Statistical analysis of over-represented words in human promoter sequences

The identification and characterization of regulatory sequence elements in the proximal promoter region of a gene can be facilitated by knowing the precise location of the transcriptional start site (TSS). Using known TSSs from over 5700 different human full-length cDNAs, this study extracted a set of 4737 distinct putative promoter regions (PPRs) from the human genome. Each PPR consisted of nucleotides from -2000 to +1000 bp, relative to the corresponding TSS. Since many regulatory regions contain short, highly conserved strings of less than 10 nucleotides, we counted eight-letter words within the PPRs, using z-scores and other related statistics to evaluate their over- and under-representation. Several over-represented eight-letter words have known biological functions described in the eukaryotic transcription factor database TRANSFAC; however, many did not. Besides calculating a P-value with the standard normal approximation associated with z-scores, we used two extra statistical controls to evaluate the significance of over-represented words. These controls have important implications for evaluating over- and under-represented words with z-scores.

Conserved fragments of transposable elements in intergenic regions: evidence for widespread recruitment of MIR- and L2-derived sequences within the mouse and human genomes

We analysed the distribution of transposable elements (TEs) in 100 aligned pairs of orthologous intergenic regions from the mouse and human genomes. Within these regions, conserved segments of high similarity between the two species alternate with segments of low similarity. Identifiable TEs comprise 40-60% of segments of low similarity. Within such segments, a particular copy of a TE found in one species has no orthologue in the other. Overall, TEs comprise only approximately 20 % of conserved segments. However, TEs from two families, MIR and L2, are rather common within conserved segments. Statistical analysis of the distributions of TEs suggests that a majority of the MIR and L2 elements present in murine intergenic regions have human orthologues. These elements must have been present in the common ancestor of human and mouse and have remained under substantial negative selection that prevented their divergence beyond recognition. If so, recruitment of MIR- and L2-derived sequences to perform a function that increases host fitness is rather common, with at least two such events per host gene. The central part of the MIR consensus sequence is over-represented in conserved segments given its background frequency in the genome, suggesting that it is under the strongest selective constraint.

Finding functional sequence elements by multiple local alignment

Algorithms that detect and align locally similar regions of biological sequences have the potential to discover a wide variety of functional motifs. Two theoretical contributions to this classic but unsolved problem are presented here: a method to determine the width of the aligned motif automatically; and a technique for calculating the statistical significance of alignments, i.e. an assessment of whether the alignments are stronger than those that would be expected to occur by chance among random, unrelated sequences. Upon exploring variants of the standard Gibbs sampling technique to optimize the alignment, we discovered that simulated annealing approaches perform more efficiently. Finally, we conduct failure tests by applying the algorithm to increasingly difficult test cases, and analyze the manner of and reasons for eventual failure. Detection of transcription factor-binding motifs is limited by the motifs' intrinsic subtlety rather than by inadequacy of the alignment optimization procedure.

The correlation error and finite-size correction in an ungapped sequence alignment

MOTIVATION

The BLAST program for comparing two sequences assumes independent sequences in its random model. The resulting random alignment matrices have correlations across their diagonals. Analytic formulas for the BLAST p-value essentially neglect these correlations and are equivalent to a random model with independent diagonals. Progress on the independent diagonals model has been surprisingly rapid, but the practical magnitude of the correlations it neglects remains unknown. In addition, BLAST uses a finite-size correction that is particularly important when either of the sequences being compared is short. Several formulas for the finite-size correction have now been given, but the corresponding errors in the BLAST p-values have not been quantified. As the lengths of compared sequences tend to infinity, it is also theoretically unknown whether the neglected correlations vanish faster than the finite-size correction.

RESULTS

Because we required certain analytic formulas, our study restricted its computer experiments to ungapped sequence alignment. We expect some of our conclusions to extend qualitatively to gapped sequence alignment, however. With this caveat, the finite-size correction appeared to vanish faster than the neglected correlations. Although the finite-size correction underestimated the BLAST p-value, it improved the approximation substantially for all but very short sequences. In practice, the Altschul-Gish finite-size correction was superior to Spouge's. The independent diagonals model was always within a factor of 2 of the true BLAST p-value, although fitting p-value parameters from it probably is unwise.

CONTACT

spouge@ncbi.nlm.nih.gov

Statistical significance of clusters of motifs represented by position specific scoring matrices in nucleotide sequences

The human genome encodes the transcriptional control of its genes in clusters of cis-elements that constitute enhancers, silencers and promoter signals. The sequence motifs of individual cis- elements are usually too short and degenerate for confident detection. In most cases, the requirements for organization of cis-elements within these clusters are poorly understood. Therefore, we have developed a general method to detect local concentrations of cis-element motifs, using predetermined matrix representations of the cis-elements, and calculate the statistical significance of these motif clusters. The statistical significance calculation is highly accurate not only for idealized, pseudorandom DNA, but also for real human DNA. We use our method 'cluster of motifs E-value tool' (COMET) to make novel predictions concerning the regulation of genes by transcription factors associated with muscle. COMET performs comparably with two alternative state-of-the-art techniques, which are more complex and lack E-value calculations. Our statistical method enables us to clarify the major bottleneck in the hard problem of detecting cis-regulatory regions, which is that many known enhancers do not contain very significant clusters of the motif types that we search for. Thus, discovery of additional signals that belong to these regulatory regions will be the key to future progress.

