Publications

* denotes equal contribution
$ denotes equal contribution
  1. L. M. Childs, F. El Moustaid, Z. Gajewski, S. Kadelka, R. Nikin-Beers, J. W. Smith, Jr., M. Walker, L. R. Johnson (2019) Linked within-host and between-host models and data for infectious diseases: a systematic review. PeerJ, doi.org/10.7717/peerj.7057 PeerJ
    Abstract
      [Hide]    The observed dynamics of infectious diseases are driven by processes across multiple scales. Here we focus on two: within-host, that is, how an infection progresses inside a single individual (for instance viral and immune dynamics), and between-host, that is, how the infection is transmitted between multiple individuals of a host population. The dynamics of each of these may be influenced by the other, particularly across evolutionary time. Thus understanding each of these scales, and the links between them, is necessary for a holistic understanding of the spread of infectious diseases. One approach to combining these scales is through mathematical modeling. We conducted a systematic review of the published literature on multi-scale mathematical models of disease transmission (as defined by combining within-host and between-host scales) to determine the extent to which mathematical models are being used to understand across-scale transmission, and the extent to which these models are being confronted with data. Following the PRISMA guidelines for systematic reviews, we identified 24 of 197 qualifying papers across 30 years that include both linked models at the within and between host scales and that used data to parameterize/calibrate models. We find that the approach that incorporates both modeling with data is under-utilized, if increasing. This highlights the need for better communication and collaboration between modelers and empiricists to build well-calibrated models that both improve understanding and may be used for prediction.
  2. D. G. Paton, L. M. Childs, M. A. Itoe, I. E. Holmdahl, C. O. Buckee, F. Catteruccia (2019) Exposing Anopheles mosquitoes to antimalarials blocks Plasmodium parasite transmission. Nature, doi.org/10.1038/s41586-019-0973-1 Nature
    Abstract
      [Hide]    Bites of Anopheles mosquitoes transmit Plasmodium falciparum parasites that cause malaria, which kills hundreds of thousands of people every year. Since the turn of this century, efforts to prevent the transmission of these parasites via the mass distribution of insecticide-treated bed nets have been extremely successful, and have led to an unprecedented reduction in deaths from malaria. However, resistance to insecticides has become widespread in Anopheles populations, which has led to the threat of a global resurgence of malaria and makes the generation of effective tools for controlling this disease an urgent public health priority. Here we show that the development of P. falciparum can be rapidly and completely blocked when female Anopheles gambiae mosquitoes take up low concentrations of specific antimalarials from treated surfaces—conditions that simulate contact with a bed net. Mosquito exposure to atovaquone before, or shortly after, P. falciparum infection causes full parasite arrest in the midgut, and prevents transmission of infection. Similar transmission-blocking effects are achieved using other cytochrome b inhibitors, which demonstrates that parasite mitochondrial function is a suitable target for killing parasites. Incorporating these effects into a model of malaria transmission dynamics predicts that impregnating mosquito nets with Plasmodium inhibitors would substantially mitigate the global health effects of insecticide resistance. This study identifies a powerful strategy for blocking Plasmodium transmission by female Anopheles mosquitoes, which has promising implications for efforts to eradicate malaria.
  3. J. C. Blackwood, L. M. Childs (2018) An introduction to compartmental modeling for the budding infectious disease modeler. Letters in Biomathematics, doi.org/10.1080/23737867.2018.1509026 Letters in Biomath
    Abstract
      [Hide]    Mathematical models are ubiquitous in the study of the transmission dynamics of infectious diseases, In particular, the classic ‘susceptible-infectious-recovered’ (SIR) paradigm provides a modeling framework that can be adapted to describe the core transmission dynamics of a range of human and wildlife diseases. These models provide an important tool for uncovering the mechanisms generating observed disease dynamics, evaluating potential control strategies, and predicting future outbreaks. With ongoing advances in computational tools as well as access to disease incidence data, the use of such models continues to increase. Here, we provide a basic introduction to disease modeling that is primarily intended for individuals who are new to developing SIR-type models. In particular, we highlight several common issues encountered when structuring and analyzing these models.
  4. N. M. Archer, N. Petersen, M. A. Clark, C. O. Buckee, L. M. Childs, M. T. Duraisingh (2018) Resistance to Plasmodium falciparum in sickle cell trait erythrocytes is driven by oxygen-dependent growth inhibition. PNAS, doi.org/10.1073/pnas.1804388115 PNAS
    Abstract
