Department, School, or Program

Interdisciplinary Studies

Degree Level



The invasion of host tissue by bacteria can lead to infection. Many pathogenic species of bacteria generate and release toxins, which amplify virulent effects. With the aid of toxins, bacteria can colonize different parts of the body, evade the host's immune system, over-activate or suppress the immune system, or obtain nutrients from the host. Generally, toxins can be classified as either exotoxins or endotoxins, depending on the location of the toxins in the bacterial cell. Exotoxins are proteins secreted by Gram-positive bacteria, while endotoxins are lipopolysachharides found within the cellular membranes of Gram-negative bacteria [1, 2]. This study focuses on exotoxins and its effects on a host.

There are many different types of bacterial exotoxins and they can be distinguished by their modes-of-action and by the time during which they are released in the bacterial growth phase. Some exotoxins are released consciously throughout all three phases of bacterial growth as a result of metabolic processes. Others are released during the logarithmic phase of bacterial growth in which bacteria grow at their maximal rate by occupying all the space and ingesting all the nutrients available in their surroundings [3]. Still others are released during the stationary phase of growth in which bacteria are in a nutrient-starved state [4]. All toxins, regardless of when they are released, can be categorized as either immune-provoking or tissue damaging toxins. As their name suggests, immune-provoking toxins interact with immune cells and activate them, while tissue damaging toxins damage the integrity of local host cells and can cause death in these cells.

Not all strains of bacteria produce toxins, and toxin-producing strains of bacteria can release a wide variety of toxins. For example, Staphylococcal aureus (S. aureus), a bacteria found endogenously on the skin and mucosal membrane of 30% of the human population, releases different types of toxins including hemolysins, nucleases, proteases, leukocidins, enterotoxins and more during an infection [5]. As a result of the release of each type of toxin, red blood cells and white blood cells are destroyed, nucleic acids and proteins are broken down, and a massive immune response is induced [6]. These findings demonstrate that several types of bacterial toxins from the same strain of bacteria can target a variety of different host cells and use multiple mechanisms to induce damage.

This study seeks to incorporate the effects of exotoxins into an existing system of differential equations that model intra-host interaction between pathogen, immune cells, and tissue damage. There is a lack of studies incorporating the effects of exotoxins into a mathematical model describing these interactions as demonstrated by previous studies that investigate and model uremic protein bound toxins in the blood that optimize dialysis treatments [7], the regulation of toxin production in Clostridium difficile [8], and toxin neutralization using antibodies in the absence of cells [9). Hence, this study which incorporates exotoxins into an existing low dimensional system of differential equations containing the population dynamics of pathogen, immune cells and tissue damage [10] is necessary. The overall goal is to incorporate the final set of differential equations describing intra-host population dynamics into a hybrid agent-based and differential equations system that models the spread of bacterial infections within a hospital ward. One of the specific goals of the current study is to incorporate the three types of tissue damaging exotoxins, and immune provoking exotoxins into the overall differential equations model. The second specific goal of this study is to derive a mathematical function that can be used to estimate parameters related to toxins in the differential equation model to accurately monitor the changes that occur in a toxin-releasing bacterial infection.

Document Type

Undergraduate Thesis - Campus Only

Publication Date



Interdisciplinary Studies Thesis
Department of Mathematics and Computer Science
Department of Biology
University of Richmond Richmond, Virginia
April 27, 2018
Co-Advisor: Dr. Lester Caudill
Co-Advisor: Dr. Krista Stenger