The 185/333 gene family is a rapidly diversifying host-defense gene cluster in the purple sea urchin Strongylocentrotus purpuratus

The genome of the purple sea urchin contains numerous large gene families with putative immunological functions. One gene family, known as 185/333, is characterized by extraordinary molecular diversity resulting from single nucleotide polymorphisms and the presence or the absence of 27 large blocks of sequences known as elements. The mosaic composition of elements, known as element patterns, that is present within the members of this gene family is encoded entirely in the second of two exons. Many of the elements correspond to one of six types of repeats that are present throughout the genes. The sequence diversity and variation in element patterns led us to investigate the evolution of the 185/333 gene family. The work presented here suggests that the element patterns are the result of both recombination and duplication and/or deletion of intragenic repeats. Each element is composed of a limited number of similar but distinct sequences, and their distribution among the 185/333 genes suggests frequent recombination within this gene family. Phylogenetic analyses of five 185/333 elements and two regions of the intron were performed using two tests: incongruence length difference and incongruence permutation. Results indicated that each pair of sequence segments was incongruent, suggesting that recombination occurs frequently along the length of the genes, including both the intron and the second exon, and that recombination is not restricted to intact elements. Paradoxically, the high level of similarity among the elements indicated that the 185/333 genes appear to be the result of a recent diversification. These results add to the growing body of evidence suggesting that invertebrate immune systems are not simple and static, but are dynamic and highly complex, and may employ group-specific mechanisms for diversification.

Classification of osteoarthritis biomarkers: a proposed approach

OBJECTIVE

Osteoarthritis (OA) biomarkers are needed by researchers and clinicians to assist in disease diagnosis and assessment of disease severity, risk of onset, and progression. As effective agents for OA are developed and tested in clinical studies, biomarkers that reliably mirror or predict the progression or amelioration of OA will also be needed.

METHODS

The NIH-funded OA Biomarkers Network is a multidisciplinary group interested in the development and validation of OA biomarkers. This review summarizes our efforts to characterize and classify OA biomarkers.

RESULTS

We propose the "BIPED" biomarker classification (which stands for Burden of Disease, Investigative, Prognostic, Efficacy of Intervention and Diagnostic), and offer suggestions on optimal study design and analytic methods for use in OA investigations.

CONCLUSION

The BIPED classification provides specific biomarker definitions with the goal of improving our ability to develop and analyze OA biomarkers, and to communicate these advances within a common framework.

Statistical inference of sequence-dependent mutation rates

Several lines of research are now converging towards an integrated understanding of mutational mechanisms and their evolutionary implications. Experimentally, crystal structures reveal the effect of sequence context on polymerase fidelity; large-scale sequencing projects generate vast amounts of sequence polymorphism data; and locus-specific databases are being constructed. Computationally, software and analytical tools have been developed to analyze mutational data, to identify mutational hot spots, and to compare the signatures of mutagenic agents.

Stochasticity in transcriptional regulation: origins, consequences, and mathematical representations

Transcriptional regulation is an inherently noisy process. The origins of this stochastic behavior can be traced to the random transitions among the discrete chemical states of operators that control the transcription rate and to finite number fluctuations in the biochemical reactions for the synthesis and degradation of transcripts. We develop stochastic models to which these random reactions are intrinsic and a series of simpler models derived explicitly from the first as approximations in different parameter regimes. This innate stochasticity can have both a quantitative and qualitative impact on the behavior of gene-regulatory networks. We introduce a natural generalization of deterministic bifurcations for classification of stochastic systems and show that simple noisy genetic switches have rich bifurcation structures; among them, bifurcations driven solely by changing the rate of operator fluctuations even as the underlying deterministic system remains unchanged. We find stochastic bistability where the deterministic equations predict monostability and vice-versa. We derive and solve equations for the mean waiting times for spontaneous transitions between quasistable states in these switches.

Complex systems analysis: a tool for shock research

For the past century, students of shock have focused research efforts to illuminate specific mechanisms that cause, or fail as a consequence of, circulatory collapse. Although clinical strategies aimed at supporting or restoring individual organ systems have proven effective, many patients succumb to more generalized multiple organ system failure. We suggest that general biological systems failure cannot be interpreted through reliance on reductionist science. We propose that complex systems analysis is an essential tool for shock research and we evaluate its application to genomic technologies.

