Quantitative Physiology of Cells and Tissues

Understanding how cells maintain their composition, volume, and electrical signals is fundamental to modern bioengineering and medicine. This text-based course bridges the gap between biology and engineering by introducing you to the quantitative principles that govern cellular processes. You will learn to describe complex biological systems using precise mathematical frameworks, moving beyond simple qualitative descriptions to true predictive understanding. By working through this comprehensive material, you will transition from a basic understanding of cell biology to a rigorous, quantitative appreciation of cellular biophysics. You will explore how physical forces, chemical gradients, and electrical potentials interact to sustain life at the cellular level, integrating modern computational thinking and data analysis techniques along the way. What you'll learn: - Understand the fundamental thermodynamic and physical principles of solute and water transport across cell membranes - Model cellular volume regulation and the maintenance of steady-state chemical compositions - Calculate membrane potentials using classical electrophysiological equations and modern computational approximations - Analyze the electrical properties of excitable membranes and the generation of action potentials - Apply quantitative frameworks to interpret experimental data from classic and modern biophysical research - Formulate mathematical equations to describe carrier-mediated transport and ion channel kinetics This course begins with foundational definitions, key terminology, and the physical chemistry of solutions, establishing a solid baseline before moving into complex mathematical models. You will progress systematically from simple diffusion to multi-compartment electrical circuits, analyzing real-world experimental scenarios through clear, written explanations and step-by-step mathematical derivations. This course is designed for beginners in quantitative biology, undergraduate students in engineering or science, and self-directed learners who want to apply mathematical rigor to biological systems. No prior background in advanced physiology is required, though a basic comfort with algebra and introductory physics is helpful. Start reading today to master the mathematical foundations of cellular life.