      [Hide]    Sickle cell trait (AS) confers partial protection against lethal Plasmodium falciparum malaria. Multiple mechanisms for this have been proposed, with a recent focus on aberrant cytoadherence of parasite-infected red blood cells (RBCs). Here we investigate the mechanistic basis of AS protection through detailed temporal mapping. We find that parasites in AS RBCs maintained at low oxygen concentrations stall at a specific stage in the middle of intracellular growth before DNA replication. We demonstrate that polymerization of sickle hemoglobin (HbS) is responsible for this growth arrest of intraerythrocytic P. falciparum parasites, with normal hemoglobin digestion and growth restored in the presence of carbon monoxide, a gaseous antisickling agent. Modeling of growth inhibition and sequestration revealed that HbS polymerization-induced growth inhibition following cytoadherence is the critical driver of the reduced parasite densities observed in malaria infections of individuals with AS. We conclude that the protective effect of AS derives largely from effective sequestration of infected RBCs into the hypoxic microcirculation.
  5. M. Walker, J. C. Blackwood, V. Brown, L. M. Childs (2018) Modelling Allee effects in a transgenic mosquito population during range expansion. Journal of Biological Dynamics, doi:10.1080/17513758.2018.1464219 JBD
    Abstract
      [Hide]    Mosquitoes are vectors for many diseases that cause significant mortality and morbidity. As mosquito populations expand their range, they may undergo mate-finding Allee effects such that their ability to successfully reproduce becomes difficult at low population density. With new technology, creating target specific gene modification may be a viable method for mosquito population control. We develop a mathematical model to investigate the effects of releasing transgenic mosquitoes into newly established, low-density mosquito populations. Our model consists of two life stages (aquatic and adults), which are divided into three genetically distinct groups: heterogeneous and homogeneous transgenic that cause female infertility and a homogeneous wild type. We perform analytical and numerical analyses on the equilibria to determine the level of saturation needed to eliminate mosquitoes in a given area. This model demonstrates the potential for a gene drive system to reduce the spread of invading mosquito populations.
  6. R. Nikin-Beers, J. C. Blackwood, L. M. Childs, S. M. Ciupe, (2018) Unraveling within-host signatures of dengue infection at the population level. Journal of Theoretical Biology, doi:10.1016/j.jtbi.2018.03.004 Pub Med
    Abstract
      [Hide]    Dengue virus causes worldwide concern with nearly 100 million infected cases reported annually. The within-host dynamics differ between primary and secondary infections, where secondary infections with a different virus serotype typically last longer, produce higher viral loads, and induce more severe disease. We build upon the variable within-host virus dynamics during infections resulting in mild dengue fever and severe dengue hemorrhagic fever. We couple these within-host virus dynamics to a population-level model through a system of partial differential equations creating an immuno-epidemiological model. The resulting multiscale model examines the dynamics of between-host infections in the presence of two circulating virus strains that involves feedback from the within-host and between-hosts interactions, encompassing multiple scales. We analytically determine the relationship between the model parameters and the characteristics of the model’s solutions, and find an analytical threshold under which infections persist in the population. Furthermore, we develop and implement a full numerical scheme for our immuno-epidemiological model, allowing the simulation of population dynamics under variable parameter conditions.
  7. O. Maxian*, A. Neufeld*, E. J. Talis*, L. M. Childs$, J. C. Blackwood$, (2017) Zika virus dynamics: When does sexual transmission matter? Epidemics, doi:10.1016/j.epidem.2017.06.003 Science Direct
    Abstract
      [Hide]    The Zika virus (ZIKV) has captured worldwide attention with the ongoing epidemic in South America and its link to severe birth defects, most notably microcephaly. ZIKV is spread to humans through a combination of vector and sexual transmission, but the relative contribution of these transmission routes to the overall epidemic remains largely unknown. Furthermore, a disparity in the reported number of infections between males and females has been observed. We develop a mathematical model that describes the transmission dynamics of ZIKV to determine the processes driving the observed epidemic patterns. Our model reveals a 4.8% contribution of sexual transmission to the basic reproductive number, R0. This contribution is too minor to independently sustain an outbreak but suggests that vector transmission is the main driver of the ongoing epidemic. We also find a minor, yet statistically significant, difference in the mean number of cases in males and females, both at the peak of the epidemic and at equilibrium. While this suggests an intrinsic disparity between males and females, the differences do not account for the vastly greater number of reported cases for females, indicative of a large reporting bias. In addition, we identify conditions under which sexual transmission may play a key role in sparking an epidemic, including temperate areas where ZIKV mosquito vectors are less prevalent.
  8. L. M. Childs*, O. F. Prosper*, (2017) Simulating within-vector generation of the malaria parasite diversity. PLoS One, doi:10.1371/journal.pone.0177941 PLoS One
    Abstract
