Georgia Institute of Technology College of Sciences

The treatment of bacterial infections with antibiotics is universally accepted as one of (if not THE) most significant contributions of medical intervention to reducing mortality and morbidity during last century. Despite their widespread use over this extended period however, basic knowledge about how antibiotics kill or prevent the growth of bacteria is only just beginning to emerge. The dose and term of antibiotic treatment has long been determined empirically and intuitively by clinicians. Only recently have antibiotic treatment protocols come under scrutiny with the aim to theoretically and experimentally rationalize treatment protocols. The aim of such scrutiny is to design protocols which maximize antibiotics’ efficacy in clearing bacterial infections and simultaneously prevent the emergence of resistance in treated patients. Central to these endeavors are the pharmacodynamics, PD (relationship between bug and drug), and the pharmacokinetics, PK (the change antibiotic concentration with time) of each bacteria : drug : host combination. The estimation of PD and PK parameters is well established and standardized worldwide and although different PK parameters are commonly employed for most of these considerations, a single PD parameter is usually used, the minimum inhibitory concentration (MIC). MICs, also utilized as the criteria for resistance are determined under conditions that are optimal to the action of the antibiotic; low densities of bacteria growing exponentially. The method for estimating MICs which is the only one officially sanctioned by the regulatory authority (Clinical and Laboratory Standards Institute) defines conditions that rarely obtain outside of the laboratory and virtually never in the bacteria infecting mammalian hosts. Real infections with clinical symptoms commonly involve very high densities of bacteria, most of which are not replicating. These populations are rarely planktonic but rather reside as colonies or within matrices called biofilms which sometimes include other species of bacteria. In the first part of my talk, I will present newly published data that describes the pharmacodynamic relationship between the sometimes pathogenic bacterium Staphylococcus aureus and antibiotics of six classes and the effects of cell density on MICs. By including density dependent MIC in a standard mathematical model of antibiotic treatment (from our lab), I show that this density-dependence may explain why antibiotic treatment fails in the absence of inherited resistance. In the second part of my talk I will consider the effects of the physiological state of clinical isolates of S. aureus on their susceptibility to different antibiotics. I present preliminary data which suggests that the duration of an infection may contribute adversely to an antibiotics chance of clearing the infection. I conclude with a brief discussion of the implications of the theoretical and experimental results for the development of antibiotic treatment protocols. As a special treat, I will outline problems of antibiotic treatment that could well be addressed with some classy mathematics.

Human Mobility in our globalised world has reached a complexity and volume of unprecedented degree. More than 60 million people travel billions of kilometres on more than 2 million international flights each week. Hundreds of millions of people commute on a complex web of highways and railroads most of which operate at their maximum capacity. Human mobility is responsible for the geographical spread of emergent human infectious diseases and plays a key role in human mediated bioinvasion, the dominant factor in the global biodiversity crisis. I will report on the recent discovery of scaling laws in global human traffic (obtained from online bill-tracking at www.wheresgeorge.com) and mathematical models that can account for it. I will present a complex network perspective on multi-scale human traffic networks, report on their statistical properties and show that they can be used to identify geographically coherent communities that only vaguely resemble administrative ones. The approach provides an operational segmentation of maps into a hierarchical set of effective regions and boundaries based on human behavior. I will briefly talk about European transportation networks, geocaching and trackable items.

The expression dynamics of interacting genes depends on the topology of the regulatory network, the quantitative nature of feedbacks and interactions between DNA, RNA and proteins, and the biochemical state of the intracellular and surrounding environment. In this talk we show that dynamics of a gene regulatory network can also depend sensitively on the copy number of genes and promoters. Genetic regulatory networks include an overrepresentation of subgraphs commonly known as network motifs. We consider positive feedback, bistable feedback, and toggle switch motifs and show that variation in gene copy number can cause a sequence of saddle-node bifurcations in the corresponding differential equations models, which leads to multiple orders of magnitude change in gene expression. A similar analysis of a 3-gene motif with successive inhibition (the ``repressilator'') reveals that changes in gene copy number can also cause a Hopf bifurcation, thus leading to a qualitative switch in system behavior among oscillatory and equilibrium dynamics. Importantly, we show that these bifurcations exist over a wide range of parameter values, thus reinforcing our claim that copy number is a key control parameter in the expression dynamics of regulatory networks.