The efficient computation of position-specific match scores with the fast fourier transform

Historically, in computational biology the fast Fourier transform (FFT) has been used almost exclusively to count the number of exact letter matches between two biosequences. This paper presents an FFT algorithm that can compute the match score of a sequence against a position-specific scoring matrix (PSSM). Our algorithm finds the PSSM score simultaneously over all offsets of the PSSM with the sequence, although like all previous FFT algorithms, it still disallows gaps. Although our algorithm is presented in the context of global matching, it can be adapted to local matching without gaps. As a benchmark, our PSSM-modified FFT algorithm computed pairwise match scores. In timing experiments, our most efficient FFT implementation for pairwise scoring appeared to be 10 to 26 times faster than a traditional FFT implementation, with only a factor of 2 in the acceleration attributable to a previously known compression scheme. Many important algorithms for detecting biosequence similarities, e.g., gapped BLAST or PSIBLAST, have a heuristic screening phase that disallows gaps. This paper demonstrates that FFT algorithms merit reconsideration in these screening applications.

Improving the accuracy of PSI-BLAST protein database searches with composition-based statistics and other refinements

PSI-BLAST is an iterative program to search a database for proteins with distant similarity to a query sequence. We investigated over a dozen modifications to the methods used in PSI-BLAST, with the goal of improving accuracy in finding true positive matches. To evaluate performance we used a set of 103 queries for which the true positives in yeast had been annotated by human experts, and a popular measure of retrieval accuracy (ROC) that can be normalized to take on values between 0 (worst) and 1 (best). The modifications we consider novel improve the ROC score from 0.758 +/- 0.005 to 0.895 +/- 0.003. This does not include the benefits from four modifications we included in the 'baseline' version, even though they were not implemented in PSI-BLAST version 2.0. The improvement in accuracy was confirmed on a small second test set. This test involved analyzing three protein families with curated lists of true positives from the non-redundant protein database. The modification that accounts for the majority of the improvement is the use, for each database sequence, of a position-specific scoring system tuned to that sequence's amino acid composition. The use of composition-based statistics is particularly beneficial for large-scale automated applications of PSI-BLAST.

Lineage-specific gene expansions in bacterial and archaeal genomes

Gene duplication is an important mechanistic antecedent to the evolution of new genes and novel biochemical functions. In an attempt to assess the contribution of gene duplication to genome evolution in archaea and bacteria, clusters of related genes that appear to have expanded subsequent to the diversification of the major prokaryotic lineages (lineage-specific expansions) were analyzed. Analysis of 21 completely sequenced prokaryotic genomes shows that lineage-specific expansions comprise a substantial fraction (approximately 5%-33%) of their coding capacities. A positive correlation exists between the fraction of the genes taken up by lineage-specific expansions and the total number of genes in a genome. Consistent with the notion that lineage-specific expansions are made up of relatively recently duplicated genes, >90% of the detected clusters consists of only two to four genes. The more common smaller clusters tend to include genes with higher pairwise similarity (as reflected by average score density) than larger clusters. Regardless of size, cluster members tend to be located more closely on bacterial chromosomes than expected by chance, which could reflect a history of tandem gene duplication. In addition to the small clusters, almost all genomes also contain rare large clusters of size > or =20. Several examples of the potential adaptive significance of these large clusters are explored. The presence or absence of clusters and their related genes was used as the basis for the construction of a similarity graph for completely sequenced prokaryotic genomes. The topology of the resulting graph seems to reflect a combined effect of common ancestry, horizontal transfer, and lineage-specific gene loss.

Candidate regulatory sequence elements for cell cycle-dependent transcription in Saccharomyces cerevisiae

Recent developments in genome-wide transcript monitoring have led to a rapid accumulation of data from gene expression studies. Such projects highlight the need for methods to predict the molecular basis of transcriptional coregulation. A microarray project identified the 420 yeast transcripts whose synthesis displays cell cycle-dependent periodicity. We present here a statistical technique we developed to identify the sequence elements that may be responsible for this cell cycle regulation. Because most gene regulatory sites contain a short string of highly conserved nucleotides, any such strings that are involved in gene regulation will occur frequently in the upstream regions of the genes that they regulate, and rarely in the upstream regions of other genes. Our strategy therefore utilizes statistical procedures to identify short oligomers, five or six nucleotides in length, that are over-represented in upstream regions of genes whose expression peaks at the same phase of the cell cycle. We report, with a high level of confidence, that 9 hexamers and 12 pentamers are over-represented in the upstream regions of genes whose expression peaks at the early G(1), late G(1), S, G(2), or M phase of the cell cycle. Some of these sequence elements show a preference for a particular orientation, and others, through a separate statistical test, for a particular position upstream of the ATG start codon. The finding that the majority of the statistically significant sequence elements are located in late G(1) upstream regions correlates with other experiments that identified the late G(1)/early S boundary as a vital cell cycle control point. Our results highlight the importance of MCB, an element implicated previously in late G(1)/early S gene regulation, as most of the late G(1) oligomers contain the MCB sequence or variations thereof. It is striking that most MCB-like sequences localize to a specific region upstream of the ATG start codon. Additional sequences that we have identified may be important for regulation at other phases of the cell cycle.