      [Hide]    Plasmodium falciparum, the most virulent human malaria parasite, undergoes asexual reproduction within the human host, but reproduces sexually within its vector host, the Anopheles mosquito. Consequently, the mosquito stage of the parasite life cycle provides an opportunity to create genetically novel parasites in multiply-infected mosquitoes, potentially increasing parasite population diversity. Despite the important implications for disease transmission and malaria control, a quantitative mapping of how parasite diversity entering a mosquito relates to diversity of the parasite exiting, has not been undertaken. To examine the role that vector biology plays in modulating parasite diversity, we develop a two-part model framework that estimates the diversity as a consequence of different bottlenecks and expansion events occurring during the vector-stage of the parasite life cycle. For the underlying framework, we develop the first stochastic model of within-vector P. falciparum parasite dynamics and go on to simulate the dynamics of two parasite subpopulations, emulating multiply infected mosquitoes. We show that incorporating stochasticity is essential to capture the extensive variation in parasite dynamics, particularly in the presence of multiple parasites. In particular, unlike deterministic models, which always predict the most fit parasites to produce the most sporozoites, we find that occasionally only parasites with lower fitness survive to the sporozoite stage. This has important implications for onward transmission. The second part of our framework includes a model of sequence diversity generation resulting from recombination and reassortment between parasites within a mosquito. Our two-part model framework shows that bottlenecks entering the oocyst stage decrease parasite diversity from what is present in the initial gametocyte population in a mosquito’s blood meal. However, diversity increases with the possibility for recombination and proliferation in the formation of sporozoites. Furthermore, when we begin with two parasite subpopulations in the initial gametocyte population, the probability of transmitting more than two unique parasites from mosquito to human is over 50% for a wide range of initial gametocyte densities.
  9. C. Peak, L. M. Childs, Y. H. Grad, C. O. Buckee, (2017) Comparing nonpharmaceutical interventions for containing emerging epidemics. PNAS, doi:10.1073/pnas.1616438114 PNAS
    Abstract
      [Hide]    Strategies for containing an emerging infectious disease outbreak must be nonpharmaceutical when drugs or vaccines for the pathogen do not yet exist or are unavailable. The success of these nonpharmaceutical strategies will depend on not only the effectiveness of isolation measures but also the epidemiological characteristics of the infection. However, there is currently no systematic framework to assess the relationship between different containment strategies and the natural history and epidemiological dynamics of the pathogen. Here, we compare the effectiveness of quarantine and symptom monitoring, implemented via contact tracing, in controlling epidemics using an agent-based branching model. We examine the relationship between epidemic containment and the disease dynamics of symptoms and infectiousness for seven case-study diseases with diverse natural histories, including Ebola, influenza A, and severe acute respiratory syndrome (SARS). We show that the comparative effectiveness of symptom monitoring and quarantine depends critically on the natural history of the infectious disease, its inherent transmissibility, and the intervention feasibility in the particular healthcare setting. The benefit of quarantine over symptom monitoring is generally maximized for fast-course diseases, but we show the conditions under which symptom monitoring alone can control certain outbreaks. This quantitative framework can guide policymakers on how best to use nonpharmaceutical interventions and prioritize research during an outbreak of an emerging pathogen.
  10. L. M. Childs*, F. Y. Cai*, E. G. Kakani*, S. N. Mitchell, D. Paton, P. Gabrieli, C. O. Buckee$, F. Catteruccia$, (2016) Disrupting Mosquito Reproduction and Parasite Development for Malaria Control. PLoS Pathogens, doi:10.1371/journal.ppat.1006060 PLoS Pathogens
    Abstract
      [Hide]    The control of mosquito populations with insecticide treated bed nets and indoor residual sprays remains the cornerstone of malaria reduction and elimination programs. In light of widespread insecticide resistance in mosquitoes, however, alternative strategies for reducing transmission by the mosquito vector are urgently needed, including the identification of safe compounds that affect vectorial capacity via mechanisms that differ from fast-acting insecticides. Here, we show that compounds targeting steroid hormone signaling disrupt multiple biological processes that are key to the ability of mosquitoes to transmit malaria. When an agonist of the steroid hormone 20-hydroxyecdysone (20E) is applied to Anopheles gambiae females, which are the dominant malaria mosquito vector in Sub Saharan Africa, it substantially shortens lifespan, prevents insemination and egg production, and significantly blocks Plasmodium falciparum development, three components that are crucial to malaria transmission. Modeling the impact of these effects on Anopheles population dynamics and Plasmodium transmission predicts that disrupting steroid hormone signaling using 20E agonists would affect malaria transmission to a similar extent as insecticides. Manipulating 20E pathways therefore provides a powerful new approach to tackle malaria transmission by the mosquito vector, particularly in areas affected by the spread of insecticide resistance.