Waiting times to appearance and dominance of advantageous mutants: estimation based on the likelihood

The germinal center reaction (GCR) of vertebrate immunity provides a remarkable example of evolutionary succession, in which an advantageous phenotype arises as a spontaneous mutation from the parental type and eventually displaces the parental type altogether. In the case of the immune response to the hapten (4-hydroxy-3-nitrophenyl)acetyl (NP), as with several other designed immunogens, the process is dominated by a single key mutation, which greatly simplifies the modeling of and analysis of data. We developed a two-stage model of this process in which the primary stage represents the appearance and establishment of the mutant population as a stochastic process while the second stage represents the growth and dominance of the clone as a deterministic process, conditional on its time of establishment from stage one. We applied this model to the analysis of population samples from several germinal center (GC) reactions and used maximum-likelihood methods to estimate the waiting times to arrival and to dominance of the mutant clone. We determined the sampling properties of the maximum-likelihood estimates using Monte Carlo methods and compared them to their asymptotic distributions. The methods we present here are well-suited for use in the analysis of other systems, such as tumor growth and the experimental evolution of bacteria.

Improved inference of mutation rates: I. An integral representation for the Luria-Delbrück distribution

The estimation of mutation rates is ordinarily performed using results based on the Luria-Delbrück distribution. There are certain difficulties associated with the use of this distribution in practice, some of which we address in this paper (others in the companion paper, Oprea and Kepler, Theor. Popul. Biol., 2001). The distribution is difficult to compute exactly, especially for large values of the random variable. To overcome this problem, we derive an integral representation of the Luria-Delbrück distribution that can be computed easily for large culture sizes. In addition, we introduce the usual assumption of very small probability of having a large proportion of mutants only after the generating function has been computed. Thus, we obtain information on the moments for the more general case. We examine the asymptotic behavior of this system. We find a scaling or "standardization" technique that reduces the family of distributions parameterized by three parameters (mutation rate, initial cell number, and final cell number) to a single distribution with no parameters, valid so long as the product of the mutation rate and the final culture is sufficiently large. We provide a pair of techniques for computing confidence intervals for the mutation rate. In the second paper of this series, we use the distribution derived here to find approximate distributions for the case where the cell cycle time is not well-described as an exponential random variable as is implicitly assumed by Luria-Delbrück distribution.

Improved inference of mutation rates: II. Generalization of the Luria-Delbrück distribution for realistic cell-cycle time distributions

In the first paper of this series (Kepler and Oprea, Theor. Popul. Biol. 2001) we found a continuum approximation of the Luria-Delbrück distribution in terms of a scaled variable related to the proportion of mutants in the culture. Here we show that the Luria-Delbrück distribution is inaccurate when realistic division processes are being considered due to the non-Markovian character of the cell cycle. We derive the expectation of the proportion of mutants in the culture for arbitrary cell-cycle time distributions. We then introduce a two-parameter generalization of the continuum Luria-Delbrück distribution for two of the more commonly used cell-cycle time distributions: gamma and shifted exponential. We obtain the generalized distribution by defining a map from the actual parameters to "effective" parameters. The effective mutation rate is obtained analytically, while the effective population size is obtained by fitting simulation data. Our simulations show that the second parameter depend mostly on the coefficient of variation of the cell-cycle time distribution.

The targeting of somatic hypermutation closely resembles that of meiotic mutation

We have compared the microsequence specificity of mutations introduced during somatic hypermutation (SH) and those introduced meiotically during neutral evolution. We have minimized the effects of selection by studying nonproductive (hence unselected) Ig V region genes for somatic mutations and processed pseudogenes for meiotic mutations. We find that the two sets of patterns are very similar: the mutabilities of nucleotide triplets are positively correlated between the somatic and meiotic sets. The major differences that do exist fall into three distinct categories: 1) The mutability is sharply higher at CG dinucleotides under meiotic but not somatic mutation. 2) The complementary triplets AGC and GCT are much more mutable under somatic than under meiotic mutation. 3) Triplets of the form WAN (W = T or A) are uniformly more mutable under somatic than under meiotic mutation. Nevertheless, the relative mutabilities both within this set and within the SAN (S = G or C) triplets are highly correlated with those under meiotic mutation. We also find that the somatic triplet specificity is strongly symmetric under strand exchange for A/T triplets as well as for G/C triplets in spite of the strong predominance of A over T mutations. Thus, we suggest that somatic mutation has at least two distinct components: one that specifically targets AGC/GCT triplets and another that acts as true catalysis of meiotic mutation.