Candidate Regulatory Sequence Elements for Cell Cycle-Dependent Transcription in Saccharomyces cerevisiae

Recent developments in genome-wide transcript monitoring have led to a rapid accumulation of data from gene expression studies. Such projects highlight the need for methods to predict the molecular basis of transcriptional coregulation. A microarray project identified the 420 yeast transcripts whose synthesis displays cell cycle-dependent periodicity. We present here a statistical technique we developed to identify the sequence elements that may be responsible for this cell cycle regulation. Because most gene regulatory sites contain a short string of highly conserved nucleotides, any such strings that are involved in gene regulation will occur frequently in the upstream regions of the genes that they regulate, and rarely in the upstream regions of other genes. Our strategy therefore utilizes statistical procedures to identify short oligomers, five or six nucleotides in length, that are over-represented in upstream regions of genes whose expression peaks at the same phase of the cell cycle. We report, with a high level of confidence, that 9 hexamers and 12 pentamers are over-represented in the upstream regions of genes whose expression peaks at the early G1, late G1, S, G2, or M phase of the cell cycle. Some of these sequence elements show a preference for a particular orientation, and others, through a separate statistical test, for a particular position upstream of the ATG start codon. The finding that the majority of the statistically significant sequence elements are located in late G1 upstream regions correlates with other experiments that identified the late G1/early S boundary as a vital cell cycle control point. Our results highlight the importance of MCB, an element implicated previously in late G1/early S gene regulation, as most of the late G1 oligomers contain the MCB sequence or variations thereof. It is striking that most MCB-like sequences localize to a specific region upstream of the ATG start codon. Additional sequences that we have identified may be important for regulation at other phases of the cell cycle.

[A companion website to this manuscript is available fromhttp://www.ncbi.nlm.nih.gov/CBBresearch/Landsman/Cell_cycle_data]

A practical method for simultaneously determining the effective burst sizes and cycle times of viruses

We describe combined analytic and experimental methods for determining reproductive statistics from time-series data. Our computational methods derive four fundamental measures from laboratory experiments: (i) average number of viral daughters; (ii) mean viral cycle time; (iii) standard deviation of the viral cycling time; and (iv) viral doubling time. Taken together, these four reproductive statistics characterize "age-specific fertility," a quantity that provides complete information on the reproduction of the average viral particle. In this paper, we emphasize applications relating to HIV and experiments for assessing cellular tropism, viral phenotypes, antiviral drugs, humoral immunity, and cytotoxic cellular immunity. Nevertheless, our method is quite flexible and applicable to the evaluation of drugs against bacterial, fungal, and parasitic infections, antineoplastic agents against cancer cells, and perturbations involving pest and wildlife releases in ecosystems.

AAA+: A Class of Chaperone-Like ATPases Associated with the Assembly, Operation, and Disassembly of Protein Complexes

Using a combination of computer methods for iterative database searches and multiple sequence alignment, we show that protein sequences related to the AAA family of ATPases are far more prevalent than reported previously. Among these are regulatory components of Lon and Clp proteases, proteins involved in DNA replication, recombination, and restriction (including subunits of the origin recognition complex, replication factor C proteins, MCM DNA-licensing factors and the bacterial DnaA, RuvB, and McrB proteins), prokaryotic NtrC-related transcription regulators, the Bacillus sporulation protein SpoVJ, Mg2+, and Co2+ chelatases, theHalobacterium GvpN gas vesicle synthesis protein, dynein motor proteins, TorsinA, and Rubisco activase. Alignment of these sequences, in light of the structures of the clamp loader δ′ subunit ofEscherichia coli DNA polymerase III and the hexamerization component of N-ethylmaleimide-sensitive fusion protein, provides structural and mechanistic insights into these proteins, collectively designated the AAA+ class. Whole-genome analysis indicates that this class is ancient and has undergone considerable functional divergence prior to the emergence of the major divisions of life. These proteins often perform chaperone-like functions that assist in the assembly, operation, or disassembly of protein complexes. The hexameric architecture often associated with this class can provide a hole through which DNA or RNA can be thread; this may be important for assembly or remodeling of DNA–protein complexes.

AAA+: A class of chaperone-like ATPases associated with the assembly, operation, and disassembly of protein complexes

Using a combination of computer methods for iterative database searches and multiple sequence alignment, we show that protein sequences related to the AAA family of ATPases are far more prevalent than reported previously. Among these are regulatory components of Lon and Clp proteases, proteins involved in DNA replication, recombination, and restriction (including subunits of the origin recognition complex, replication factor C proteins, MCM DNA-licensing factors and the bacterial DnaA, RuvB, and McrB proteins), prokaryotic NtrC-related transcription regulators, the Bacillus sporulation protein SpoVJ, Mg2+, and Co2+ chelatases, the Halobacterium GvpN gas vesicle synthesis protein, dynein motor proteins, TorsinA, and Rubisco activase. Alignment of these sequences, in light of the structures of the clamp loader delta' subunit of Escherichia coli DNA polymerase III and the hexamerization component of N-ethylmaleimide-sensitive fusion protein, provides structural and mechanistic insights into these proteins, collectively designated the AAA+ class. Whole-genome analysis indicates that this class is ancient and has undergone considerable functional divergence prior to the emergence of the major divisions of life. These proteins often perform chaperone-like functions that assist in the assembly, operation, or disassembly of protein complexes. The hexameric architecture often associated with this class can provide a hole through which DNA or RNA can be thread; this may be important for assembly or remodeling of DNA-protein complexes.

Increase of primary HIV-1 production in human peripheral blood mononuclear cells by intermittent medium replenishment

Mitogen-stimulated human peripheral blood mononuclear cells (H-PBMCs) are conventionally used to culture primary human immunodeficiency virus type-1 (HIV-1) isolates in vitro. In this study, we attempt to increase the quality of primary HIV-1 stocks harvested from H-PBMC culture using medium replenishment procedures. Experimental/analysis results indicate that more frequent medium replenishment may not lead to improved quantity and quality of harvested virus stock titers, as determined by the viral core (p24) antigen content, viral infectivity, and viral particle-to-infectious unit ratio. This finding implies the conditioning factor(s) present in H-PBMC culture may be important for primary HIV-1 production. The optimal rate for intermittent medium replenishment to achieve the lowest viral particle-to-infectious unit ratio is around 0.25 volume/volume/day.

