MOTIVATION LETTER The Conjunctive Consolidation Threshold model, a tripartite pharmacological framework for reward-memory encoding prevention, required numerical methods that did not exist in the addiction neuroscience literature. I built them. Over twelve months as an independent researcher in Lagos, with no institutional affiliation and no supervisor, I specified the system as a set of coupled ordinary differential equations, solved them using an RK45 integrator in Python, and validated the parameter space with Bayesian MCMC inference in PyMC. The result: encoding probability dropped from 0.855 to 0.122, an 85.8 percent reduction, with super-additivity of 12.8 percentage points above the sum of individual drug effects. All five pre-registered hypotheses were confirmed. This work is now on Zenodo and OSF as three sole-authored preprints. A review article is under review at Neuroscience and Biobehavioral Reviews. A co-authored paper is under review at Alcohol. Kent Berridge at Michigan, Samuel Gershman at Harvard, Nathaniel Daw at Princeton, and Marcelo Mattar at NYU have endorsed the framework. A provisional patent on the core architecture is scheduled for Q3 2026. The Computational Mathematics programme at the U.S. National Science Foundation is the correct home for the next phase of this work. The CCT model is fundamentally a problem in computational mathematics: a high-dimensional dynamical system with stochastic transitions, a Bayesian inference layer for population heterogeneity, and a topological data analysis pipeline for drug-protein interaction screening that I built into the TOPOLOGIX platform. The NSF mission to advance fundamental mathematical sciences aligns directly with the formal specification I published at OSF 10.17605/OSF.IO/EMY4U, which defines the CCT as a piecewise-deterministic Markov process with state-dependent switching rates. I am a Nigerian pharmacist with a B.Pharm from the University of Ibadan, CGPA 5.1 out of 7.0, German equivalent 1.9. I am 29 years old, currently working as National Product Manager at Synthcare in Lagos. I am applying for MSc programmes starting October 2026 at the Medical University of Graz and the University of Graz in Austria. This NSF grant would fund the computational mathematics component of my research between now and matriculation, and support the development of the IMPRINT addiction-liability screening platform and the GATE neural-stimulation safety evaluation system, both of which depend on the mathematical framework I have already validated. The grant would support continued independent work: extending the ODE model to a stochastic differential equation formulation, running sensitivity analyses on the Bayesian posterior distributions, and integrating the TOPOLOGIX persistent homology pipeline with the CCT dynamics to predict off-target effects in the reward circuitry. The NSF Computational Mathematics programme funds exactly this kind of method development at the intersection of dynamical systems, probability, and applied topology. RESEARCH STATEMENT The Conjunctive Consolidation Threshold model addresses a specific mathematical problem: how to prevent the encoding of reward-memory associations in the mesolimbic dopamine system using a combination of pharmacological agents that act on distinct molecular targets. The model posits that memory consolidation requires simultaneous activation of three subsystems, dopamine D1 receptor signaling, NMDA receptor-dependent plasticity, and cAMP response element-binding protein transcription, and that blocking any two of these pathways is insufficient to prevent encoding. Only when all three are suppressed below a conjunctive threshold does consolidation fail. I formalized this as a system of three coupled ODEs representing the activity of each subsystem over time, with drug concentration as the control parameter. The equations are: dD/dt = alphaD CD(t) (1 - D/KD) - betaD * D dN/dt = alphaN CN(t) (1 - N/KN) - betaN * N dC/dt = alphaC CC(t) (1 - C/KC) - betaC * C where D, N, and C represent the activation levels of the D1, NMDA, and CREB subsystems respectively, CX(t) are drug concentration profiles from a two-compartment pharmacokinetic model, alphaX and betaX are rate constants, and KX are saturation constants. The encoding probability P_enc is a sigmoidal function of the product D N C, with threshold theta and steepness kappa: P_enc = 1 / (1 + exp(-kappa (D N * C - theta))) I solved this system using an RK45 integrator with adaptive step size in scipy.integrate.solve_ivp, with drug concentration profiles generated from a two-compartment PK model parameterized with literature values for a D1 antagonist, an NMDA antagonist, and a CREB inhibitor. The Bayesian MCMC component used PyMC with four chains, 2000 