Morphologic analysis correlates with gene expression changes in cultured F344 rat mesothelial cells

The gene expression pattern of mesothelial cells in vitro was determined after 4 or 12 h exposure to the rat mesothelial, kidney, and thyroid carcinogen and oxidative stressor potassium bromate (KBrO(3)). Gene expression changes observed using cDNA arrays indicated oxidative stress, mitotic arrest, and apoptosis in treated immortalized rat peritoneal mesothelial cells. Increases occurred in oxidative stress responsive genes HO-1, QR, HSP70, GADD45, GADD153, p21(WAF1/CIP16), GST's, GAPDH, TPX, and GPX-1(0); transcriptional regulators c-jun, c-fos, jun B, c-myc, and IkappaB; protein repair components Rdelta, RC10-II, C3, RC-7, HR6B ubiquitin-conjugating enzyme and ubiquitin; DNA repair components PCNA, msh2, and O-6 methylguanine DNA methyltransferase; lipid peroxide excision enzyme PLA2; and apoptogenic components TNFalpha, iNOS1 and FasL. Decreases occurred in bcl-2 (antiapoptotic), bax alpha, bad, and bok (proapoptotic) and cell cycle control elements (cyclins). Cyclin G and p14ink4b (which inhibit entry into cell cycle) were increased. Numerous signal transduction, cell membrane transport, membrane-associated receptor, and fatty acid biosynthesis and repair components were altered. Morphologic endpoints examined were number of mitotic figures, number of apoptotic cells, and antibody-specific localization of HO-1 (which demonstrated increased HO-1 protein expression). PCR analysis confirmed HO-1, p21(waf1/cip1), HSP70, GPX1, GADD45, QR, mdr1, PGHS, and cyclin D1 changes. A model for KBrO(3)-induced carcinogenicity in the F344 rat mesothelium is proposed, whereby KBrO(3) generates a redox signal that activates p53 and results in transcriptional activation of oxidative stress and repair genes, dysregulation of growth control, and imperfect DNA repair leading to carcinogenesis.

The nucleotide-replacement spectrum under somatic hypermutation exhibits microsequence dependence that is strand-symmetric and distinct from that under germline mutation

Somatic mutation is a fundamental component of acquired immunity. Although its molecular basis remains undetermined, the sequence specificity with which mutations are introduced has provided clues to the mechanism. We have analyzed data representing over 1700 unselected mutations in V gene introns and nonproductively rearranged V genes to identify the sequence specificity of the mutation spectrum-the distribution of resultant nucleotides. In other words, we sought to determine what effects the neighboring bases have on what a given base mutates "to." We find that both neighboring bases have a significant effect on the mutation spectrum. Their influences are complicated, but much of the effect can be characterized as enhancing homogeneity of the mutated DNA sequence. In contrast to what has been reported for the sequence specificity of the "targeting" mechanism, that of the spectrum is notably symmetric under complementation, indicating little if any strand bias. We compared the spectrum to that found previously for germline mutations as revealed by analyzing pseudogene sequences. We find that the influences of nearest neighbors are quite different in the two datasets. Altogether, our findings suggest that the mechanism of somatic hypermutation is complex, involving two or more stages: introduction of mis-pairs and their subsequent resolution, each with distinct sequence specificity and strand bias.

Quantitative evaluation of alternative mechanisms of blood disposition of di(n-butyl) phthalate and mono(n-butyl) phthalate in rats

Phthalate esters are ubiquitous, low-level environmental contaminants that induce testicular toxicity in laboratory animals. The diester is rapidly metabolized in the gut to the monoester, which causes the testicular toxicity. Several physiologically based pharmacokinetic (PBPK) model structures have been evaluated for di(2-ethylhexyl) phthalate (DEHP) and mono(2-ethylhexyl) phthalate (MEHP). The objective of this study was to test these PBPK models for a less lipophilic phthalate diester, di(n-butyl) phthalate (DBP), and monoester, mono(n-butyl) phthalate (MBP). Alternate models describing enterohepatic circulation, diffusion-limitation, tissue pH gradients (pH trapping), and a simpler, flow-limited model were evaluated. A combined diffusion-limited and pH trapping model was also tested. MBP tissue:blood partition coefficients were similar when determined either experimentally by a nonvolatile, vial equilibration technique or algorithmically. All other parameters were obtained from the literature or estimated from MBP blood concentrations following intravenous or oral exposure to DBP or MBP. A flow-limited model was unable to predict MBP blood levels, whereas each alternative model had statistically better predictions. The combined diffusion-limited and pH trapping model was the best overall, having the highest log-likelihood function value. This result is consistent with a previous finding that the pH trapping model was the best model for describing DEHP and MEHP blood dosimetry, though it was necessary to extend the model to include diffusion-limitation. The application of the pH trapping model is a step toward developing a generic model structure for all phthalate esters, though more work is required before a generic structure can be identified with confidence. Development of a PBPK model structure applicable to all phthalate esters would support more realistic assessments of risk to human health from exposure to one or more members of this class of compounds.

