Biophysics

Physics of biological systems, molecules, membranes, transport, biomechanics, and biological signals.

General idea of the topic

Biophysics investigates living processes using quantitative physical laws and methods: non-equilibrium open-system thermodynamics, macromolecular statistical mechanics, membrane electrophysiology, and low-Reynolds-number microhydrodynamics. Biological organisms are open physical systems that continuously dissipate free energy to maintain ordered structural complexity (Prigogine dissipative structures), evading thermodynamic equilibrium.

This node covers transmembrane resting potentials (Nernst-Planck and Goldman-Hodgkin-Katz equations), nerve impulse conduction (Hodgkin-Huxley model), biological polymer elasticity (DNA, proteins), and molecular motors (kinesin, ATP synthase).

What you will truly understand

You will understand how electrochemical concentration gradients of ions ($Na^+, K^+, Cl^-$) across the lipid bilayer establish a negative resting potential (approx. $-70\text{ mV}$), which upon depolarization triggers all-or-none action potentials driven by voltage-gated ion channels.

You will model entropic polymer elasticity in DNA using the Freely Jointed Chain (FJC) and Worm-Like Chain (WLC) statistical models.

Recommended learning route

1. Membrane thermodynamics and transport: Fickian diffusion, osmotic pressure, Nernst equilibrium, and Goldman-Hodgkin-Katz equation.
2. Cellular electrophysiology: lipid bilayer capacitance, RC equivalent circuits, neuronal cable equations, and Hodgkin-Huxley action potential kinetics.
3. Macromolecular statistical mechanics: entropic spring elasticity of DNA, helix-coil transitions, and protein free energy folding landscapes.
4. Low Reynolds number bio-hydrodynamics: Purcell's life at low Reynolds number ($Re \ll 1$), Stokes drag, rotational diffusion, and molecular motor ratchet mechanisms.

Physical criterion you must acquire

Recognizing that cellular mechanics operate entirely in the non-inertial overdamped regime ($Re \ll 1$), where motion ceases instantly when forces vanish and thermal Brownian kicks dominate.

Connection with real problems

• Neurophysics and neural engineering of high-bandwidth Brain-Computer Interfaces (BCIs).
• Targeted nanomedicine delivery vehicles using lipid nanoparticles.
• Single-molecule force spectroscopy using optical tweezers and Atomic Force Microscopy (AFM).

Final goal of the topic

Master the physical, electrical, and thermodynamic principles of biophysics to model cellular dynamics and macromolecular systems quantitatively.