A cytopathic infectivity assay of human immunodeficiency virus type 1 in human primary macrophages

In addition to CD4+ T lymphocytes, cells of monocyte/macrophage lineage are a major target for human immunodeficiency virus type 1 (HIV-1) infection. In vitro studies of HIV-1 infection in human monocyte-derived macrophages can be undertaken by a reproducible cell-based assay. A macrophage-based infectivity assay was developed based on the semi-quantitative scoring of HIV-1 induced cytopathology in monolayer macrophage cultures. The assay exhibited dilution-dependent linearity with all three primary macrophage-tropic isolates tested. The end-point infectivity titers determined by this assay correlated with the results obtained by detecting viral p24 antigen in the culture supernatant. The applications of the assay in both neutralization and anti-viral protocols yielded identical results with the more time-consuming and costly p24 formats. Since the assay offers a simple and low-cost method of measuring HIV-1 infectivity in human primary macrophages, it can be used quite easily for large-scale screening or evaluation of candidate vaccines and anti-viral agents.

Human plasma enhances the infectivity of primary human immunodeficiency virus type 1 isolates in peripheral blood mononuclear cells and monocyte-derived macrophages

Physiological microenvironments such as blood, seminal plasma, mucosal secretions, or lymphatic fluids may influence the biology of the virus-host cell and immune interactions for human immunodeficiency virus type 1 (HIV-1). Relative to media, physiological levels of human plasma were found to enhance the infectivity of HIV-1 primary isolates in both phytohemagglutinin-stimulated peripheral blood mononuclear cells and monocyte-derived macrophages. Enhancement was observed only when plasma was present during the virus-cell incubation and resulted in a 3- to 30-fold increase in virus titers in all of the four primary isolates tested. Both infectivity and virion binding experiments demonstrated a slow, time-dependent process generally requiring between 1 and 10 h. Human plasma collected in anticoagulants CPDA-1 and heparin, but not EDTA, exhibited this effect at concentrations from 90 to 40%. Furthermore, heat-inactivated plasma resulted in a loss of enhancement in peripheral blood mononuclear cells but not in monocyte-derived macrophages. Physiological concentrations of human plasma appear to recruit additional infectivity, thus increasing the infectious potential of the virus inoculum.

Viral multiplicity of attachment and its implications for human immunodeficiency virus therapies

The multiplicity of attachment (MOA) of a virion in any particular time interval is the average number of cellular attachment opportunities that must be blocked to keep the virion in suspension. MOA is usually proportional to incubation time and cell concentration. Low MOA (like low multiplicity of infection) is required for reproducible assay of adsorptive blockers, and high MOA by itself can produce spurious synergies between adsorptive blockers, e.g., soluble CD4 (sCD4) and some antibodies. Poliovirus and human immunodeficiency virus (HIV) data show that viral neutralization conforms quantitatively to MOA and kinetic theory over large ranges of incubation times and target cell concentrations. Extrapolating sCD4 data beyond conditions achievable in vitro to those in vivo predicts that sCD4 concentrations above the strain-specific sCD4-gp120 dissociation constant are required to block lymphoid HIV significantly, in at least semiquantitative agreement with clinical results. The extrapolation is applicable to humoral neutralization data as well. MOA analysis also indicates that although completely stopping the attachment of individual virions to cells may still be an effective therapeutic strategy against established HIV infection, merely retarding attachment probably is not. The concept of MOA holds great promise for improving the therapeutic relevance of in vitro data and can be applied to any infectious agent, to many processes that impair or enhance infection steps, and to many assay end points, not just infection.

Statistical analysis of sparse infection data and its implications for retroviral treatment trials in primates

Reports on retroviral primate trials rarely publish any statistical analysis. Present statistical methodology lacks appropriate tests for these trials and effectively discourages quantitative assessment. This paper describes the theory behind VACMAN, a user-friendly computer program that calculates statistics for in vitro and in vivo infectivity data. VACMAN's analysis applies to many retroviral trials using i.v. challenges and is valid whenever the viral dose-response curve has a particular shape. Statistics from actual i.v. retroviral trials illustrate some unappreciated principles of effective animal use: dilutions other than 1:10 can improve titration accuracy; infecting titration animals at the lowest doses possible can lower challenge doses; and finally, challenging test animals in small trials with more virus than controls safeguards against false successes, "reuses" animals, and strengthens experimental conclusions. The theory presented also explains the important concept of viral saturation, a phenomenon that may cause in vitro and in vivo titrations to agree for some retroviral strains and disagree for others.