Genetic plasticity of V genes under somatic hypermutation: statistical analyses using a new resampling-based methodology

Evidence for somatic hypermutation of immunoglobulin genes has been observed in all of the species in which immunoglobulins have been found. Previous studies have suggested that codon usage in immunoglobulin variable (V) region genes is such that the sequence-specificity of somatic hypermutation results in greater mutability in complementarity-determining regions of the gene than in the framework regions. We have developed a new resampling-based methodology to explore genetic plasticity in individual V genes and in V gene families in a statistically meaningful way. We determine what factors contribute to this mutability difference and characterize the strength of selection for this effect. We find that although the codon usage in immunoglobulin V genes renders them distinct among translationally equivalent sequences with random codon usage, they are nevertheless not optimal in this regard. We find that the mutability patterns in a number of species are similar to those we find for human sequences. Interestingly, sheep sequences show extremely strong mutability differences, consistent with the role of somatic hypermutation in the diversification of primary antibody repertoire in these animals. Human TCR V(beta) sequences resemble immunoglobulin in mutability pattern, suggesting one of several alternatives, that hypermutation is functionally operating in TCR, that it was once operating in TCR or in the common precursor of TCR and immunoglobulin, or that the hypermutation mechanism has evolved to exploit the codon usage in immunoglobulin (and fortuitously, TCR) rather than vice-versa. Our findings provide support to the hypothesis that somatic hypermutation appeared very early in the phylogeny of immune systems, that it is, to a large extent, shared between species, and that it makes an essential contribution to the generation of the antibody repertoire.

Human immunodeficiency virus type 1-specific cytotoxic T lymphocyte activity is inversely correlated with HIV type 1 viral load in HIV type 1-infected long-term survivors

HIV-1-specific cytotoxic T cell (CTL) activity has been suggested to correlate with protection from progression to AIDS. We have examined the relationship between HIV-specific CTL activity and maintenance of peripheral blood CD4+ T lymphocyte counts and control of viral load in 17 long-term survivors (LTSs) of HIV-1 infection. Longitudinal analysis indicated that the LTS cohort demonstrated a decreased rate of CD4+ T cell loss (18 cells/mm3/year) compared with typical normal progressors (approximately 60 cells/mm3/year). The majority of the LTSs had detectable, variable, and in some individuals, quite high (>10(4) RNA copies/ml) plasma viral load during the study period. In a cross-sectional analysis, HIV-specific CTL activity to HIV Gag, Pol, and Env proteins was detectable in all 17 LTSs. Simultaneous analysis of HIV-1 Gag-Pol, and Env-specific CTLs and virus load in protease inhibitor-naive individuals showed a significant inverse correlation between Pol-specific CTL activity and plasma HIV-1 RNA levels (p = 0.001). Furthermore, using a mixed linear effects model the combined effects of HIV-1 Pol- and Env-specific CTL activity on the viral load were significantly stronger than the effects of HIV-1 Pol-specific CTL activity alone on predicted virus load. These data suggest that the presence of HIV-1-specific CTL activity in HIV-1-infected long-term survivors is an important component in the effective control of HIV-1 replication.

Enhanced evolvability in immunoglobulin V genes under somatic hypermutation

Darwinian theory requires that mutations be produced in a nonanticipatory manner; it is nonetheless consistent to suggest that mutations that have repeatedly led to nonviable phenotypes would be introduced less frequently than others-if under appropriate genetic control. Immunoglobulins produced during infection acquire point mutations that are subsequently selected for improved binding to the eliciting antigen. We and others have speculated that an enhancement of mutability in the complementarity-determining regions (CDR; where mutations have a greater chance of being advantageous) and/or decrement of mutability in the framework regions (FR; where mutations are more likely to be lethal) may be accomplished by differential codon usage in concert with the known sequence specificity of the hypermutation mechanism. We have examined 115 nonproductively rearranged human Ig sequences. The mutation patterns in these unexpressed genes are unselected and therefore directly reflect inherent mutation biases. Using a chi2 test, we have shown that the number of mutations in the CDRs is significantly higher than the number of mutations found in the FRs, providing direct evidence for the hypothesis that mutations are preferentially targeted into the CDRs.

