Modeling Physiological Processes That Relate Toxicant Exposure and Bacterial Population Dynamics

Quantifying effects of toxicant exposure on metabolic processes is crucial to predicting microbial growth patterns in different environments. Mechanistic models, such as those based on Dynamic Energy Budget (DEB) theory, can link physiological processes to microbial growth. Here we expand the DEB framework to include explicit consideration of the role of reactive oxygen species (ROS). Extensions considered are: (i) additional terms in the equation for the ‘‘hazard rate’’ that quantifies mortality risk ; (ii) a variable representing environmental degradation ; (iii) a mechanistic description of toxic effects linked to increase in ROS production and aging acceleration, and to non-competitive inhibition of transport channels ; (iv) a new representation of the ‘‘lag time’’ based on energy required for acclimation. We estimate model parameters using calibrated Pseudomonas aeruginosa optical density growth data for seven levels of cadmium exposure. The model reproduces growth patterns for all treatments with a single common parameter set, and bacterial growth for treatments of up to 150 mg(Cd)/L can be predicted reasonably well using parameters estimated from cadmium treatments of 20 mg(Cd)/L and lower. Our approach is an important step towards connecting levels of biological organization in ecotoxicology. The presented model reveals possible connections between processes that are not obvious from purely empirical considerations, enables validation and hypothesis testing by creating testable predictions, and identifies research required to further develop the theory

Clinical and cost-effectiveness of contingency management for cannabis use in early psychosis: the CIRCLE randomised clinical trial

Background Cannabis is the most commonly used illicit substance among people with psychosis. Continued cannabis use following the onset of psychosis is associated with poorer functional and clinical outcomes. However, finding effective ways of intervening has been very challenging. We examined the clinical and cost-effectiveness of adjunctive contingency management (CM), which involves incentives for abstinence from cannabis use, in people with a recent diagnosis of psychosis. Methods CIRCLE was a pragmatic multi-centre randomised controlled trial. Participants were recruited via Early Intervention in Psychosis (EIP) services across the Midlands and South East of England. They had had at last one episode of clinically diagnosed psychosis (affective or non-affective); were aged 18 to 36; reported cannabis use in at least 12 out of the previous 24 weeks; and were not currently receiving treatment for cannabis misuse, or subject to a legal requirement for cannabis testing. Participants were randomised via a secure web-based service 1:1 to either an experimental arm, involving 12 weeks of CM plus a six-session psychoeducation package, or a control arm receiving the psychoeducation package only. The total potential voucher reward in the CM intervention was £240. The primary outcome was time to acute psychiatric care, operationalised as admission to an acute mental health service (including community alternatives to admission). Primary outcome data were collected from patient records at 18 months post-consent by assessors masked to allocation. The trial was registered with the ISRCTN registry, number ISRCTN33576045. Results: 551 participants were recruited between June 2012 and April 2016. Primary outcome data were obtained for 272 (98%) in the CM (experimental) group and 259 (95%) in the control group. There was no statistically significant difference in time to acute psychiatric care (the primary outcome) (HR 1.03, 95% CI 0.76, 1.40) between groups. By 18 months, 90 (33%) of participants in the CM group, and 85 (30%) of the control groups had been admitted at least once to an acute psychiatric service. Amongst those who had experienced an acute psychiatric admission, the median time to admission was 196 days (IQR 82, 364) in the CM group and 245 days (IQR 99,382) in the control group. Cost-effectiveness analyses suggest that there is an 81% likelihood that the intervention was cost-effective, mainly resulting from higher mean inpatient costs for the control group compared with the CM group, however the cost difference between groups was not statistically significant. There were 58 adverse events, 27 in the CM group and 31 in the control group. Conclusions Overall, these results suggest that CM is not an effective intervention for improving the time to acute psychiatric admission or reducing cannabis use in psychosis, at least at the level of voucher reward offered

Summary of state variables, units, and dynamic equations.

<p>Bacterial production rate and scaled functional response () are not state variables, but have been defined separately for brevity. Non-dimensional variables have been labeled ‘n.d.’. Subscript ‘+’ signifies that only positive values of the expression are considered, with the expression set to zero if its value turns out to be negative.</p

Simulating the control.

<p>Cell concentration and all state variables of the model except acclimation and bioaccumulation (not applicable for control). Upper left corner: data (circles), best fit of the standard model (dotted line) and best fit of the model extended by including environmental degradation (solid line). See text for discussion.</p

Simulations of all treatments with a single parameter set.

<p>Best fit set of parameter values used (listed in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0026955#pone-0026955-t002" target="_blank">Table 2</a>). The inset is showing the first 5 hours of the experiment.</p

Predicting high exposures.

<p>Exposures of 37.5, 75, 115, and 150 mg/L predicted using fits only of data on control and low exposures (10 and 20 mg/L). Data points marked with ‘x’: data used in fitting; ‘o’: data used for comparison only. Dashed line: fitted treatments (, , , and ). Solid line: predicted treatments.</p

Parameters, units, and fitted values.

<p>Concentration denotes an amount of per volume of substrate, density denotes an amount per structural volume of bacteria, and n.d. stands for ‘non-dimensional’. Coefficient scales initial substrate C-mol concentration to unity, and structural cell C-mol to calibrated optical density.</p

Outline of the model.

<p>Bacteria assimilate substrate into energy reserves, which are utilized to fuel growth (linked to increase in cell concentration), maintenance and acclimation. Products related to respiration degrade the environment, reducing the ability of bacteria to utilize energy reserves. Both toxicants and degradation of the supernatant inhibit assimilation of the substrate, and absorbed toxicants bioaccumulate in bacterial cells. Toxicants in the cell, as well as the cell's own metabolism, increase aging acceleration (by creating damage-inducing compounds), thus increasing the hazard rate, and mortality.</p

Overview of population dynamics.

<p>Top panels show dependence of maximum growth rate (left) and time to maximum growth rate (right) calculated from the model (solid line) and measured by Priester <i>et al.</i> (2009 <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0026955#pone.0026955-Priester1" target="_blank">[20]</a>) (dotted line). Bottom left panel shows time to maximum energy density as a function of exposure concentration. Bottom right panel shows growth rates for all treatments during the first 30 hours of the experiment.</p