  11. W. R. Shaw, P. Marcenac, L. M. Childs, C. O. Buckee, F. Baldini, S. P. Sawadogo, R. K. Dabire, A. Diabate, F. Catteruccia, (2016) Wolbachia infection in natural Anopheles populations affect egg laying and negatively correlate with Plasmodium development. Nature Communications, 7:11772. doi:10.1038/ncomms11772 PubMed
    Abstract
      [Hide]    The maternally inherited alpha-proteobacterium Wolbachia has been proposed as a tool to block transmission of devastating mosquito-borne infectious diseases like dengue and malaria. Here we study the reproductive manipulations induced by a recently identified Wolbachia strain that stably infects natural mosquito populations of a major malaria vector, Anopheles coluzzii, in Burkina Faso. We determine that these infections significantly accelerate egg laying but do not induce cytoplasmic incompatibility or sex-ratio distortion, two parasitic reproductive phenotypes that facilitate the spread of other Wolbachia strains within insect hosts. Analysis of 221 blood-fed A. coluzzii females collected from houses shows a negative correlation between the presence of Plasmodium parasites and Wolbachia infection. A mathematical model incorporating these results predicts that infection with these endosymbionts may reduce malaria prevalence in human populations. These data suggest that Wolbachia may be an important player in malaria transmission dynamics in Sub-Saharan Africa.

