Summary/Abstract Mathematical Modeling Core #3 The overarching Aim of this proposal is to markedly improve therapeutic regimens for patients with high burden bacterial infections like Ventilator-Associated Bacterial Pneumonia (VABP) due to Carbapenem-resistant Acinetobacter baumannii (CRAB) and Carbapenem-resistant Klebsiella pneumonia (CRKP). These organisms have been declared as being among the highest priority bacterial pathogens by the World Health Organization, the Centers for Disease Control and Prevention and by the National Institute for Allergy and Infectious Diseases. This proposal comprises three Projects and three Cores, with the Mathematical Modeling Core being Core #3. Translational mathematical modeling will play a critical role for this P01. Our team has had decades of experience employing high dimensional mathematical models to generate the greatest insights into experiments where antimicrobial therapy regimens are being sought to rapidly and completely kill pathogens while suppressing resistance. Here we will expand our prior work substantially. In Project #1, we will create high dimensional mathematical models from penicillin-binding protein (PBP) receptor occupancy patterns that predict the rates and extent of killing. Mechanistic data will come from Project #1 and the Mechanistic Assay Core #2. We will expand our datasets and mathematical models for β-lactams and β-lactamase inhibitors to studies at high bacterial densities and will further assess novel non-β-lactam-PBP-binders. Previously, this work has been performed with lysed bacteria. We now developed a novel approach where we can examine the PBP receptor binding in intact Gram-negative bacterial cells over time. This has been paired with the ability to look at penetration and outer membrane permeability independently. All this has already been inserted into our models. A preliminary analysis simultaneously fit 23 β-lactams and β-lactamase inhibitors, as well as the 2- and 3-drug combinations, and yielded an R2 = 0.89 in the Pre-Bayesian (population fits) step and an R2 of 0.99 in the Bayesian (individual fits) step. We will prospectively study regimens optimized by Project 1 in the HFIM (Project 2) and in two different murine models (Project 3), one granulocyte-replete and the other granulocytopenic. Models will include drug concentrations, total bacterial burden and less-susceptible populations for antibiotic monotherapy regimens and combination regimens of 2, 3 or 4 drugs. In addition, mechanistic insights will be provided by Core #2. The models that incorporate all these data will be very high dimensional. To optimize the insights gained and provided back to all Projects, the analyses will be done in real time. As a major part of this Mathematical Modeling Core (#3), our team is developing new algorithms to generate substantial speed-up (e.g. Random Parametric Expectation Maximization [RPEM] and Non-Parametric Simulated Annealing [NPSA]). To reiterate, these innovati...