warmup and 4000 sampling iterations each, to estimate posterior distributions over the nine free parameters (three alpha, three beta, three K) conditioned on the pre-registered outcome that triple combination reduces encoding probability below 0.2 while no double combination does. The results confirmed all five hypotheses. H1: triple combination reduces Penc from 0.855 to 0.122. H2: no double combination reduces Penc below 0.5. H3: the effect is super-additive, with observed reduction exceeding the sum of individual reductions by 12.8 percentage points. H4: the effect is robust to parameter variation within physiologically plausible ranges. H5: the model predicts a therapeutic window between 0.3 and 0.7 of the maximum tolerated dose for each drug. The next phase requires extending this deterministic ODE framework to a stochastic differential equation formulation that accounts for random fluctuations in receptor occupancy and synaptic noise. I will use the Euler-Maruyama method to simulate the SDE system and compare the distribution of first-passage times below the threshold against the deterministic predictions. I will also integrate the TOPOLOGIX pipeline, which uses persistent homology on bipartite simplicial complexes constructed from drug-protein interaction fingerprints, to predict which off-target proteins in the reward circuitry might be affected by the triple combination. This requires computing Vietoris-Rips filtrations on the distance matrix between drug fingerprints and protein binding site descriptors, then extracting persistent homology features in dimensions 0, 1, and 2 using Ripser and Gudhi. The NSF Computational Mathematics programme supports this work because it is fundamentally a project in numerical analysis, stochastic simulation, and computational topology applied to a concrete biological system. The methods are generalizable to any multi-target pharmacological intervention, and the code is all open-source on GitHub under Apache 2.0 licenses. CHECKLIST - [ ] Complete NSF Grant Application Form (SF 424 R&R) - [ ] Project Summary (one page, 200 words or fewer) - [ ] Project Description (15 pages maximum, including figures and references) - [ ] References Cited (no page limit, single-spaced) - [ ] Biographical Sketch (NSF format, two pages maximum) - [ ] Budget and Budget Justification (NSF SF 424 R&R Budget Form) - [ ] Current and Pending Support (NSF format) - [ ] Facilities, Equipment, and Other Resources (two pages maximum) - [ ] Data Management Plan (two pages maximum) - [ ] Mentoring Plan (if requesting postdoctoral support, one page) - [ ] Letters of Collaboration from Kent Berridge, Samuel Gershman, Nathaniel Daw, Marcelo Mattar - [ ] Copy of B.Pharm certificate from University of Ibadan - [ ] Copy of PCN pharmacist license - [ ] ORCID iD and GitHub profile URL on cover page - [ ] Preprint DOIs: OSF 10.17605/OSF.IO/KG7B5, OSF 10.17605/OSF.IO/EMY4U, Zenodo 10.5281/zenodo.20492472 - [ ] Provisional patent filing receipt (Q3 2026, include expected filing date) EDITOR NOTES - Eligibility risk: NSF grants typically require U.S. institutional affiliation or U.S. citizenship. Eniola is a Nigerian citizen based in Lagos with no U.S. affiliation. Verify whether the NSF Computational Mathematics programme allows independent researchers without U.S. institutional sponsorship. If not, identify a U.S.-based collaborator willing to serve as PI or co-PI. Samuel Gershman at Harvard or Nathaniel Daw at Princeton are possible hosts. - Budget justification needed: The grant amount is unspecified. Prepare a budget for computational resources (HPC credits, cloud computing for MCMC and TDA), conference travel (Society for Neuroscience, Computational Neuroscience), publication fees for open-access journals, and a modest stipend for the period between now and MSc matriculation in October 2026. Total should be in the 50,000 to 100,000 USD range. - Missing detail: The profile does not specify whether Eniola has a U.S. Social Security Number or ITIN, which is required for NSF grant payments to individuals. If not, explore whether the grant can be administered through a U.S. university or non-profit fiscal sponsor. - Verification needed: Confirm that the review article is indeed under review at Neuroscience and Biobehavioral Reviews and that the co-authored paper is under review at Alcohol. Include manuscript numbers if available. - Personal detail gap: The profile does not include the names of any U.S.-based mentors or sponsors who could write letters of support beyond the four named collaborators. Identify at least one additional letter writer who can speak to Eniola's mathematical abilities, such as a mathematics or computational science faculty member at a U.S. institution who has reviewed the CCT preprints.