  12. J.C. Blackwood* and L. M. Childs*, (2016) The role of interconnectivity in control of an Ebola epidemic. Scientific Reports, 6:29262. doi:10.1038/srep29262 PubMed
    Abstract
      [Hide]    Several West African countries - Liberia, Sierra Leone and Guinea - experienced significant morbidity and mortality during the largest Ebola epidemic to date, from late 2013 through 2015. The extent of the epidemic was fueled by outbreaks in large urban population centers as well as movement of the pathogen between populations. During the epidemic there was no known vaccine or drug, so effective disease control required coordinated efforts that include both standard medical and community practices such as hospitalization, quarantine and safe burials. Due to the high connectivity of the region, control of the epidemic not only depended on internal strategies but also was impacted by neighboring countries. In this paper, we use a deterministic framework to examine the role of movement between two populations in the overall success of practices designed to minimize the extent of Ebola epidemics. We find that it is possible for even small amounts of intermixing between populations to positively impact the control of an epidemic on a more global scale.

  13. H. H. Chang, L. M. Childs, and C. O. Buckee, (2016) Variation in infection length and superinfection enhance selection efficiency in the human malaria parasite. Scientific Reports, 6:26370. doi:10.1038/srep26370 PubMed
    Abstract
      [Hide]    The capacity for adaptation is central to the evolutionary success of the human malaria parasite Plasmodium falciparum. Malaria epidemiology is characterized by the circulation of multiple, genetically diverse parasite clones, frequent superinfection, and highly variable infection lengths, a large number of which are chronic and asymptomatic. The impact of these characteristics on the evolution of the parasite is largely unknown, however, hampering our understanding of the impact of interventions and the emergence of drug resistance. In particular, standard population genetic frameworks do not accommodate variation in infection length or superinfection. Here, we develop a population genetic model of malaria including these variations, and show that these aspects of malaria infection dynamics enhance both the probability and speed of fixation for beneficial alleles in complex and non-intuitive ways. We find that populations containing a mixture of short- and long-lived infections promote selection efficiency. Interestingly, this increase in selection efficiency occurs even when only a small fraction of the infections are chronic, suggesting that selection can occur efficiently in areas of low transmission intensity, providing a hypothesis for the repeated emergence of drug resistance in the low transmission setting of Southeast Asia.

  14. N. Obaldia III, G. S. Dow, L. Gerena, D. Kyle, W. Otero, P. Y. Mantel, N. Baro, R. Daniels, A. Mukherjee, L. M. Childs, C. O. Buckee, M. T. Duraisingh, S. K. Volkman, D. F. Wirth, and M. Marti, (2016) Altered drug susceptibility during host adaptation of a Plasmodium falciparum strain in a non-human primate model. Scientific Reports. doi:10.1038/srep21216 PubMed
    Abstract
      [Hide]    Infections with Plasmodium falciparum, the most pathogenic of the Plasmodium species affecting man, have been reduced in part due to artemisinin-based combination therapies. However, artemisinin resistant parasites have recently emerged in South-East Asia. Novel intervention strategies are therefore urgently needed to maintain the current momentum for control and elimination of this disease. In the present study we characterize the phenotypic and genetic properties of the multi drug resistant (MDR) P. falciparum Thai C2A parasite strain in the non-human Aotus primate model, and across multiple passages. Aotus infections with C2A failed to clear upon oral artesunate and mefloquine treatment alone or in combination, and ex vivo drug assays demonstrated reduction in drug susceptibility profiles in later Aotus passages. Further analysis revealed mutations in the pfcrt and pfdhfr loci and increased parasite multiplication rate (PMR) across passages, despite elevated pfmdr1 copy number. Altogether our experiments suggest alterations in parasite population structure and increased fitness during Aotus adaptation. We also present data of early treatment failures with an oral artemisinin combination therapy in a pre-artemisinin resistant P. falciparum Thai isolate in this animal model.

