Potential new therapeutic modality revealed through agent-based modeling of the neuromuscular junction and acetylcholinesterase inhibition
© Chapleau et al.; licensee BioMed Central Ltd. 2014
Received: 22 September 2014
Accepted: 24 September 2014
Published: 2 October 2014
One of the leading causes of death and illness within the agriculture industry is through unintentionally ingesting or inhaling organophosphate pesticides. OP intoxication directly inhibits acetylcholinesterase, resulting in an excitatory signaling cascade leading to fasciculation, loss of control of bodily fluids, and seizures.
Our model was developed using a discrete, rules-based modeling approach in NetLogo. This model includes acetylcholinesterase, the nicotinic acetylcholine receptor responsible for signal transduction, a single release of acetylcholine, organophosphate inhibitors, and a theoretical novel medical countermeasure. We have parameterized the system considering the molecular reaction rate constants in an agent-based approach, as opposed to apparent macroscopic rates used in differential equation models.
Our model demonstrates how the cholinergic crisis can be mitigated by therapeutic intervention with an acetylcholinesterase activator. Our model predicts signal rise rates and half-lives consistent with in vitro and in vivo data in the absence and presence of inhibitors. It also predicts the efficacy of theoretical countermeasures acting through three mechanisms: increasing catalytic turnover of acetylcholine, increasing acetylcholine binding affinity to the enzyme, and decreasing binding rates of inhibitors.
We present a model of the neuromuscular junction confirming observed acetylcholine signaling data and suggesting that developing a countermeasure capable of reducing inhibitor binding, and not activator concentration, is the most important parameter for reducing organophosphate (OP) intoxication.
Inadvertent or intentional ingestion of organophosphate (OP) pesticide is a common occurrence in agricultural areas  and OP nerve agents remain a threat in chemical terrorism . Efforts to develop new therapeutic treatments for OP poisonings are frequently resulting in new oxime-based reactivators , stoichiometric bioscavengers , or catalytic scavengers . These treatments rely upon knowledge and identification of an acute exposure, must be administered within a narrow therapeutic window, and are not broad treatments but are selective for specific OPs. Despite these limitations, the currently deployed OP therapeutics used in the U.S. (the Mark 1 pralidoxime/atropine autoinjector and pyridostigmine bromide) have been in use since the 1950s.
Current advanced computational models of OP intoxication are constructed as physiologically-based pharmacokinetic (PBPK) models in order to estimate target tissue dosimetry. These models are then connected to pharmacodynamic (PD) models to predict the biological response at the target site. Such models exist for paraoxon [6, 7], diazinon [8, 9], chlorpyrifos , diisopropylfluorophosphate (DFP) [7, 10], and more recently for soman . The model for paraoxon poisoning was developed for the rainbow trout while the models for diazinon and DFP, in contrast, were validated against rat and human in vivo data. More broadly applicable models were developed for soman  and for dermal absorption of pesticides such as parathion and fenthion . The primary advantage of these PBPK models is that they can provide an accurate estimate of population behaviors and predict systemic outcomes.
Compared with ODEs, ABM constructs are readily adapted to spatial dimensions ; are stochastic by nature; can easily incorporate new information by adding more agent-types or modifying rules without rewriting the entire simulation; and reproduce emergent behaviors through parallelism and stochasticity . Models in the ABM paradigm can be assembled even when complete knowledge of the system being simulated is lacking, as, for example, in the case herein where the characteristics of an enzyme activator are theoretical. Finally, ABMs describe the behavior of individuals such that the simulation does not always follow the average behavior that the ODE description would provide, thus taking into account the often significant impact of “outlier events” on the overall biological process. Although the system outcome from each ABM run is different, multiple runs provide a non-parametric means to explore the variability of outcomes, including the impact of rare events, eventually converging with the ODE-based results.
Traditional ODE models can be successfully employed to predict macroscopic effects that are changing in a continual manner; however they fall short in modeling dynamic processes such as biological systems that can change properties over time . The NMJ modeled here is a particularly unique example of a dynamic biological system. The model includes a single release of acetylcholine (2000 molecules) from the neuron into a 50 nm2 region of the junction, containing 25 acetylcholinesterase molecules (biologically, these are tetramers treated individually) on each side of the junction and 50 nicotinic acetylcholine receptors (nAChR). When an individual acetylcholine molecule interacts with either the enzyme or the receptor, the agents both change.
Results and discussion
The model described here permits small molecular agents (i.e. ACh, inhibitor, and activator) to travel through the neuromuscular junction and interact with proteins (i.e. AChE or nAChR), binding and dissociating according to their state. Each agent is a biological entity and the interactions between protein and small molecule are based upon experimentally determined rate constants. As with the real-world, this model is limited in that interactions can only occur when two criteria are satisfied: two agents must be in physical proximity to each other, and they each must be capable of binding (i.e. no partner for ACh, and 0 or 1 partner for nAChR). To maintain consistency with the reality of a single endosome release, the model is spatially constrained along the y-axis to the junction distance, while the x-axis is allowed to remain unconstrained to simulate diffusion into and out of the region of interest.
Predicted therapeutic parameters for preventing OP-induced intoxication
Target e.p.p. duration
By using an ABM, we take into account the dynamic nature of the activation event. In this case, the binding of a single activator agent to a single enzyme agent will transiently alter the behavior of that enzyme (for example, reducing the inhibitor’s binding affinity). With an ODE-based model, this small nuance of a single agent changing activity would be lost due to the averaging achieved by considering the populations of all enzyme agents. Within the context of this model, and the example just provided, a single activator binding to a single enzyme would account for a change of only 2% of the enzymes present, a negligible signal in the ODE yet one that we have shown to produce significant emergent behavior using the ABM.
Our model supports the hypothesis that as a potential therapeutic route, allosteric AChE activators provide a novel and useful approach for treating OP intoxication. Although our model does not rule out other methods and mechanisms of action, we contend that isolation and targeting the most effective allosteric therapies could produce life-saving effects by partially ameliorating the deleterious actions of AChE inhibitor binding.
nAChR: cannot move; can bind one or two ACh molecules; can convert from closed and bound to open and bound with either one or two ACh ligands; can convert from open with two ligands to desensitized with two ligands; can release either ligand
AChE: cannot move; can bind single ACh molecule; can convert ACh to product; can bind inhibitor; can be aged by inhibitor; can bind activator; can release activator or ACh
ACh: can move with diffusion; can bind to nAChR or AChE; can be converted to product
Inhibitor: can move with diffusion; can bind to AChE; can induce AChE aging
Activator: can move with diffusion; can bind to AChE; can alter AChE activities
Product: disappears upon formation; increases accounting tracker by 1 unit
Inhibitor parameters for model
k-inh (M-1 min-1)
7.4 * 10 6
2.7* 10 7
9.2* 10 7
4.9* 10 8
1.2* 10 8
4.4* 10 8
1.2* 10 6
1.3* 10 5
Supporting information available
The complete NetLogo code is included as supplemental information and is also available at the NetLogo model library (http://ccl.northwestern.edu/netlogo/models/community/index.cgi) Additional file 1.
RRC is a protein biochemist, and an expert in enzyme inhibition. PJR is a biological modeler with extensive experience in ODE modeling in advanced biology, physics and mathematics. JJS is a board-certified toxicologist, a medicinal chemist, and expert in acetylcholinesterase inhibition by OPs. JMG is a board-certified toxicologist, a biological modeler, and expert in the toxicology and modeling of OP pesticides and nerve agents.
The authors thank Dr. Yaroslav Chushak, C. Erik Hack, Tammie Covington, Christopher Ruark and Amanda Hanes for comments and insight.
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