Factors underlying spontaneous inactivation and susceptibility to neutralization of human immunodeficiency virus

To determine the factors governing inactivation and neutralization, physical, chemical, and biological assays were performed on a molecular clone of human immunodeficiency type 1 (HIV-1HXB3). This included quantitative electron microscopy, gp120 and p24 enzyme-linked immunosorbent assays, reverse, transcriptase assays, and quantitative infectivity assays. For freshly harvested stocks, the ratio of infectious to noninfectious viral particles ranged from 10(-4) to 10(-7) in viral stocks containing 10(9) to 10(10) physical particles per milliliter. There were relatively few gp120 knobs per HIV particle, mean approximately 10 when averaged over the total particle count. Each HIV particle contained a mean approximately 5 x 10(-17) g of p24 and approximately 2 x 10(-16) g of RNA polymerase, corresponding to about 1200 and 80 molecules, respectively. The spontaneous shedding of gp120 envelope proteins from virions was exponential, with a half-life approximately 30 hr. The loss of RNA polymerase activity in virons was also exponential, with a half-life approximately 40 hr. The physical breakup of virions and the dissolution of p24 core proteins were slow (half-life greater than 100 hr) compared to the gp120 shedding and polymerase loss rates. The decay of HIV-1 infectivity was found to obey superimposed single- and multihit kinetics. At short preincubation times, the loss of infectivity correlated with spontaneous shedding of gp120 from virions. At longer times, an accelerating decay rate indicated that HIV requires a minimal number of gp120 molecules for efficient infection of CD4+ cells. The blocking activity of recombinant soluble CD4 (sCD4) and phosphonoformate (foscarnet) varied with the number of gp120 molecules and number of active RNA polymerase molecules per virion, respectively. These results demonstrate that the physical state of virions greatly influences infectivity and neutralization. The knowledge gained from these findings will improve the reliability of in vitro assays, enhance the study of wild-type strains, and facilitate the evaluation of potential HIV therapeutics and vaccines.

Blocking of human immunodeficiency virus infection depends on cell density and viral stock age

Quantitative infectivity assays were used to study how the blocking activity of soluble CD4 (sCD4) is affected by sCD4 concentration, target cell density, and viral stock age. During incubation with 20 nM sCD4, human immunodeficiency virus type 1 (HIV-1) stocks underwent irreversible inactivation. In contrast, inactivation with 2 nM sCD4 was almost entirely reversible. At lower sCD4 concentrations (less than or equal to 2 nM) and target cell densities of 6.25 x 10(4) ml-1, sCD4 blocking activity for HIV-1 gave a gp120-sCD4 association constant (Kassoc) of 1.7 x 10(9) M-1, which agrees with chemical measurements. At the higher density of 1.6 x 10(7) cells ml-1, however, the blocking activity was 20-fold less. During incubation of HIV-1 stock optimized for infectivity by rapid harvest, sCD4 blocking activity increased 20-fold during a 3-h window. These results show that competitive blocking activity depends strongly on target cell density and virion age. Thus, unappreciated variations in HIV stocks and assay conditions may hinder comparisons of blockers from laboratory to laboratory, and the age of HIV challenge stocks may influence studies of drug and vaccine efficacy. The results also suggest that blocking of viral particles in lymphoid compartments will require very high competitive blocker concentrations, which may explain the refractory outcomes from sCD4-based drug trials in humans.

Fast optimal alignment

Algorithms often align sequences by minimizing a cost. Such algorithms usually operate by aligning successively longer subsequences until they finish the alignment. Efficient algorithms, such as those of Fickett and Ukkonen, speed the computation by ignoring bad subalignments. A general principle underlies the efficiency of these two algorithms: inequalities can direct computations to promising subalignments. Hence inequalities can be used to suggest alignment algorithms. Inequalities for unweighted end-gaps, affine and concave gap weights, etc., are discussed, and empirical results evaluating new algorithms for single indel costs and weighted end-gaps are presented. Empirical results show the new algorithms are, under certain circumstances, much faster than known algorithms.

HIV requires multiple gp120 molecules for CD4-mediated infection

Binding of glycoprotein gp120 to the T cell-surface receptor CD4 is a crucial step in CD4-dependent infection of a target cell by the human immunodeficiency virus (HIV). Blocking some or all gp120 molecules on the viral surface should therefore inhibit infection. Consequently, competitive receptor inhibitors, such as soluble synthetic CD4 (sCD4), synthetic CD4 peptides and immunoglobulins, have been investigated in vitro and in vivo, but little is known about the molecular mechanisms of these inhibitors. We have now quantitatively examined blocking by soluble CD4 in the hope of gaining insight into the complex process of viral binding, adsorption and penetration. At low sCD4 concentrations, the inhibition in three HIV strains is proportional to the binding of gp120. The biological association constant (gp120-sCD4 Kassoc) for HIV-2NIHZ is (8.5 +/- 0.5) x 10(7) M-1, whereas Kassoc for HIV-1HXB3 (1.4 +/- 0.2) and HIV-1MN (1.7 +/- 0.1) x 10(9) M-1 are 15-20-fold larger. For all three viral strains, the biological Kassoc from infectivity assays is comparable to the chemical Kassoc. The inhibitory action of sCD4 at high concentrations, however, is not fully explained by simple proportionality with the binding to gp120. Positive synergy in blocking of infection occurs after about half the viral gp120s molecules are occupied, and is identical for all three viral strains, despite the large differences in Kassoc. Our method of measuring the viral-cell receptor Kassoc directly from infectivity assays is applicable to immunoglobulins, to other viruses and to assays using primary or transformed cell lines.

Analytic results for quantifying HIV infectivity

In a separate paper, we developed a mathematical model describing HIV infection and used it to suggest experiments for quantifying characteristic viral parameters. In this paper we generalize the model to any well-mixed assay system. We also present complete and rigorous derivations of fundamental results needed for the design and analysis of HIV infectivity assays. The model is applicable to infectious agents with multiple receptors for their target cell (e.g. HIV, Epstein-Barr virus and Plasmodium), and to blockers (both reversible and irreversible), as long as blocker and target cells are the same diffusion compartment.

