Lauren M. Childs

Stability diagram for the forced Kuramoto model

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.

MULTISCALE MODEL OF CRISPR-INDUCED COEVOLUTIONARY DYNAMICS: DIVERSIFICATION AT THE INTERFACE OF LAMARCK AND DARWIN

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.

Targeting Human Transmission Biology for Malaria Elimination

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.

CRISPR-Induced Distributed Immunity in Microbial Populations

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.

Wolbachia infections in natural Anopheles populations affect egg laying and negatively correlate with Plasmodium development

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.

Trade-offs in antibody repertoires to complex antigens

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.

Zika virus dynamics: When does sexual transmission matter?

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.

Dissecting the determinants of malaria chronicity: why within-host models struggle to reproduce infection dynamics

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.

Disrupting Mosquito Reproduction and Parasite Development for Malaria Control

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.

From Inflammation to Wound Healing: Using a Simple Model to Understand the Functional Versatility of Murine Macrophages

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.