@article{elston_kepler_2001, title={A linear two-state model with complex dynamics}, volume={280}, ISSN={["0375-9601"]}, DOI={10.1016/S0375-9601(01)00052-4}, abstractNote={We study the dynamics of a stochastic two-state model in which all forces are linear. While conceptually simple, we show that the behavior of this system is surprisingly complex. The moments of the system undergo a series of bifurcations as either the overall fluctuation rate or the ratio between the two transition rates is varied. The system displays the very counterintuitive behavior in which all its spatial moments diverge in time, and yet the mean time to escape from a region that includes the origin is infinite. Finally, the system displays resonant activation in a particularly transparent way.}, number={4}, journal={PHYSICS LETTERS A}, author={Elston, TC and Kepler, TB}, year={2001}, month={Feb}, pages={204–208} }
 @article{oprea_kepler_2001, title={Improved inference of mutation rates - II. Generalization of the Luria-Delbruck distribution for realistic cell-cycle time distributions}, volume={59}, ISSN={["0040-5809"]}, DOI={10.1006/tpbi.2000.1504}, abstractNote={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.}, number={1}, journal={THEORETICAL POPULATION BIOLOGY}, author={Oprea, M and Kepler, TB}, year={2001}, month={Feb}, pages={49–59} }
 @article{kepler_elston_2001, title={Stochasticity in transcriptional regulation: Origins, consequences, and mathematical representations}, volume={81}, ISSN={["0006-3495"]}, DOI={10.1016/S0006-3495(01)75949-8}, abstractNote={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.}, number={6}, journal={BIOPHYSICAL JOURNAL}, author={Kepler, TB and Elston, TC}, year={2001}, month={Dec}, pages={3116–3136} }
 @article{radmacher_kepler_2001, title={Waiting times to appearance and dominance of advantageous mutants: estimation based on the likelihood}, volume={170}, number={1}, journal={Mathematical Biosciences}, author={Radmacher, M. D. and Kepler, T. B.}, year={2001}, pages={59–77} }
 @article{keys_wallace_kepler_conolly_2000, title={Quantitative evaluation of alternative mechanisms of blood disposition of di(n-butyl) phthalate and mono(n-butyl) phthalate in rats}, volume={53}, ISSN={["1096-0929"]}, DOI={10.1093/toxsci/53.2.173}, abstractNote={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.}, number={2}, journal={TOXICOLOGICAL SCIENCES}, author={Keys, DA and Wallace, DG and Kepler, TB and Conolly, RB}, year={2000}, month={Feb}, pages={173–184} }
 @article{cowell_kepler_2000, title={The nucleotide-replacement spectrum under somatic hypermutation exhibits microsequence dependence that is strand-symmetric and distinct from that under germline mutation}, volume={164}, ISSN={["1550-6606"]}, DOI={10.4049/jimmunol.164.4.1971}, abstractNote={Abstract}, number={4}, journal={JOURNAL OF IMMUNOLOGY}, author={Cowell, LG and Kepler, TB}, year={2000}, month={Feb}, pages={1971–1976} }
 @article{cowell_kim_humaljoki_berek_kepler_1999, title={Enhanced evolvability in immunoglobulin V genes under somatic hypermutation}, volume={49}, ISSN={["0022-2844"]}, DOI={10.1007/PL00006530}, abstractNote={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.}, number={1}, journal={JOURNAL OF MOLECULAR EVOLUTION}, author={Cowell, LG and Kim, HJ and Humaljoki, T and Berek, C and Kepler, TB}, year={1999}, month={Jul}, pages={23–26} }
 @article{oprea_kepler_1999, title={Genetic plasticity of V genes under somatic hypermutation: Statistical analyses using a new resampling-based methodology}, volume={9}, ISSN={["1088-9051"]}, DOI={10.1101/gr.9.12.1294}, abstractNote={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 individualVgenes and inVgene 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 immunoglobulinVgenes 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 TCRVβsequences 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.}, number={12}, journal={GENOME RESEARCH}, author={Oprea, M and Kepler, TB}, year={1999}, month={Dec}, pages={1294–1304} }
 @article{betts_krowka_kepler_davidian_christopherson_kwok_louie_eron_sheppard_frelinger_1999, title={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}, volume={15}, ISSN={["1931-8405"]}, DOI={10.1089/088922299310313}, abstractNote={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.}, number={13}, journal={AIDS RESEARCH AND HUMAN RETROVIRUSES}, author={Betts, MR and Krowka, JF and Kepler, TB and Davidian, M and Christopherson, C and Kwok, S and Louie, L and Eron, J and Sheppard, H and Frelinger, JA}, year={1999}, month={Sep}, pages={1219–1228} }