Quantifying the infectivity of human immunodeficiency virus

We have developed a mathematical model that quantifies lymphocyte infection by human immunodeficiency virus (HIV) and lymphocyte protection by blocking agents such as soluble CD4. We use this model to suggest standardized parameters for quantifying viral infectivity and to suggest techniques for calculating these parameters from well-mixed infectivity assays. We discuss the implications of the model for our understanding of the infectious process and virulence of HIV in vivo.

T cell multideterminant regions in the human immunodeficiency virus envelope: toward overcoming the problem of major histocompatibility complex restriction

Helper T cell determinants should be an important component of an anti-human immunodeficiency virus (HIV) vaccine aimed at either antibody or cytotoxic T cell immunity. However, model protein studies have raised concern about the usefulness of any single determinant, because a given determinant is likely to be seen by only a small subset of major histocompatibility complex (MHC) types within the population. Here, we use 44 peptides, including ones predicted and not predicted on the basis of amphipathicity to be potential T cell sites, to locate T cell antigenic determinants recognized by mice of four MHC haplotypes immunized with the whole gp 160 envelope protein. Although the preselection of peptides necessitates caution in a statistical analysis, alpha-amphipathic peptides predominated among sites eliciting the strongest response. Although we have not tested the entire sequence, we have identified six multideterminant regions, in which overlapping peptides are recognized by mice of either three or all four MHC types. Four of the six regions have sequences relatively conserved among HIV-1 isolates. The existence of such multideterminant regions recognized by multiple MHC haplotypes suggests the possibility that use of peptides longer than a minimal determinant and containing several overlapping determinants may be a possible approach to circumvent the serious problem of MHC restriction in peptide vaccines aimed at eliciting T cell immunity.

Protein antigenic structures recognized by T cells: potential applications to vaccine design

In summary, our results using the model protein antigen myoglobin indicated, in concordance with others, that helper T lymphocytes recognize a limited number of immunodominant antigenic sites of any given protein. Such immunodominant sites are the focus of a polyclonal response of a number of different T cells specific for distinct but overlapping epitopes. Therefore, the immunodominance does not depend on the fine specificity of any given clone of T cells, but rather on other factors, either intrinsic or extrinsic to the structure of the antigen. A major extrinsic factor is the MHC of the responding individual, probably due to a requirement for the immunodominant peptides to bind to the MHC of presenting cells in that individual. In looking for intrinsic factors, we noted that both immunodominant sites of myoglobin were amphipathic helices, i.e., helices having hydrophilic and hydrophobic residues on opposite sides. Studies with synthetic peptides indicated that residues on the hydrophilic side were necessary for T-cell recognition. However, unfolding of the native protein was shown to be the apparent goal of processing of antigen, presumably to expose something not already exposed on the native molecule, such as the hydrophobic sides of these helices. We propose that such exposure is necessary to interact with something on the presenting cell, such as MHC or membrane, where we have demonstrated the presence of antigenic peptides by blocking of presentation of biotinylated peptide with avidin. The membrane may serve as a short-term memory of peptides from antigens encountered by the presenting cell, for dynamic sampling by MHC molecules to be available for presentation to T cells. These ideas, together with the knowledge that T-cell recognition required only short peptides and therefore had to be based only on primary or secondary structure, not tertiary folding of the native protein, led us to propose that T-cell immunodominant epitopes may tend to be amphipathic structures. An algorithm to search for potential amphipathic helices from sequence information identified 18 of 23 known immunodominant T-cell epitopes from 12 proteins (p less than 0.001). Another statistical approach confirmed the importance of amphipathicity and also supported the importance of helical structure that had been proposed by others. It suggested that peptides able to form a stable secondary structure, especially a helix, more commonly formed immunodominant epitopes. We used this approach to predict potential immunodominant epitopes for induction of T-cell immunity in proteins of clinical relevance, such as the malarial circumsporozoite protein and the AIDS viral envelope.(ABSTRACT TRUNCATED AT 400 WORDS)

Hydrophobicity scales and computational techniques for detecting amphipathic structures in proteins

Protein segments that form amphipathic alpha-helices in their native state have periodic variation in the hydrophobicity values of the residues along the segment, with a 3.6 residue per cycle period characteristic of the alpha-helix. The assignment of hydrophobicity values to amino acids (hydrophobicity scale) affects the display of periodicity. Thirty-eight published hydrophobicity scales are compared for their ability to identify the characteristic period of alpha-helices, and an optimum scale for this purpose is computed using a new eigenvector method. Two of the published scales are also characterized by eigenvectors. We compare the usual method for detecting periodicity based on the discrete Fourier transform with a method based on a least-squares fit of a harmonic sequence to a sequence of hydrophobicity values. The two become equivalent for very long sequences, but, for shorter sequences with lengths commonly found in alpha-helices, the least-squares procedure gives a more reliable estimate of the period. The analog to the usual Fourier transform power spectrum is the "least-squares power spectrum", the sum of squares accounted for in fitting a sinusoid of given frequency to a sequence of hydrophobicity values. The sum of the spectra of the alpha-helices in our data base peaks at 97.5 degrees, and approximately 50% of the helices can account for this peak. Thus, approximately 50% of the alpha-helices appear to be amphipathic, and, of those that are, the dominant frequency at 97.5 degrees rather than 100 degrees indicates that the helix is slightly more open than previously thought, with the number of residues per turn closer to 3.7 than 3.6. The extra openness is examined in crystallographic data, and is shown to be associated with the C terminus of the helix. The alpha amphipathic index, the key quantity in our analysis, measures the fraction of the total spectral area that is under the 97.5 degrees peak, and is a characteristic of hydrophobicity scales that is consistent for different sets of helices. Our optimized scale maximizes the amphipathic index and has a correlation of 0.85 or higher with nine previously published scales. The most surprising feature of the optimized scale is that arginine tends to behave as if it were hydrophobic; i.e. in the crystallographic data base it has a tendency to be on the hydrophobic face of teh amphipathic helix. Although the scale is optimal only for predicting alpha-amphipathicity, it also ranks high in identifying beta-amphipathicity and in distinguishing interior from exterior residues in a protein.(ABSTRACT TRUNCATED AT 400 WORDS)

