Population Size-Dependent Dynamics of Bacterial Response to Antibiotics

Antibiotic resistance is on the rise throughout the world and poses an increasing risk to our health systems. Understanding how bacteria respond to drugs in complex environments can help us manage our current arsenal of drugs in a more effective way. Past work has primarily focused on mechanistic responses by bacteria that confer resistant to specific drugs, and this molecular level understanding is essential. Yet bacteria live in large and possibly heterogeneous populations, and it's often not clear how known molecular scale events lead to large scale behavior like survival or extinction. In this thesis I make use of quantitative in-vitro experiments and mathematical models to understand and predict the population level dynamics of bacterial communities in the presence of drugs. Traditional methods for investigations at this scale suffer from some experimental limitations which I am able to overcome using new custom hardware. Using such tools, my experiments can include both precise measurements of a bacterial population over time while also including precise control of the growth environment. I can use this control to respond to the population in some way, such as holding a size threshold for it, or use it to stress the population in a specific manner, such as using differing drug dosing protocols. This versatility has allowed me to perform new and interesting investigations about the bacterial population respond to drugs in various settings, three of such experiments make up this thesis. In the first chapter, I show that the efficacy of many common drugs is dependent upon the density of the bacterial population in E. faecalis. I am able to quantify the amount to which several common drugs inhibit the growth rate of a bacterial population at different densities within exponential phase growth. In general, if such a density dependence for a drug exists, the drug is less effective at growth inhibition the denser the population is. I also investigate the cause of this effect, and find that the resulting change in pH of the environment from cellular growth can explain the effect for a couple of drugs. These results are then used to create a mathematical model that shows that a treatment regime could possibly lead to treatment failure when populations are very dense. In the presence of resistant sub-populations this density-dependent inhibition then leads to counter-intuitive dynamics, and this is the subject of Chapter 2. Using ampicillin and constant drug influx, these counter-intuitive dynamics include preferential survival of low-density populations over high-density counterparts. Using a model to understand this system, I show that this result comes from the pH driven density effect, and disappears when pH modulation of the environment is not possible. Finally, I show how competitive suppression can limit growth of drug resistant populations for a sufficiently high-density population. Using sub-inhibitory amounts of drug, I show that a mixed population of bacteria can be held at a high density far past when a non-suppressed resistant sub-population would have completely taken over the population. par As a whole, my work in this thesis helps to underscore the importance of density-driven community level interactions in determining the fate of bacterial populations exposed to antibiotics.PHDBiophysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/151523/1/karslaja_1.pd

Population Density Modulates Drug Inhibition and Gives Rise to Potential Bistability of Treatment Outcomes for Bacterial Infections

<div><p>The inoculum effect (IE) is an increase in the minimum inhibitory concentration (MIC) of an antibiotic as a function of the initial size of a microbial population. The IE has been observed in a wide range of bacteria, implying that antibiotic efficacy may depend on population density. Such density dependence could have dramatic effects on bacterial population dynamics and potential treatment strategies, but explicit measures of per capita growth as a function of density are generally not available. Instead, the IE measures MIC as a function of initial population size, and population density changes by many orders of magnitude on the timescale of the experiment. Therefore, the functional relationship between population density and antibiotic inhibition is generally not known, leaving many questions about the impact of the IE on different treatment strategies unanswered. To address these questions, here we directly measured real-time per capita growth of <i>Enterococcus faecalis</i> populations exposed to antibiotic at fixed population densities using multiplexed computer-automated culture devices. We show that density-dependent growth inhibition is pervasive for commonly used antibiotics, with some drugs showing increased inhibition and others decreased inhibition at high densities. For several drugs, the density dependence is mediated by changes in extracellular pH, a community-level phenomenon not previously linked with the IE. Using a simple mathematical model, we demonstrate how this density dependence can modulate population dynamics in constant drug environments. Then, we illustrate how time-dependent dosing strategies can mitigate the negative effects of density-dependence. Finally, we show that these density effects lead to bistable treatment outcomes for a wide range of antibiotic concentrations in a pharmacological model of antibiotic treatment. As a result, infections exceeding a critical density often survive otherwise effective treatments.</p></div

Density dependence of antibiotic leads to bistable treatment outcomes and potential treatment failure in a pharmacokinetic / pharmakodynamic (PK/PD) model of infection.