 @article{gangi-peterson_sorscher_reynolds_kepler_mitchell_1999, title={Nucleotide pool imbalance and adenosine deaminase deficiency induce alterations of N-region insertions during V(D)J recombination}, volume={103}, ISSN={["0021-9738"]}, DOI={10.1172/JCI4320}, abstractNote={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.}, number={6}, journal={JOURNAL OF CLINICAL INVESTIGATION}, author={Gangi-Peterson, L and Sorscher, DH and Reynolds, JW and Kepler, TB and Mitchell, BS}, year={1999}, month={Mar}, pages={833–841} }
 @article{keys_wallace_kepler_conolly_1999, title={Quantitative evaluation of alternative mechanisms of blood and testes disposition of di(2-ethylhexyl) phthalate and mono(2-ethylhexyl) phthalate in rats}, volume={49}, ISSN={["1096-6080"]}, DOI={10.1093/toxsci/49.2.172}, abstractNote={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.}, number={2}, journal={TOXICOLOGICAL SCIENCES}, author={Keys, DA and Wallace, DG and Kepler, TB and Conolly, RB}, year={1999}, month={Jun}, pages={172–185} }
 @article{cowell_crowder_kepler_1998, title={Density-dependent prenatal androgen exposure as an endogenous mechanism for the generation of cycles in small mammal populations}, volume={190}, ISSN={["1095-8541"]}, DOI={10.1006/jtbi.1997.0543}, abstractNote={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}, number={1}, journal={JOURNAL OF THEORETICAL BIOLOGY}, author={Cowell, LG and Crowder, LB and Kepler, TB}, year={1998}, month={Jan}, pages={93–106} }
 @article{kepler_perelson_1998, title={Drug concentration heterogeneity facilitates the evolution of drug resistance}, volume={95}, ISSN={["0027-8424"]}, DOI={10.1073/pnas.95.20.11514}, abstractNote={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.}, number={20}, journal={PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA}, author={Kepler, TB and Perelson, AS}, year={1998}, month={Sep}, pages={11514–11519} }
 @inbook{kepler_bartl_1998, title={Plasticity under somatic mutation in antigen receptors}, volume={229}, booktitle={Somatic diversification of immune responses (Current topics in microbiology and immunology ; 229)}, publisher={Berlin; New York: Springer}, author={Kepler, T. B. and Bartl, S.}, editor={G. Kelsoe and Flajnik, M. F.Editors}, year={1998}, pages={149–162} }
 @article{radmacher_kelsoe_kepler_1998, title={Predicted and inferred waiting times for key mutations in the germinal centre reaction: Evidence for stochasticity in selection}, volume={76}, ISSN={["1440-1711"]}, DOI={10.1046/j.1440-1711.1998.00753.x}, abstractNote={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.}, number={4}, journal={IMMUNOLOGY AND CELL BIOLOGY}, author={Radmacher, MD and Kelsoe, G and Kepler, TB}, year={1998}, month={Aug}, pages={373–381} }
 @article{cowell_kepler_janitz_lauster_mitchison_1998, title={The distribution of variation in regulatory gene segments, as present in MHC class II promoters}, volume={8}, ISSN={["1549-5469"]}, DOI={10.1101/gr.8.2.124}, abstractNote={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.}, number={2}, journal={GENOME RESEARCH}, author={Cowell, LG and Kepler, TB and Janitz, M and Lauster, R and Mitchison, NA}, year={1998}, month={Feb}, pages={124–134} }
 @article{kepler_1997, title={Codon bias and plasticity in immunoglobulins}, volume={14}, ISSN={["0737-4038"]}, DOI={10.1093/oxfordjournals.molbev.a025803}, abstractNote={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.}, number={6}, journal={MOLECULAR BIOLOGY AND EVOLUTION}, author={Kepler, TB}, year={1997}, month={Jun}, pages={637–643} }
 @article{kepler_borrero_rugerio_mccray_clarke_1996, title={Interdependence of N nucleotide addition and recombination site choice in V(D)J rearrangement}, volume={157}, number={10}, journal={Journal of Immunology}, author={Kepler, T. B. and Borrero, M. and Rugerio, B. and McCray, S. K. and Clarke, S. H.}, year={1996}, pages={4451} }
 @article{han_hathcock_zheng_kepler_hodes_kelsoe_1995, title={Cellular interaction in germinal-centers - roles of cd40 ligand and b7-2 in established germinal-centers}, volume={155}, number={2}, journal={Journal of Immunology}, author={Han, S. H. and Hathcock, K. and Zheng, B. and Kepler, T. B. and Hodes, R. and Kelsoe, G.}, year={1995}, pages={556–567} }