  15. L. M. Childs, E. B. Baskerville, and S. Cobey, (2015) Trade-offs in antibody repertoires to complex antigens. Philosophical Transactions of the Royal Society of London B: Biological Sciences, 370(1676). doi:10.1098/rstb.2014.0245 PubMed
    Abstract
      [Hide]    Pathogens vary in their antigenic complexity. While some pathogens such as measles present a few relatively invariant targets to the immune system, others such as malaria display considerable antigenic diversity. How the immune response copes in the presence of multiple antigens, and whether a trade-off exists between the breadth and efficacy of antibody (Ab)-mediated immune responses, are unsolved problems. We present a theoretical model of affinity maturation of B-cell receptors (BCRs) during a primary infection and examine how variation in the number of accessible antigenic sites alters the Ab repertoire. Naive B cells with randomly generated receptor sequences initiate the germinal centre (GC) reaction. The binding affinity of a BCR to an antigen is quantified via a genotype-phenotype map, based on a random energy landscape, that combines local and distant interactions between residues. In the presence of numerous antigens or epitopes, B-cell clones with different specificities compete for stimulation during rounds of mutation within GCs. We find that the availability of many epitopes reduces the affinity and relative breadth of the Ab repertoire. Despite the stochasticity of somatic hypermutation, patterns of immunodominance are strongly shaped by chance selection of naive B cells with specificities for particular epitopes. Our model provides a mechanistic basis for the diversity of Ab repertoires and the evolutionary advantage of antigenically complex pathogens.

  16. S. K. Nilsson*, L. M. Childs*, C. O. Buckee, and M. Marti, (2015) Targeting human transmission biology for malaria elimination. PLoS Pathogens, 11(6):e1004871. doi:10.1371/journal.ppat.1004871 PubMed
    Abstract
      [Hide]    Malaria remains one of the leading causes of death worldwide, despite decades of public health efforts. The recent commitment by many endemic countries to eliminate malaria marks a shift away from programs aimed at controlling disease burden towards one that emphasizes reducing transmission of the most virulent human malaria parasite, Plasmodium falciparum. Gametocytes, the only developmental stage of malaria parasites able to infect mosquitoes, have remained understudied, as they occur in low numbers, do not cause disease, and are difficult to detect in vivo by conventional methods. Here, we review the transmission biology of P. falciparum gametocytes, featuring important recent discoveries of genes affecting parasite commitment to gametocyte formation, microvesicles enabling parasites to communicate with each other, and the anatomical site where immature gametocytes develop. We propose potential parasite targets for future intervention and highlight remaining knowledge gaps.

  17. L. M. Childs and C. O. Buckee, (2015) Dissecting the determinants of malaria chronicity: why within-host models struggle to reproduce infection dynamics. Journal of the Royal Society Interface, 12(104):20142379. doi:10.1098/rsif.2014.1379 PubMed
    Abstract
      [Hide]    The duration of infection is fundamental to the epidemiological behaviour of any infectious disease, but remains one of the most poorly understood aspects of malaria. In endemic areas, the malaria parasite Plasmodium falciparum can cause both acute, severe infections and asymptomatic, chronic infections through its interaction with the host immune system. Frequent superinfection and massive parasite genetic diversity make it extremely difficult to accurately measure the distribution of infection lengths, complicating the estimation of basic epidemiological parameters and the prediction of the impact of interventions. Mathematical models have qualitatively reproduced parasite dynamics early during infection, but reproducing long-lived chronic infections remains much more challenging. Here, we construct a model of infection dynamics to examine the consequences of common biological assumptions for the generation of chronicity and the impact of co-infection. We find that although a combination of host and parasite heterogeneities are capable of generating chronic infections, they do so only under restricted parameter choices. Furthermore, under biologically plausible assumptions, co-infection of parasite genotypes can alter the course of infection of both the resident and co-infecting strain in complex non-intuitive ways. We outline the most important puzzles for within-host models of malaria arising from our analysis, and their implications for malaria epidemiology and control.

