Spatiotemporal Evolution of Erythema Migrans, the Hallmark Rash of Lyme Disease Dhruv K. Vig † and Charles W. Wolgemuth †‡ * † Department of Molecular and Cellular Biology and ‡ Department of Physics, University of Arizona, Tucson, Arizona ABSTRACT To elucidate pathogen-host interactions during early Lyme disease, we developed a mathematical model that explains the spatiotemporal dynamics of the characteristic first sign of the disease, a large (R5-cm diameter) rash, known as an erythema migrans. The model predicts that the bacterial replication and dissemination rates are the primary factors controlling the speed that the rash spreads, whereas the rate that active macrophages are cleared from the dermis is the principle determinant of rash morphology. In addition, the model supports the clinical observations that antibiotic treatment quickly clears spirochetes from the dermis and that the rash appearance is not indicative of the efficacy of the treatment. The quantitative agreement between our results and clinical data suggest that this model could be used to develop more efficient drug treatments and may form a basis for modeling pathogen-host interactions in other emerging infectious diseases. INTRODUCTION A goal of modern biomedical research is to develop patient- specific treatment plans. A potential step in this direction would be determining effective, noninvasive measures that correlate clinical observations with states of disease. In the case of infections, the ability to achieve this goal re- quires a clear link between the microscopic pathogen-host interactions and the macroscopic, observable host response. Quantitative modeling of pathogen-host dynamics can potentially bridge the gap between these seemingly dispa- rate length scales. Here we explore this hypothesis in the context of Lyme disease, the most prevalent vector-borne illness in the United States and the sixth most notifiable disease in the nation, which, if untreated, can lead to com- plications in the heart, joints, or nervous system (1,2). Specifically, we consider how pathogen-host interactions lead to the spatial and temporal evolution of erythema migrans (EM), the characteristic rash that is typically the first indicator of the disease. Lyme disease is transmitted to humans by a bite from Ixodes scapularis ticks infected with the bacterium Borrelia burgdorferi. In the tick, the spirochetes inhabit the midgut. During feeding, the bacteria replicate and a small fraction leave the midgut and migrate to the salivary glands, where they are then transported into the dermis of the host via the saliva (3). It takes at least 48 h for the spirochetes to move from the gut into the dermis (2,3), and the tick remains attached to the host for ~4–5 days (2,3). Therefore, at the end of the bloodmeal, a small inoc- ulum of spirochetes is introduced into the dermis at the bite site. In the dermis, the spirochetes replicate and begin to disseminate both locally and hematogenously. While migration through the dermis can be fairly rapid (at speeds of a few microns per second (4)), the spirochetes also bind to extracellular matrix (ECM) proteins and can become transiently adhered to the matrix (4,5). The tick bite along with the presence of the spirochetes in the dermis activates the innate immune response, which includes uptake of spirochetes by immune effector cells (2,6,7). Consequently, dendritic cells release cytokines that act as a signal to monocytes from the bloodstream to differentiate into phagocytic cells, such as macrophages (8,9). The release of proinflammatory cytokines by macro- phages leads to further recruitment of innate immune cells and T cells to the infected region (2,7). This inflammatory cascade also causes hyperemia in the capillaries, leading to the characteristic rash that is usually the first symptom of infection (2,3). The EM rash, then, serves as a marker for the innate immune response during the initial stages of Lyme disease and should be sensitive to the pathogen-host dynamics that accompany this disease. But what features of the spiro- chetal infection and immune response are the most impor- tant factors of the spread of this rash? Clearly, because most infections do not produce similar rashes, the behavior of the bacterium must be important. Here we hypothesize that the motility of the bacterium is a prime factor and that the details of the immune response are less important. To test this hypothesis, we developed a mathematical model that contains many of the basic features of the dynamics of each of these processes (Fig. 1 and Materials and Methods). We show that this minimalistic model is sufficient to explain the clinically observed progression of the early stages of Lyme disease and predicts which pathogen-host interactions are most relevant in determining the morphology and spreading rate of the EM rash. These results suggest that this simple yet quantitative model can be informative about the efficacy of antibiotics. Simulations then predicted the Submitted October 15, 2013, and accepted for publication December 11, 2013. *Correspondence: wolg@email.arizona.edu Editor: Reka Albert. Ó 2014 by the Biophysical Society 0006-3495/14/02/0763/6 $2.00 http://dx.doi.org/10.1016/j.bpj.2013.12.017 Biophysical Journal Volume 106 February 2014 763–768 763