Prediction of immunodominant helper T cell antigenic sites from the primary sequence

We have used a data base of 23 known immunodominant helper T cell antigenic sites located on 12 proteins to systematically develop an optimized algorithm for predicting T cell antigenic sites. The algorithm is based on the amphipathic helix model in which antigenic sites are postulated to be helices with one face predominantly polar and the opposite face predominantly apolar. Such amphipathic structures can form when the polarity of residues along the sequence varies with a more or less regular period. Hence they can be identified by methods (so called power spectrum procedures) that detect periodic variations in properties of a sequence. The choice of power spectrum procedure, hydrophobicity scale, and model parameters are examined. An algorithm is tested by comparing the predicted amphipathic segments with the locations of the known T cell sites, counting the number of matches, and calculating the probability of getting this number by chance alone. The optimum algorithm, which predicts the largest number of sites with the lowest chance probability, uses the Fauchere-Pliska hydrophobicity scale and a least squares fit of a sinusoid as its power spectrum procedure. By applying this algorithm, 18 of the 23 known sites are identified (75% sensitivity) with a high degree of significance (p less than 0.001). The success of the algorithm supports the hypothesis that stable amphipathic helices are fundamentally important in determining immunodominance. This approach may be of practical value in designing synthetic vaccines aimed at T cell immunity.

Prediction of immunodominant helper T cell antigenic sites from the primary sequence

We have used a data base of 23 known immunodominant helper T cell antigenic sites located on 12 proteins to systematically develop an optimized algorithm for predicting T cell antigenic sites. The algorithm is based on the amphipathic helix model in which antigenic sites are postulated to be helices with one face predominantly polar and the opposite face predominantly apolar. Such amphipathic structures can form when the polarity of residues along the sequence varies with a more or less regular period. Hence they can be identified by methods (so called power spectrum procedures) that detect periodic variations in properties of a sequence. The choice of power spectrum procedure, hydrophobicity scale, and model parameters are examined. An algorithm is tested by comparing the predicted amphipathic segments with the locations of the known T cell sites, counting the number of matches, and calculating the probability of getting this number by chance alone. The optimum algorithm, which predicts the largest number of sites with the lowest chance probability, uses the Fauchere-Pliska hydrophobicity scale and a least squares fit of a sinusoid as its power spectrum procedure. By applying this algorithm, 18 of the 23 known sites are identified (75% sensitivity) with a high degree of significance (p less than 0.001). The success of the algorithm supports the hypothesis that stable amphipathic helices are fundamentally important in determining immunodominance. This approach may be of practical value in designing synthetic vaccines aimed at T cell immunity.

Strong conformational propensities enhance T cell antigenicity

The ability to predict T cell antigenic peptides would have important implications for the development of artificial vaccines. As a first step towards prediction, this report uses a new statistical technique to discover and evaluate peptide properties correlating with T cell antigenicity. This technique employs Monte Carlo computer experiments and is applicable to many problems involving protein or DNA. The technique is used to evaluate the contribution of various peptide properties to helper T cell antigenicity. The properties investigated include amphipathicities (alpha and beta), conformational propensities (alpha, beta, turn and coil), and the correlates of alpha-helices, such as the absence of helix-breakers and the positioning of the residues which stabilize alpha-helical dipoles. We also investigate segmental amphipathicity. (A peptide has this property when it contains at least two disjoint subpeptides, one hydrophobic, one hydrophilic.) Statistical correlations and stratifications assessed independent contributions to T cell antigenicity. The findings presented here have important implications for the manufacture of peptide vaccines. These implications are as follows: if possible, peptide vaccines should probably be those protein segments which have a propensity to form amphipathic alpha-helices, which do not have regions with a propensity to coil conformations, and which have a lysine at their COOH-terminus. The last two observations are of particular use in manufacturing peptides vaccines: they indicate where the synthetic peptides should be terminated. These implications are supported by the findings given below. The significances (p values) support the following statistical generalites about antigenic conformations: most helper T cell antigenic sites are amphipathic alpha-helices; alpha-helical amphipathicity and propensity to an alpha-helical conformation contribute independently to T cell antigenicity; there is evidence that some T cell antigenic sites are beta conformations instead of alpha-helices; T cell antigenic sites avoid random coiled conformations; and T cell antigenic sites are usually not segmentally amphipathic. alpha-Helical amphipathicity was significant, but segmental amphipathicity was not. This has implications for the dimensions of the structure interacting with the hydrophobic portion of an amphipathic T cell antigenic site. Lysines are unusually frequent at the COOH-terminal of T cell antigenic sites, even after accounting for tryptic digests. These lysines can stabilize alpha-helical peptides by a favorable interaction with alpha-helical dipoles.(ABSTRACT TRUNCATED AT 400 WORDS)