  18. L. M. Childs, N. N. Abuelezam, C. Dye, S. Gupta, M. B. Murray, B. Williams, and C. O. Buckee, (2015) Modelling challenges in context: Lessons from malaria, HIV and tuberculosis. Epidemics, 10:102-107. doi:10.1016/j.epidem.2015.02.002 PubMed
    Abstract
      [Hide]    Malaria, HIV, and tuberculosis (TB) collectively account for several million deaths each year, with all three ranking among the top ten killers in low-income countries. Despite being caused by very different organisms, malaria, HIV, and TB present a suite of challenges for mathematical modellers that are particularly pronounced in these infections, but represent general problems in infectious disease modelling, and highlight many of the challenges described throughout this issue. Here, we describe some of the unifying challenges that arise in modelling malaria, HIV, and TB, including variation in dynamics within the host, diversity in the pathogen, and heterogeneity in human contact networks and behaviour. Through the lens of these three pathogens, we provide specific examples of the other challenges in this issue and discuss their implications for informing public health efforts.

  19. B. I. Coleman, K. M. Skillman, R. H. Y. Jiang, L. M. Childs, L. M. Altenhofen, M. Ganter, Y. Leung, I. Goldowitz, B. F. C. Kafsack, M. Marti, M. Llinas, C. O. Buckee, and M. T. Duraisingh, (2014) A Plasmodium falciparum histone deacetylase links parasite persistence and sexual conversion. Cell Host Microbe, 16(2):177-86. doi:10.1016/j.chom.2014.06.014 PubMed
    Abstract
      [Hide]    The asexual forms of the malaria parasite Plasmodium falciparum are adapted for chronic persistence in human red blood cells, continuously evading host immunity using epigenetically regulated antigenic variation of virulence-associated genes. Parasite survival on a population level also requires differentiation into sexual forms, an obligatory step for further human transmission. We reveal that the essential nuclear gene, P. falciparum histone deacetylase 2 (PfHda2), is a global silencer of virulence gene expression and controls the frequency of switching from the asexual cycle to sexual development. PfHda2 depletion leads to dysregulated expression of both virulence-associated var genes and PfAP2-g, a transcription factor controlling sexual conversion, and is accompanied by increases in gametocytogenesis. Mathematical modeling further indicates that PfHda2 has likely evolved to optimize the parasite's infectious period by achieving low frequencies of virulence gene expression switching and sexual conversion. This common regulation of cellular transcriptional programs mechanistically links parasite transmissibility and virulence.

  20. L. M. Childs*, W. E. England*, M. J. Young, J. S. Weitz, and R. J. Whitaker, (2014) CRISPR-induced distributed immunity in microbial populations. PLoS ONE, 9(7):e0101710. doi:10.1371/journal.pone.0101710 PubMed
    Abstract
      [Hide]    In bacteria and archaea, viruses are the primary infectious agents, acting as virulent, often deadly pathogens. A form of adaptive immune defense known as CRISPR-Cas enables microbial cells to acquire immunity to viral pathogens by recognizing specific sequences encoded in viral genomes. The unique biology of this system results in evolutionary dynamics of host and viral diversity that cannot be fully explained by the traditional models used to describe microbe-virus coevolutionary dynamics. Here, we show how the CRISPR-mediated adaptive immune response of hosts to invading viruses facilitates the emergence of an evolutionary mode we call distributed immunity - the coexistence of multiple, equally-fit immune alleles among individuals in a microbial population. We use an eco-evolutionary modeling framework to quantify distributed immunity and demonstrate how it emerges and fluctuates in multi-strain communities of hosts and viruses as a consequence of CRISPR-induced coevolution under conditions of low viral mutation and high relative numbers of viral protospacers. We demonstrate that distributed immunity promotes sustained diversity and stability in host communities and decreased viral population density that can lead to viral extinction. We analyze sequence diversity of experimentally coevolving populations of Streptococcus thermophilus and their viruses where CRISPR-Cas is active, and find the rapid emergence of distributed immunity in the host population, demonstrating the importance of this emergent phenomenon in evolving microbial communities.

