Brynja Kohler

A systematic approach to vaccine complexity using an automaton model of the cellular and humoral immune system I. Viral characteristics and polarized responses

A modern approach to vaccination faces the compound complexity of microorganism behavior and immune response triggering and regulation. Since computational modeling can yield useful guidelines for biological experimentation, we have used IMMSIM(3), a cellular automaton model for simulating humoral- and cell-mediated responses, to explore a wide range of virus-host relations. Sixty-four virtual viruses were generated by an assortment of speed of growth, infectivity level and lethal load. The outcome of the infections, as influenced by the immune response and the bolstering of cures, obtained by vaccine presensitization are illustrated in this first article. The results of the in machina experiments allow us to relate the success rate of responses to certain combinations of viral parameters and by freezing one or the other branch, and to determine that some viruses are more susceptible to humoral, and others to cellular responses, depending either on single parameters or combinations thereof. This finding allows prediction of which infection may be susceptible to polarized ((Th)(1)>Th(2) and Th(1)<Th(2)) responses and will eventually help designing vaccines whose action relies on antagonizing both the specificity and the behavior of the invader. A second, not lesser, result of this study is the finding that humoral and cellular responses, while cooperating, towards the cure of the infected body, also show significant patterns of competition and mutual thwarting.

IMMSIM, a flexible model for in machina experiments on immune system responses

This paper describes the basic structure and the developments of IMMSIM, a modified cellular automaton to simulate chance encounters and discrete effects of cell-cell and cell-molecule interactions in the lymphoid system. Thanks to its flexibility, this model has proven a useful tool in theoretical immunology, experimental research and educational applications. Of the various versions available, we show here the most advanced one (IMMSIM3), that incorporates both humoral and cellular responses. We describe the results obtained by simulating the responses to viral infection, the impact of viral behavior on the quality of response needed to reach a cure, the cooperation/competition relation between cellular and humoral branches and the effect of vaccination.

Leading Students to Investigate Diffusion as a Model of Brine Shrimp Movement

Integrating experimental biology laboratory exercises with mathematical modeling can be an effective tool to enhance mathematical relevance for biologists and to emphasize biological realism for mathematicians. This paper describes a lab project designed for and tested in an undergraduate biomathematics course. In the lab, students follow and track the paths of individual brine shrimp confined in shallow salt water in a Petri dish. Students investigate the question, “Is the movement well characterized as a 2-dimensional random walk?” Through open, but directed discussions, students derive the corresponding partial differential equation, gain an understanding of the solution behavior, and model brine shrimp dispersal under the experimental conditions developed in class. Students use data they collect to estimate a diffusion coefficient, and perform additional experiments of their own design tracking shrimp migration for model validation. We present our teaching philosophy, lecture notes, instructional and lab procedures, and the results of our class-tested experiments so that others can implement this exercise in their classes. Our own experience has led us to appreciate the pedagogical value of allowing students and faculty to grapple with open-ended questions, imperfect data, and the various issues of modeling biological phenomena.

Carrying BioMath education in a Leaky Bucket.

In this paper, we describe a project-based mathematical lab implemented in our Applied Mathematics in Biology course. The Leaky Bucket Lab allows students to parameterize and test Torricelli’s law and develop and compare their own alternative models to describe the dynamics of water draining from perforated containers. In the context of this lab students build facility in a variety of applied biomathematical tools and gain confidence in applying these tools in data-driven environments. We survey analytic approaches developed by students to illustrate the creativity this encourages as well as prepare other instructors to scaffold the student learning experience. Pedagogical results based on classroom videography support the notion that the Biology-Applied Math Instructional Model, the teaching framework encompassing the lab, is effective in encouraging and maintaining high-level cognition among students. Research-based pedagogical approaches that support the lab are discussed.

Mass action in two-sex population models: encounters, mating encounters and the associated numerical correction

Ideal gas models are a paradigm used in Biology for the phenomenological modelling of encounters between individuals of different types. These models have been used to approximate encounter rates given densities, velocities and distance within which an encounter certainly occurs. When using mass action in two-sex populations, however, it is necessary to recognize the difference between encounters and mating encounters. While the former refers in general to the (possibly simultaneous) collisions between particles, the latter represents pair formation that will produce offspring. The classical formulation of the law of mass action does not account this difference. In this short paper, we present an alternative derivation of the law of mass action that uses dimensional reduction together with simulated data. This straightforward approach allows to correct the expression for the rate of mating encounters between individuals in a two-sex population with relative ease. In addition, variability in mating encounter rates (due to environmental stochasticity) is numerically explored through random fluctuations on the new mass action proportionality constant. The simulations show how the conditioned time to extinction in a population subject to a reproductive Allee effect is affected.