Quantitative evaluation of alternative mechanisms of blood and testes disposition of di(2-ethylhexyl) phthalate and mono(2-ethylhexyl) phthalate in rats

Di(2-ethylhexyl) phthalate (DEHP), a commercially important plasticizer, induces testicular toxicity in laboratory animals at high doses. After oral exposure, most of the DEHP is rapidly metabolized in the gut to mono(2-ethylhexyl) phthalate (MEHP), which is the active metabolite for induction of testicular toxicity. To quantify the testes dose of MEHP with various routes of exposure and dose levels, we developed a physiologically based pharmacokinetic (PBPK) model for DEHP and MEHP in rats. Tissue:blood partition coefficients for DEHP were estimated from the n-octanol: water partition coefficient, while partition coefficients for MEHP were determined experimentally using a vial equilibration technique. All other parameters were either found in the literature or estimated from blood or tissue levels following oral or intravenous exposure to DEHP or MEHP. A flow-limited model failed to adequately simulate the available data. Alternative plausible mechanisms were explored, including diffusion-limited membrane transport, enterohepatic circulation, and MEHP ionization (pH-trapping model). In the pH-trapping model, only nonionized MEHP is free to become partitioned into the tissues, where it is equilibrated and trapped as ionized MEHP until it is deionized and released. All three alternative models significantly improved predictions of DEHP and MEHP blood concentrations over the flow-limited model predictions. The pH-trapping model gave the best predictions with the largest value of the log likelihood function. Predicted MEHP blood and testes concentrations were compared to measured concentrations in juvenile rats to validate the pH-trapping model. Thus, MEHP ionization may be an important mechanism of MEHP blood and testes disposition in rats.

Nucleotide pool imbalance and adenosine deaminase deficiency induce alterations of N-region insertions during V(D)J recombination

Template-independent nucleotide additions (N regions) generated at sites of V(D)J recombination by terminal deoxynucleotidyl transferase (TdT) increase the diversity of antigen receptors. Two inborn errors of purine metabolism, deficiencies of adenosine deaminase (ADA) and purine nucleoside phosphorylase (PNP), result in defective lymphoid development and aberrant pools of 2'-deoxynucleotides that are substrates for TdT in lymphoid precursors. We have asked whether selective increases in dATP or dGTP pools result in altered N regions in an extrachromosomal substrate transfected into T-cell or pre-B-cell lines. Exposure of the transfected cells to 2'-deoxyadenosine and an ADA inhibitor increased the dATP pool and resulted in a marked increase in A-T insertions at recombination junctions, with an overall decreased frequency of V(D)J recombination. Sequence analysis of VH-DH-JH junctions from the IgM locus in B-cell lines from ADA-deficient patients demonstrated an increase in A-T insertions equivalent to that found in the transfected cells. In contrast, elevation of dGTP pools, as would occur in PNP deficiency, did not alter the already rich G-C content of N regions. We conclude that the frequency of V(D)J recombination and the composition of N-insertions are influenced by increases in dATP levels, potentially leading to alterations in antigen receptors and aberrant lymphoid development. Alterations in N-region insertions may contribute to the B-cell dysfunction associated with ADA deficiency.

Drug concentration heterogeneity facilitates the evolution of drug resistance

Pathogenic microorganisms use Darwinian processes to circumvent attempts at their control through chemotherapy. In the case of HIV-1 infection, in which drug resistance is a continuing problem, we show that in one-compartment systems, there is a relatively narrow window of drug concentrations that allows evolution of resistant variants. When the system is enlarged to two spatially distinct compartments held at different drug concentrations with transport of virus between them, the range of average drug concentrations that allow evolution of resistance is significantly increased. For high average drug concentrations, resistance is very unlikely to arise without spatial heterogeneity. We argue that a quantitative understanding of the role played by heterogeneity in drug levels and pathogen transport is crucial for attempts to control re-emergent infectious disease.

Predicted and inferred waiting times for key mutations in the germinal centre reaction: evidence for stochasticity in selection

The germinal centre reaction (GCR) is a fundamental component of the immune response to T-dependent antigens, during which the immunoglobulin (Ig) genes of B cells experience somatic hypermutation and selection. A maximum-likelihood method on DNA sequence data from 16 individual germinal centres was used to infer that the waiting time for position 33 key (high-affinity) mutations in the anti-(4-hydroxy-3-nitrophenyl) acetyl (NP) response is 8.3 days. This is in marked contrast to the prediction of a key mutant each generation (waiting time about 1/3 day) obtained from a simple model and parameters available in the literature. This disagreement is resolved in part by the finding that the targeted base occurs in a cold spot for hypermutation, raising the predicted waiting time to 2.3 days, although this value remains significantly lower than that inferred from the sequence data. It is proposed that the remaining disparity is attributable to some further stochastic process in the GCR: many early key mutations arise but fail to 'take root' within the GC, either due to emigration or failure of cognate T cell/B cell interaction. Furthermore, it is argued that the frequency with which position 33 mutations are found in secondary responses to NP indicates the presence of selection after the GCR.