<p><b>A.</b> Main panel<b>:</b> Theoretical (solid and dashed lines) and numerical (shaded region) phase diagrams indicate treatment outcomes in PK/PD model as a function of initial cell density (ranging from 0 to the carrying capacity, C) and initial antibiotic concentration D₀. Solid red lines, stable fixed points of population density (theory). Dashed red lines, unstable fixed points (theory). The curved dashed red line is the phase boundary (separatrix) indicating the critical density above which a population will survive. A region of growth bistability, where treatment can lead to success or failure depending on initial cell density, exists for antibiotic concentrations <i>K</i>₀<i>γ</i>(0) ≤ <i>D</i>₀ ≤ <i>K</i>₀<i>γ</i>(<i>C</i>), where K₀ is the MIC and γ(n) is a nonlinear function that depends on the maximum drug kill rate (g_min), the Hill coefficient (h), the drug decay rate (k_d), and the dosing period T (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005098#pcbi.1005098.s001" target="_blank">S1 Text</a>). Shaded regions indicate treatment failure in numerical solutions of the PK/PD model. Upper right inset: numerical solution of PK/PD equations for five different initial densities (indicated by red and black squares on the phase diagram). Lower inset: temporal dynamics of antibiotic concentration. For numerical phase diagram and simulations, g_min = -0.05 and ε = 0.9. Simulations in insets correspond to D₀ = 200 (in units of MIC, K₀). <b>B.</b> Phase diagrams from both theory (solid and dashed lines) and numerical simulations (shaded region) for increasing maximum kill rates (g_min = -0.25, -1, -2 from top to bottom) and populations densities on the order of 10⁸ cells/mL (corresponding to the OD ranges measured here). g_min is measured in units of g_max; biologically, g_max≈1 hr^-1 for bacteria, so one can also view these units as inverse hours. <b>C.</b> Initial dose of antibiotic (units of MIC, K₀) required to clear infections of density OD = 0 (dashed red), OD = 0.4 (blue line), and OD = 0.8 (red line) for different maximum kill rates for the case with no density dependence (ε = 0, left), modest density dependence (ε = 0.5, middle), and strong density dependence (ε = 0.9, right). In all panels, the Hill coefficient h = 2, k_d = ½, and T = 8, corresponding to a treatment period of 8 hours and a natural drug decay rate of ½ hr^-1. Qualitatively similar results are found for other parameters (Figure G of <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005098#pcbi.1005098.s001" target="_blank">S1 Text</a>).</p

Density dependence of antibiotic inhibition partially due to local pH changes.

<p>A. Top row: Steady state population growth was measured as a function of cell density (here schematically represented by low, medium, and high density) by holding each vial at a constant density while exposing cells to constant drug concentration in highly buffered media. Bottom row: Different culture vials were all held at low-density (OD = 0.2) but grown in BHI supplemented with HCl to achieve pH = 7.5, 6.8, and 6.0, which correspond to pH of steady state cultures held at OD = 0.2, 0.5, and 0.8, respectively. B. Red curves, regular media. Black dashed curves, buffered media. Blue dotted curves, external pH modulation. Tigecycline concentration 50 ug/mL; Ampicillin concentration 200 ng/mL;C. Red curves, regular media. Black dashed curves, buffered media. Ciprofloxacin concentration 200 ng/mL, Spectinomycin concentration 150 ug/mL. Statistically significant differences between growth at lowest and highest densities (0.2 and 0.8), intermediate densities (0.4 and 0.6), or both are indicated by *, **, and ***, respectively. See also Figure D in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005098#pcbi.1005098.s001" target="_blank">S1 Text</a>. Error bars are +/- 1.96 standard error (95% confidence intervals).</p