distribution is presented, which is applicable when the number of cells analyzed per animal is variable.     

Thermodynamic integration calculations of binding free energy difference for Gly-169 mutation in subtilisin BPN′

The binding free energy difference for the Gly-169 → Ala-169 (G169A) mutation in subtilisin BPN′ complexed with a tripeptide substrate analogue is explored using the thermodynamic integration approach. The structure of the mutant enzyme–substrate complex obtained from free energy simulation is in good agreement with experimental X-ray refinement. The near perfect reversibility is obtained in the present work for ensuring the correctness of the free energy calculations. The results of the binding free energy difference are close to similar experimental data. © 1993 Wiley-Liss, Inc.