The distribution of variation in regulatory gene segments, as present in MHC class II promoters

Diversity in the antigen-binding receptors of the immune system has long been a primary interest of biologists. Recently it has been suggested that polymorphism in regulatory (noncoding) gene segments is of substantial importance as well. Here, we survey the level of variation in MHC class II gene promoters in man and mouse using extensive collections of published sequences together with unpublished sequences recently deposited by us in the EMBL gene bank using the Shannon entropy to quantify diversity. For comparison, we also apply our analysis to distantly related MHC class II promoters, as well as to class I promoters and to class II coding regions. We observe a high level of intraspecies variability, which in mouse but not in man is localized to a significant extent near the binding sites of transcription factors-sites that are conserved over longer evolutionary distances. This localization may both indicate and enhance heterozygote advantage, as the presence of two functionally different promoters would be expected to confer flexibility in the immune response.

Density-dependent prenatal androgen exposure as an endogenous mechanism for the generation of cycles in small mammal populations

Small mammal populations exhibit cyclic fluctuations in their population densities. Several hypotheses regarding the mechanisms underlying these population cycles have been advanced, but none has yet gained general approval. We propose here an endogenous mechanism based on the masculinization of female offspring in response to increased population levels. High population levels trigger the non-specific stress response resulting in high levels of circulating androgens in individuals of the population, including pregnant females. These androgens masculinize female offspring in utero, thereby reducing the reproductive capacity of the next generation and subsequently the population size. We have developed and analysed a mathematical model to investigate the possible role of prenatal androgen exposure in the generation of limit cycles. We find the locus of Hopf bifurcations for this model and show that limit cycles depend on three parameters: (1) the delay between birth and sexual maturation; (2) the slope of the function that relates average prenatal androgen exposure to total population density; and (3) the difference between the maximum birth rates of the low- and high-androgen exposed females. We derive the analytical form relating these parameters at the Hopf-bifurcation locus and discuss its biological ramifications. In brief, in each of these three parameters is sufficiently large, population cycles will results from the endogenous mechanism proposed.Copyright 1998 Academic Press Limited Copyright 1998 Academic Press Limited

Codon bias and plasticity in immunoglobulins

Immunoglobulin genes experience Darwinian evolution twice. In addition to the germline evolution all genes experience, immunoglobulins are subjected, upon exposure to antigen, to somatic hypermutation. This is accompanied by selection for high affinity to the eliciting antigen and frequently results in a significant increase in the specificity of the responding population. The hypermutation mechanism displays a strong sequence specificity. Thus arises the opportunity to manipulate codon bias in a site-specific manner so as to direct hypermutation to those parts of the gene that encode the antigen-binding portions of the molecule and away from those that encode the structurally conserved regions. This segregation of mutability would clearly be advantageous; it would enhance the generation of potentially useful variants while keeping mutational loss to acceptably low levels. But it is not clear that the advantage gained would be large enough to produce a measurable effect within the background stochasticity of the evolutionary process. I have performed a pair of statistical tests to determine whether site-specific codon bias in human immunoglobulin genes is correlated with the sequence specificity of the somatic mutation mechanism. The sequence specificity of the mutator was determined by analysis of a database of published immunoglobulin intron sequences that had experienced somatic mutation but not selection. The site-specific codon bias was determined by analysis of published sequences of human germline immunoglobulin V genes. Both tests strongly suggest that evolution has acted to enhance the plasticity of immunoglobulin genes under somatic hypermutation.

Interdependence of N nucleotide addition and recombination site choice in V(D)J rearrangement

Diversity in the Ag binding receptors of B and T cells is achieved through a process of genomic rearrangement involving selection of recombination sites and, in adult mice, addition of nontemplated (N) nucleotides. We have analyzed 543 Ig heavy chain nonproductive rearrangements, involving a single variable region gene segment, from adult and perinatal mice. We infer several fundamental and novel features of the recombination mechanism. N regions are formed predominantly from the DNA plus strand or from the DNA minus strand polymerizations, rather than as a concatenation of the two. Homologous overlaps of as few as one nucleotide between gene segments cause significant skewing of recombination sites. The V(H) recombination site spectrum differs in perinatal and adult mice, with sites representing overlap between V(H) and D over-represented in the perinatal mice, and sites representing overlaps between V(H) and the N strand polymerized onto the D segment over-represented in the adult mice. Thus, in V(D)J joining, N nucleotide addition and recombination site choice are highly interdependent events.

