### Abstract

The sections in this article are:

- 1 Thermodynamics
- 1.1 Maximal Work Is Attained on Reversible Paths
- 1.2 Changes in Free Energy Are Obtained from Chemical Potentials: Free Energy per Mole
- 1.3 Solutes in Phase Equilibrium
- 1.4 Osmotic Equilibrium
- 1.5 Chemiosmotic Coupling

- 2 Diffusion
- 2.1 Flux Is Proportional to the Concentration Gradient: Fick's First Law
- 2.2 Conservation of Matter: Fick's Second Law
- 2.3 Progress of Diffusion: Mean Square Displacement = 2 Dt
- 2.4 Randomly Diffusing Molecules Spread Out in a Normal Distribution
- 2.5 The Diffusion Front, Where Solute Depletion Ends and Accumulation Begins, Moves as 2nDt
- 2.6 Diffusion Transients in Thin Membranes Are Very Rapid
- 2.7 Permeation through Membranes Takes Place in At Least Three Steps
- 2.8 The Exchange Time for Filling or Emptying of Cells Equals V/PA
- 2.9 In Simple Exponential Processes, the Time Constant = the Mean Residence Time
- 2.10 Cytoplasmic Diffusion Transients Are Rapid
- 2.11 Unstirred Layers Can Be a Significant Barrier
- 2.12 Membrane Diffusion Is Assumed to Be Rate‐Limiting for Plasma Membranes
- 2.13 Selective Permeability of Lipid Bilayers Is Determined Primarily by Solubility

- 3 Water Transport
- 3.1 Water Transport Can Be Driven by Three Different Gradients
- 3.2 In Lipid Membranes Water Transport Occurs by Solubility‐Diffusion Mechanism, with Pf = Posm = Pd
- 3.3 Osmotic Gradients Generate Hydraulic Pressure Gradients in Aqueous Channels
- 3.4 In Narrow Channels the Ratio Posmotic/Pdiffusion = the Number of Water Molecules Contained within the Channel
- 3.5 Coupling of Solute and Solvent Transport Is Described by the Kedem‐Katchalsky Equations

- 4 Ionic Diffusion
- 4.1 Diffusion with Superimposed Drift Due to External Forces
- 4.2 Ions Transported by Simple Diffusion Follow the Ussing Flux Ratio Relation
- 4.3 Bulk Solutions Carry No Net Charge
- 4.4 The Constant Field Is a Convenient Idealization
- 4.5 Conductance Depends on Ionic Concentrations
- 4.6 Permeability Ratios Can Be Measured by Changes in Membrane Potential
- 4.7 An Electrogenic Pump Contributes to Ψm
- 4.8 Channels Can Be Incorporated into the Nernst‐Planck Formulation

- 5 Energy Barriers
- 5.1 The Born Energy Estimates the Work Required to Transfer an Ion from One Medium to Another
- 5.2 Born Energy, Image Forces, Dipole Potentials, and Hydrophobic Interactions Contribute to the Energy Barriers of Lipid Bilayers
- 5.3 Solvation Energies Are Important Determinants of Channel Accessibility
- 5.4 Surface Potentials Modify the Transmembrane Potential as Well as Local Ion Concentrations
- 5.5 Transport across Energy Barriers
- 5.6 Eyring Rate Theory: Rate Constants Depend on Ψ
- 5.7 Kinetic Approaches

- 6 Channels
- 6.1 Single‐Occupancy Channels with Binding Sites Show Saturation Kinetics
- 6.2 Competition, Unidirectional Flux, and the Ussing Flux Ratio
- 6.3 Single‐Occupancy Channels: Voltage Dependence in Symmetric Channels
- 6.4 Single‐Occupancy‐Channel Results Can Be Generalized to N Sites
- 6.5 Multiple Occupancy

- 7 Simple Carriers
- 7.1 Net Flux
- 7.2 Unidirectional Flux
- 7.3 Equilibrium at the Boundaries
- 7.4 Rate‐Limiting Steps at the Boundaries
- 7.5 Energy‐driven Simple Carrier Systems

- 8 Cotransport
- 8.1 Thermodynamics: Cotransport Can Move Solutes “Uphill”
- 8.2 Kinetic Description
- 8.3 General Net Flux
- 8.4 Unidirectional Fluxes
- 8.5 Kinetics of Simultaneous Binding of mA and nB Resembles Simple Carrier Kinetics When Carrier Concentrations Are Replaced with the Product AmBn
- 8.6 Relations between the Net Flux Equation Parameters and the Michaelis‐Menten—type Parameters for 1:1 Stoichiometry

- 9 Countertransport
- 9.1 Thermodynamics
- 9.2 Kinetic Models
- 9.3 Ping‐Pong Model
- 9.4 Sequential Model
- 9.5 Generalization to m‐n Stoichiometry for Simultaneous Binding

- 10 Fluctuating Barriers: Channels and Carriers
- 10.1 Channel Transport Properties Depend on the Rate of Transition between the Conformations
- 10.2 Channels with Fluctuating Barriers Do Not Show Michaelis‐Menten Kinetics
- 10.3 Channels with Fluctuating Barriers Can Show Carrier Kinetics