The major factors determining drug responses are the input and disposition rates controlling pharmacokinetics, drug distribution to the site of action (biophase), the mechanism of drug action in altering mediator or receptor levels, and turnover and transduction processes. A major advance in quantifying pharmacologic responses came from our recognition that diverse pharmacodynamic effects can be characterized using a family of four basic (and extended) indirect response models. These (and most) models require analysis using differential equations which usually cannot be fully solved analytically. This project seeks to characterize and quantify the general properties of drugs acting on turnover processes which are important for numerous body functions, structures, or biomarkers. Our specific aims include further analysis of extended indirect response models (with and without precursor compartments) for responses following multiple dose administration that are not predictable from single- dose studies; continued development of multiple-pool lifespan-based indirect response models that mimic hematopoietic and other cellular differentiation cascades for drugs capable of altering the turnover or life-span of natural cells; development of advanced pharmacodynamic models of target-mediated drug disposition for systems where drug action alters the turnover of target-expressing cells, drug competes with endogenous ligands, and the mechanism of drug binding is allosteric or noncompetitive in nature; and the development and evaluation of mechanism-based transit compartment pharmacodynamic models that can emulate cellular signal transduction cascades and bridge molecular biology and macro- scale pharmacodynamic responses with a focus on anticancer drugs. Advanced methods of calculus and simulations will be employed to seek exact or approximate solutions or behaviors of these models to identify how the onset, extent, return, duration, integrals of response (flux), and steady-states of response are controlled, to recover meaningful parameters more easily from experimental data, and to discriminate among diverse models available to describe typical data sets. These efforts will yield improved insights and methods for understanding and characterizing the time-course of drug responses as related to major drug- and system-specific properties manifesting from mechanisms of physiology and pharmacologic action. PUBLIC HEALTH RELEVANCE: The major factors determining the intensity and time-course of drug responses are related to how the body processes the drug, pharmacologic mechanisms of action, and turnover of physiologic structures and functions. These drug and system properties are complex. This proposal seeks to utilize mathematical and computer modeling to improve the understanding of how drugs elicit their effects. Such efforts enable the integration of large amounts of information to efficiently explore new drug targets and provide methods for improving utilization of current drugs for treating various diseases.