Interdependence of N nucleotide addition and recombination site choice in V(D)J rearrangement

Diversity in the Ag binding receptors of B and T cells is achieved through a process of genomic rearrangement involving selection of recombination sites and, in adult mice, addition of nontemplated (N) nucleotides. We have analyzed 543 Ig heavy chain nonproductive rearrangements, involving a single variable region gene segment, from adult and perinatal mice. We infer several fundamental and novel features of the recombination mechanism. N regions are formed predominantly from the DNA plus strand or from the DNA minus strand polymerizations, rather than as a concatenation of the two. Homologous overlaps of as few as one nucleotide between gene segments cause significant skewing of recombination sites. The V(H) recombination site spectrum differs in perinatal and adult mice, with sites representing overlap between V(H) and D over-represented in the perinatal mice, and sites representing overlaps between V(H) and the N strand polymerized onto the D segment over-represented in the adult mice. Thus, in V(D)J joining, N nucleotide addition and recombination site choice are highly interdependent events.

Modeling and optimization of populations subject to time-dependent mutation

It has become clear that many organisms possess the ability to regulate their mutation rate in response to environmental conditions. So the question of finding an optimal mutation rate must be replaced by that of finding an optimal mutation schedule. We show that this task cannot be accomplished with standard population-dynamic models. We then develop a "hybrid" model for populations experiencing time-dependent mutation that treats population growth as deterministic but the time of first appearance of new variants as stochastic. We show that the hybrid model agrees well with a Monte Carlo simulation. From this model, we derive a deterministic approximation, a "threshold" model, that is similar to standard population dynamic models but differs in the initial rate of generation of new mutants. We use these techniques to model antibody affinity maturation by somatic hypermutation. We had previously shown that the optimal mutation schedule for the deterministic threshold model is phasic, with periods of mutation between intervals of mutation-free growth. To establish the validity of this schedule, we now show that the phasic schedule that optimizes the deterministic threshold model significantly improves upon the best constant-rate schedule for the hybrid and Monte Carlo models.

Cellular interaction in germinal centers. Roles of CD40 ligand and B7-2 in established germinal centers

Costimulatory interactions between T and B lymphocytes are crucial for T cell activation and B cell proliferation and differentiation. We have compared the roles of CD40L and B7-2 in the initiation and maturation of humoral immunity by administering anti-CD40 ligand (L) or anti-B7-2 Ab during the early (days -1 to 3) or late (days 6-10) phases of primary responses to thymus-dependent (Td) and -independent (Ti) Ags. Germinal center (GC) formation in response to a Td Ag was inhibited completely by the early administration of anti-CD40L or anti-B7-2 Abs. Later in the response, established GCs remained sensitive to anti-CD40L but were resistant to treatment with anti-B7-2. However, Ig hypermutation was reduced dramatically in GCs of anti-B7-2-treated mice and humoral memory was impaired. Early administration of anti-CD40L reduced serum Ab levels to approximately 10% of controls, whereas early treatment with anti-B7-2 reduced Ab production by only 50%. Later treatments with either Ab had no effect on Ab production. Response to a type II Ti Ag was more resistant than Td responses to interruption of costimulatory interactions. Our findings suggest that the costimulatory roles of CD40:CD40L and B7-2:CD28/CTLA-4 differ in the GC; administration of anti-CD40L abrogates an established GC reaction, whereas Ab to B7-2 suppresses Ig hypermutation and entry into the B cell memory compartment. Once B cells have entered the differentiation pathway to Ab production, neither CD40L nor B7-2 is necessary for their continued differentiation and persistence.

Cellular interaction in germinal centers. Roles of CD40 ligand and B7-2 in established germinal centers

Costimulatory interactions between T and B lymphocytes are crucial for T cell activation and B cell proliferation and differentiation. We have compared the roles of CD40L and B7-2 in the initiation and maturation of humoral immunity by administering anti-CD40 ligand (L) or anti-B7-2 Ab during the early (days -1 to 3) or late (days 6-10) phases of primary responses to thymus-dependent (Td) and -independent (Ti) Ags. Germinal center (GC) formation in response to a Td Ag was inhibited completely by the early administration of anti-CD40L or anti-B7-2 Abs. Later in the response, established GCs remained sensitive to anti-CD40L but were resistant to treatment with anti-B7-2. However, Ig hypermutation was reduced dramatically in GCs of anti-B7-2-treated mice and humoral memory was impaired. Early administration of anti-CD40L reduced serum Ab levels to approximately 10% of controls, whereas early treatment with anti-B7-2 reduced Ab production by only 50%. Later treatments with either Ab had no effect on Ab production. Response to a type II Ti Ag was more resistant than Td responses to interruption of costimulatory interactions. Our findings suggest that the costimulatory roles of CD40:CD40L and B7-2:CD28/CTLA-4 differ in the GC; administration of anti-CD40L abrogates an established GC reaction, whereas Ab to B7-2 suppresses Ig hypermutation and entry into the B cell memory compartment. Once B cells have entered the differentiation pathway to Ab production, neither CD40L nor B7-2 is necessary for their continued differentiation and persistence.