  21. N. L. Held, L. M. Childs, M. Davison, J. S. Weitz, R. J. Whitaker, and D. Bhaya, (2013) CRISPR-Cas systems to probe ecological diversity and host-viral interactions. CRISPR-Cas Systems. Springer-Verlag Berlin Heidelberg. doi:10.1007/978-3-642-34657-6-9 Springer
  22. L. M. Childs, N. Held, M. Young, R. Whittaker, and J. Weitz, (2012) Multi-scale Model of CRISPR-induced Coevolutionary dynamics: Diversification at the interface of Lamarck and Darwin. Evolution, 66(7):2015--2029. doi:10.1111/j.1558-5646.2012.01595.x PubMed
    Abstract
      [Hide]    The CRISPR (Clustered Regularly Interspaced Short Palindromic Repeats) system is a recently discovered type of adaptive immune defense in bacteria and archaea that functions via directed incorporation of viral and plasmid DNA into host genomes. Here, we introduce a multiscale model of dynamic coevolution between hosts and viruses in an ecological context that incorporates CRISPR immunity principles. We analyze the model to test whether and how CRISPR immunity induces host and viral diversification and the maintenance of many coexisting strains. We show that hosts and viruses coevolve to form highly diverse communities. We observe the punctuated replacement of existent strains, such that populations have very low similarity compared over the long term. However, in the short term, we observe evolutionary dynamics consistent with both incomplete selective sweeps of novel strains (as single strains and coalitions) and the recurrence of previously rare strains. Coalitions of multiple dominant host strains are predicted to arise because host strains can have nearly identical immune phenotypes mediated by CRISPR defense albeit with different genotypes. We close by discussing how our explicit eco-evolutionary model of CRISPR immunity can help guide efforts to understand the drivers of diversity seen in microbial communities where CRISPR systems are active.

  23. L. M. Childs, M. Paskow, S. Morris, M. Hesse and S. Strogatz, (2011) From inflammation to wound healing: using a simple model to understand the functional versatility of murine macrophages. Bulletin of Mathematical Biology. doi:10.1007/s11538-011-9637-5 PubMed
    Abstract
      [Hide]    Macrophages are fundamental cells of the innate immune system. Their activation is essential for such distinct immune functions as inflammation (pathogen-killing) and tissue repair (wound healing). An open question has been the functional stability of an individual macrophage cell: whether it can change its functional profile between different immune responses such as between the repair pathway and the inflammatory pathway. We studied this question theoretically by constructing a rate equation model for the key substrate, enzymes and products of the pathways; we then tested the model experimentally. Both our model and experiments show that individual macrophages can switch from the repair pathway to the inflammation pathway but that the reverse switch does not occur.

  24. L. M. Childs and S. Strogatz, (2008) Stability diagram for the Forced Kuramoto model. CHAOS, 18: 043128. doi 10.1063/1.3049136 ArXiv
    Abstract
      [Hide]    We analyze the periodically forced Kuramoto model. This system consists of an infinite population of phase oscillators with random intrinsic frequencies, global sinusoidal coupling, and external sinusoidal forcing. It represents an idealization of many phenomena in physics, chemistry and biology in which mutual synchronization competes with forced synchronization. In other words, the oscillators in the population try to synchronize with one another while also trying to lock onto an external drive. Previous work on the forced Kuramoto model uncovered two main types of attractors, called forced entrainment and mutual entrainment, but the details of the bifurcations between them were unclear. Here we present a complete bifurcation analysis of the model for a special case in which the infinite-dimensional dynamics collapse to a two-dimensional system. Exact results are obtained for the locations of Hopf, saddle-node, and Takens-Bogdanov bifurcations. The resulting stability diagram bears a striking resemblance to that for the weakly nonlinear forced van der Pol oscillator.

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