Cardiac Membrane Biophysics

Cardiac Membrane Biophysics is the study of the physical principles and electrical properties governing the behavior of cardiac cell membranes. It focuses on how ionic gradients, membrane permeability, and electrical forces interact to generate and regulate the electrical activity essential for cardiac function, including the initiation and propagation of action potentials that underlie the heartbeat.

Electrical Properties of the Cardiac Cell Membrane

The cardiac cell membrane acts as a selective barrier separating the intracellular and extracellular environments. It is electrically polarized due to differences in ion concentrations across the membrane and the selective permeability to these ions. This polarization establishes a resting membrane potential, typically around −85 to −90 mV in ventricular myocytes, which is essential for excitability.

The membrane's electrical behavior can be modeled as an electrical circuit consisting of resistive and capacitive elements. Ion channels represent variable conductances (resistors), and the lipid bilayer behaves as a capacitor, storing and separating charge. The interplay between ionic currents and the membrane capacitance shapes the time-dependent changes in membrane voltage during the cardiac action potential.

Ionic Gradients and Electrochemical Potential

Ions such as potassium (K⁺), sodium (Na⁺), calcium (Ca²⁺), and chloride (Cl⁻) are unevenly distributed across the cardiac cell membrane. These concentration differences create chemical gradients that drive diffusion. Simultaneously, the electrical gradient created by the membrane potential influences ion movement, together comprising the electrochemical driving force.

The electrochemical potential (μ_i) for an ion i is the sum of its chemical potential and electrical potential, determining the direction and magnitude of ion fluxes across the membrane. Ion pumps and transporters, such as the Na⁺/K⁺ ATPase, maintain these gradients by active transport against electrochemical forces.

Ionic Equilibrium Potentials

Each ion has an equilibrium potential (also called the Nernst potential), the membrane voltage at which there is no net flow of that ion across the membrane because the electrical and chemical driving forces are balanced. The Nernst potential for ion i is calculated by the Nernst equation:

where R is the gas constant, T is absolute temperature, z is the ion valence, F is Faraday's constant, and [i]_out and [i]_in are the extracellular and intracellular ion concentrations, respectively.

The equilibrium potentials set the baseline for understanding how ionic currents flow during different phases of the cardiac action potential.

Membrane Permeability and Resting Potential

The resting membrane potential is primarily determined by the permeability of the membrane to K⁺ ions through inward-rectifier potassium channels (IK1), which allow K⁺ to move freely according to its electrochemical gradient. The membrane is much less permeable to Na⁺ and Ca²⁺ at rest.

The Goldman-Hodgkin-Katz (GHK) equation describes the resting membrane potential by accounting for the permeability and concentration gradients of multiple ions simultaneously:

where P_K, P_Na, and P_Cl are the permeabilities of potassium, sodium, and chloride ions, respectively.

Electrochemical Driving Force and Ionic Current

The net ionic current for a given ion depends on both its electrochemical driving force and the membrane permeability or conductance to that ion. The driving force is the difference between the membrane potential (V_m) and the ion's equilibrium potential (E_i):

The ionic current I_i is described by Ohm’s law for ionic flow:

where g_i is the membrane conductance for ion i, which depends on the number and state of ion channels.

Membrane Conductance and Current-Voltage Relations

Membrane conductance is dynamic and voltage-dependent, as ion channels open and close in response to changes in membrane potential and other factors like intracellular calcium or phosphorylation state. Different ion channels have characteristic current-voltage (I-V) relationships, determining how ionic currents change with membrane voltage.

For example, voltage-gated sodium channels responsible for the rapid depolarization phase open transiently at threshold voltages, allowing a rapid inward Na⁺ current that drives the upstroke of the action potential. Potassium channels contribute outward currents that repolarize the membrane, with diverse kinetics and voltage dependencies.

Membrane Capacitance and Electrical Time Dependence

The lipid bilayer membrane acts as a capacitor, storing charge on its surfaces. The capacitance (C_m) of the cardiac cell membrane is typically around 1 µF/cm². The membrane capacitance introduces a time-dependent component to voltage changes because charging or discharging the capacitor requires time proportional to the product of capacitance and membrane resistance (or inverse conductance).

This electrical property explains the finite time course of voltage changes during the cardiac action potential, contributing to the characteristic shape and duration of the electrical signal.

Net Membrane Current and Voltage Dynamics

The overall membrane current (I_m) at any instant is the sum of all ionic currents and the capacitive current:

This equation underlies the cardiac action potential's voltage dynamics, where ion channel gating kinetics and ionic gradients interact to produce the temporal profile of membrane voltage changes.

The integrated biophysical understanding of ionic currents, membrane permeability, and electrical properties is crucial for explaining normal cardiac electrophysiological function and the basis of arrhythmias and other cardiac pathologies.