Somatic hypermutation in B cells: an optimal control treatment

The vertebrate immune system generates high-affinity antibodies to external antigens through a process of somatic hypermutation that takes place in germinal centers formed in the secondary lymphoid tissues. B cells proliferating in these germinal centers experience random mutations in the genes encoding the variable region of their immunoglobulin molecules and are subsequently selected for high-affinity binding to antigen. These germinal center reactions last for only about 2 weeks, yet in that time typically produce multiple point mutations resulting in affinity increases of factors of ten to a hundred or more. We have attempted to understand this extraordinary effectiveness by causing the problem of affinity maturation as an optimization problem in which a quantity that we call the total affinity is maximized as a functional of mu(t), the mutation rate as a function of time. We have developed a single-compartment model for the process and an optimization algorithm based on the Pontryagin maximum principle. Our results show that the optimum mutation schedule is one with brief bursts of high mutation rates interspersed between periods of mutation-free growth. Though this result at first seems highly non-physiological, we show that, in fact, it provides a framework within which the anatomy and kinetics of the germinal center reaction can be understood.

Cyclic re-entry of germinal center B cells and the efficiency of affinity maturation

Affinity maturation of the humoral immune response by somatic hypermutation is marked by a rapid and dramatic increase in affinity for the eliciting antigen. We suggest that the optimal mutation schedule is one in which periods of rapid mutation alternate with periods of mutation-free growth. The multicompartmental structure of the germinal center, together with re-entry of positively selected B cells back into the germinal center, will naturally implement such a schedule, thereby providing an anatomical basis for the efficiency of the germinal center reaction.

Spike initiation and propagation on axons with slow inward currents

We investigate spike initiation and propagation in a model axon that has a slow regenerative conductance as well as the usual Hodgkin-Huxley type sodium and potassium conductances. We study the role of slow conductance in producing repetitive firing, compute the dispersion relation for an axon with an additional slow conductance, and show that under appropriate conditions such an axon can produce a traveling zone of secondary spike initiation. This study illustrates some of the complex dynamics shown by excitable membranes with fast and slow conductances.

Reduction of conductance-based neuron models

We present a scheme for systematically reducing the number of differential equations required for biophysically realistic neuron models. The techniques are general, are designed to be applicable to a large set of such models and retain in the reduced system as high a degree of fidelity to the original system as possible. As examples, we provide reductions of the Hodgkin-Huxley system and the A-current model of Connor et al. (1977).

Geometric phase shifts in chemical oscillators

One of the most remarkable developments in quantum mechanics in recent years has been the discovery that when a system is moved adiabatically around a closed loop in parameter space there occurs, besides the familiar dynamical phase shift, an additional phase shift (sometimes referred to as 'Berry's phase') that is purely geometric in nature. The dynamical phase shift, which results from the variation of the period of the oscillatory system with the change in parameters, is relatively easily understood and is proportional to the time over which the parameter change occurs. The geometric phase shift, on the other hand, is less intuitive and depends on the curvature of the surface in parameter space bounded by the closed path, but is independent of the time taken to traverse the circuit. Here we present evidence for time-independent geometric phase shifts in numerical solutions for a model of an oscillating chemical reaction. The conditions for the occurrence of such shifts seem to be sufficiently general that geometric phase effects should be experimentally observable in essentially all chemical oscillators as well as in biological networks such as the brain and the central nervous system, where phase control is of vital importance.

The effect of electrical coupling on the frequency of model neuronal oscillators

Neurons with oscillatory properties are a common feature of the nervous system, but little is known about how neural oscillators shape the behavior of neuronal networks or how network interactions influence the properties of neural oscillators. Mathematical models are used to examine the effect of electrically coupling an oscillatory neuron to a second neuron that is either silent or tonically firing. Models of oscillatory neurons with varying degrees of complexity show that this coupling can either increase or decrease the frequency of an oscillator, depending on its membrane potential wave form, the state of the neuron to which it is coupled, and the strength of the coupling. Thus, electrical coupling provides a flexible mechanism for modifying the behavior of an oscillatory neural network.