Cell Physiology/Part 1

🔲Cell Membrane and Transport

The cell membrane is the fundamental barrier that defines the cell, controls molecular traffic, and maintains the electrochemical gradients essential for life. Understanding membrane function requires both molecular biology and electrical engineering perspectives.

⚡ The Membrane as an Electrical Circuit

Cell membranes can be modeled as electrical circuits, a concept that revolutionized our understanding of physiology. This analogy, pioneered by Hodgkin and Huxley in 1952, allows us to use circuit theory to predict and understand cellular electrical behavior.

Circuit Components

  • •Capacitor (Cm): Lipid bilayer (~1 µF/cm²) stores charge
  • •Resistors (R): Ion channels provide conductance pathways
  • •Batteries (E): Ion gradients create electromotive force (Nernst potentials)
  • •Current sources: Ion pumps maintain gradients (active transport)

Governing Equations

Ohm's Law:I = g(Vm - E)
Capacitor:Ic = Cm(dVm/dt)
Kirchhoff:Itotal = Ic + ΣIionic

⚡Interactive Membrane Equivalent Circuit

Membrane Equivalent CircuitExtracellularIntracellularCm1 µF/cm²gNa+60mVgK-90mVgCl-70mVgL-70mVVm-85.7 mV

Channel Conductances (mS/cm²)

g_Na:1.0
g_K:36.0
g_Cl:0.3
g_L:0.3
C_m:1.0 µF/cm²
I_inj:0 µA/cm²

Calculated Parameters

Membrane Potential:-85.69 mV
Input Resistance:26.6 Ω·cm²
Time Constant:0.03 ms
Total Conductance:37.6 mS/cm²
Individual Currents (µA/cm²):
I_Na: -145.69I_K: 155.11I_Cl: -4.71I_L: -4.71
Try this: Increase g_Na and watch the membrane depolarize. Then increase g_K to see hyperpolarization. The membrane potential is determined by the weighted average of equilibrium potentials!

🧮Nernst Potential Calculator

37°C (310.1 K)
Equilibrium Potential (EK)
-89.1 mV
Nernst Equation:
E = (RT/zF) × ln([X]o/[X]i)
Simplified (at 37°C):
E = (61.5/1) × log₁₀(5/140)
E = -89.0 mV
Potassium: Primary determinant of resting membrane potential

🔬Membrane Structure

The plasma membrane follows the fluid mosaic modelproposed by Singer and Nicolson (1972). It consists of:

Lipid Bilayer

  • • Phospholipids (~50%)
  • • Cholesterol (~20%)
  • • Glycolipids (~5%)
  • • Thickness: 7-8 nm

Membrane Proteins

  • • Integral proteins
  • • Peripheral proteins
  • • Channels & transporters
  • • Receptors & enzymes

Key Properties

  • • Selective permeability
  • • Fluidity (lateral diffusion)
  • • Asymmetry
  • • Self-sealing

🚚Transport Mechanisms

TypeEnergyDirectionExamplesCircuit Analog
Simple DiffusionNone (passive)Down gradientO₂, CO₂, steroidsResistor (fixed)
Facilitated DiffusionNone (passive)Down gradientGlucose (GLUT), ionsVariable resistor
Primary ActiveATP hydrolysisAgainst gradientNa⁺/K⁺-ATPase, Ca²⁺-ATPaseCurrent source + battery
Secondary ActiveIon gradientMixedSGLT, Na⁺/Ca²⁺ exchangerCoupled current sources
VesicularATP + GTPBulk transportEndocytosis, exocytosis—

🔋The Na⁺/K⁺-ATPase: The Cell's Power Plant

The sodium-potassium pump is the most important active transporter, consuming ~25% of cellular ATP (up to 70% in neurons). It maintains the ionic gradients that power secondary transport and enable electrical signaling.

Pump Cycle (per ATP)

3 Na⁺→ OUT
2 K⁺→ IN
Net: +1 charge OUT(electrogenic)

Circuit Representation

In circuit terms, the Na⁺/K⁺-ATPase acts as a current source that continuously pumps current outward, contributing about -5 to -10 mV to the resting membrane potential.

Ipump = Imax × f([Na]i) × f([K]o) × f([ATP])

Chapter Topics

1.1

Membrane Structure

Lipid bilayer, proteins, and the fluid mosaic model

1.2

Passive Transport

Diffusion, facilitated transport, and osmosis

1.3

Active Transport

ATP-driven pumps and secondary active transport

1.4

Vesicular Transport

Endocytosis, exocytosis, and membrane trafficking

1.5

Membrane Potential

Nernst equation, GHK, and resting potential

⚡

Circuit Model

Interactive electrical equivalent circuit with Hodgkin-Huxley

📐 Key Equations

Nernst Equation
EX = (RT/zF) ln([X]o/[X]i)
Goldman-Hodgkin-Katz
Vm = (RT/F) ln(PK[K]o + PNa[Na]o + ...)
Fick's Law
J = -D (dC/dx)
Membrane Time Constant
τ = Rm × Cm
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