Strong conformational propensities enhance T cell antigenicity

The ability to predict T cell antigenic peptides would have important implications for the development of artificial vaccines. As a first step towards prediction, this report uses a new statistical technique to discover and evaluate peptide properties correlating with T cell antigenicity. This technique employs Monte Carlo computer experiments and is applicable to many problems involving protein or DNA. The technique is used to evaluate the contribution of various peptide properties to helper T cell antigenicity. The properties investigated include amphipathicities (alpha and beta), conformational propensities (alpha, beta, turn and coil), and the correlates of alpha-helices, such as the absence of helix-breakers and the positioning of the residues which stabilize alpha-helical dipoles. We also investigate segmental amphipathicity. (A peptide has this property when it contains at least two disjoint subpeptides, one hydrophobic, one hydrophilic.) Statistical correlations and stratifications assessed independent contributions to T cell antigenicity. The findings presented here have important implications for the manufacture of peptide vaccines. These implications are as follows: if possible, peptide vaccines should probably be those protein segments which have a propensity to form amphipathic alpha-helices, which do not have regions with a propensity to coil conformations, and which have a lysine at their COOH-terminus. The last two observations are of particular use in manufacturing peptides vaccines: they indicate where the synthetic peptides should be terminated. These implications are supported by the findings given below. The significances (p values) support the following statistical generalites about antigenic conformations: most helper T cell antigenic sites are amphipathic alpha-helices; alpha-helical amphipathicity and propensity to an alpha-helical conformation contribute independently to T cell antigenicity; there is evidence that some T cell antigenic sites are beta conformations instead of alpha-helices; T cell antigenic sites avoid random coiled conformations; and T cell antigenic sites are usually not segmentally amphipathic. alpha-Helical amphipathicity was significant, but segmental amphipathicity was not. This has implications for the dimensions of the structure interacting with the hydrophobic portion of an amphipathic T cell antigenic site. Lysines are unusually frequent at the COOH-terminal of T cell antigenic sites, even after accounting for tryptic digests. These lysines can stabilize alpha-helical peptides by a favorable interaction with alpha-helical dipoles.(ABSTRACT TRUNCATED AT 400 WORDS)

Improving sequence-matching algorithms by working from both ends

Recent algorithms (e.g. Ukkonen, Fickett) align nucleic acid sequences (starting from the left) by bounding the allowed distance between subsequences by d, aligning, then incrementing d until all of both sequences are aligned. Aligning from both ends is more efficient. If the single-ended algorithm has computational cost CNk (C, k = constants; N = sequence length), the double-ended algorithm often has cost C(N/2)k.

On a model for the structure of circular mitochondrial genomes in higher plants

The mitochondrial genome of some higher plants consists of a discrete set of circular molecules. The heterogeneity found in the number of circles and their size is puzzling. In some plants evidence exists that indicates that these circular DNA molecules undergo intermolecular and intramolecular recombination events. The result of these events is that two small circles can combine to give one large circle or one large circle can break up into two small circles. Here we pursue the idea that such recombination events are responsible for the variability in genome composition. Treating the recombination events as chemical reactions we derive the equilibrium size distribution of circles. In Brassica campestris there are two basic subunits, circles A and B, containing 135 and 83 kilobases, respectively. By restriction-enzyme mapping one can determine in a multimeric circle, the number of interfaces between A- and B-derived DNA. Using a combinatorial argument we predict the frequency of such interfaces and compare our predictions with published data. A number of suggestions are made for additional experimental tests of the recombinational theory of genomic diversity.

Analytic results for finite systems of ringed flory polymers

We examine Flory's RAf model of polymerization for a finite closed system of N monomers. Monomers have f functional groups of type A. Random stepwise reaction between A's, regardless of ring formation, bonds the monomers together.We give exact statistics for the resulting polymer distribution and verify the results of the Falk and Thomas computer simulation. As N → ∞, Flory's modification of the Stockmayer distribution gives the distribution of finite polymers, and cyclization is confined to the gel.Similar results hold for Flory's AgRBf−g model.

A reinterpretation of the evidence for an interaction between Clq and pairs of immunoglobulin molecules in an immune lattice

An error in a previous article [Cohen S. (1968) J. Immun. 100, 407-413] was discovered which invalidates it as evidence that IgG immune complexes activate the classical complement pathway by an interaction involving pairs of antibody molecules, so-called doublet formation. The error concerns the correction to be made for the observed 8% residual activity of the modified antibody preparation used. When appropriate correction factors are applied, the data are found not to be consistent with the hypothesis of doublet formation. The analysis presented here has no bearing on the original article's experimental techniques, nor on its demonstration of co-operation between IgG molecules during complement fixation.

A Reason for Pleomerism

Pleomerism, the increase in vertebral number with maximum recorded length for species within a family, may be explained for fish by hydrodynamic considerations. A model is developed that suggests that the upper limits of the slope of the relation between log vertebral number and log length should be 0.43 in laminar flow and 0.35 in turbulent flow. These slopes are compared with those of previous studies only with difficulty because (1) those values were for predictive rather than functional regressions, (2) the slope will depend on the range in length of various species across temperature zones, and (3) no distinction was made between structural and locomotor vertebrae. Variations in shape also complicate the relation between vertebral count and length, there are latitudinal factors involved, and maximum length is probably only a weak correlate of the length at which natural selection may be concentrated. When these factors are considered, it is to be expected that observations would provide only a rough approximation to theory.The theory underlying the model is also used to derive a formula for the stride length of fish motion that is then compared with empirical results. Key words: vertebrae counts, body size, locomotion, hydrodynamic equations, mathematical model, stride length