Unit 4: Electrical phenomena in the biological system - Subjective Questions

An excitable cell is a cell capable of generating and propagating electrical signals (action potentials) in response to an adequate stimulus, owing to the presence of voltage-gated ion channels in its membrane.

Key properties of excitable cells:

• Resting membrane potential: They maintain a stable negative potential (typically mV in neurons) across the membrane at rest.
• Excitability: They respond to stimuli that reach a threshold by rapidly changing membrane permeability.
• Presence of voltage-gated channels: Predominantly , , and channels that open/close in response to voltage changes.
• All-or-none response: Once threshold is reached, a full action potential is generated.
• Conductivity: They can propagate signals over distances without decrement.

Examples: Neurons, skeletal/cardiac/smooth muscle cells, and some endocrine cells.

Non-excitable cells (e.g., epithelial cells, red blood cells) also possess a resting potential but lack the machinery to generate regenerative action potentials.

Origin of the resting membrane potential:

• The membrane is selectively permeable, mainly to at rest.
• Unequal distribution of ions (, , , and impermeant anions) is maintained by the -ATPase pump.
• diffuses out down its concentration gradient, leaving the inside negative until an electrical gradient opposes further diffusion — this equilibrium gives the resting potential (about mV).

Derivation of the Nernst equation:

At equilibrium the electrical work equals the chemical (diffusional) work. The electrochemical potential of an ion is:

At equilibrium, :

Rearranging:

where:

• = gas constant ()
• = absolute temperature (K)
• = valence of the ion
• = Faraday's constant ()

At , converting to :

An action potential (AP) is a rapid, transient reversal of membrane potential. Its phases are:

1. Resting state: Membrane at mV; voltage-gated and channels closed.

2. Depolarization (rising phase):

• Stimulus brings membrane to threshold ( mV).
• Voltage-gated channels open rapidly; rushes in.
• Membrane potential shoots up towards mV.

3. Repolarization (falling phase):

• channels inactivate.
• Voltage-gated channels open; flows out.
• Membrane potential returns towards negative values.

4. Hyperpolarization (undershoot):

• channels close slowly, causing excess efflux.
• Potential dips below resting level ( mV).

5. Return to rest: pump restores ionic gradients.

Diagram (described): A graph of membrane potential (mV) versus time (ms) showing a sharp spike from mV up to mV, followed by a rapid fall below mV and gradual return to baseline.

Key features:

• All-or-none: AP occurs fully or not at all.
• Refractory periods: Absolute (no new AP) and relative (needs stronger stimulus).

The Ionic Hypothesis, proposed by Hodgkin and Huxley (1952) from experiments on the squid giant axon, explains the electrical activity of nerve membranes in terms of ion movements.

Main postulates:

• The membrane potential is determined by the selective permeability of the membrane to different ions and their concentration gradients.
• The resting potential is dominated by permeability.
• During excitation, there is a sequential and voltage-dependent change in ionic permeability:
  • First, a rapid increase in permeability causes depolarization.
  • Then, permeability falls and permeability rises, causing repolarization.
• Each ion moves towards its own equilibrium (Nernst) potential when the membrane becomes permeable to it.
• The ionic currents are independent and can be described by separate conductances and .

Significance:

• Provided a quantitative mathematical model of the action potential.
• Established that the AP is a regenerative process driven by voltage-gated conductance changes.
• Earned Hodgkin and Huxley the Nobel Prize in Physiology (1963).

Summary:

• Graded potentials are local, small changes that decay with distance and can add together to reach threshold.
• Action potentials are large, uniform, regenerative signals that carry information over long distances without loss.

The Goldman-Hodgkin-Katz (GHK) equation calculates the resting membrane potential when the membrane is permeable to multiple ions simultaneously, weighting each by its permeability.

GHK equation (for , , ):

where is the permeability of ion . Note that terms are reversed because it is an anion.

Difference from the Nernst equation:

• Nernst equation considers only a single ion at equilibrium:

• GHK equation accounts for the relative permeabilities of several ions together, giving the actual steady-state .
• Nernst gives the equilibrium potential of one ion; GHK gives the weighted resting potential.
• When one ion's permeability dominates, the GHK equation reduces to the Nernst equation for that ion.

Membrane proteins are proteins embedded in or associated with the lipid bilayer, essential for many cellular functions including electrical signaling.

Structural classification:

• Integral (intrinsic) proteins: Span the bilayer (transmembrane); held by hydrophobic interactions. Example: ion channels, transporters.
• Peripheral (extrinsic) proteins: Loosely attached to membrane surface via electrostatic bonds. Example: certain enzymes, cytoskeletal anchors.
• Lipid-anchored proteins: Covalently bound to lipids.

Functional classification (relevant to electrical activity):

• Ion channels: Form aqueous pores for passive ion flow (e.g., voltage-gated , , channels).
• Carrier/transport proteins: Bind and move solutes (e.g., glucose transporter).
• Pumps (active transporters): Use ATP to move ions against gradients (e.g., -ATPase).
• Receptors: Bind signaling molecules (e.g., ligand-gated channels like nicotinic ACh receptor).
• Enzymes and structural proteins.

Significance in electrical phenomena:

• Channels and pumps together create and maintain the electrochemical gradients that underlie the resting potential and action potential.

Voltage-gated ion channels are integral membrane proteins whose opening/closing is controlled by changes in membrane potential.

Structure:

• Made of subunits with multiple transmembrane segments (typically 6 segments per domain, four domains in channels).
• Contain a voltage sensor (positively charged S4 segment) that moves in response to voltage changes.
• A selectivity filter allows only specific ions to pass.
• A gate that opens or closes the pore.

Gating mechanism:

• channels: Have an activation gate (m) and an inactivation gate (h).
  • At rest: activation gate closed.
  • On depolarization: activation gate opens rapidly ( influx), then inactivation gate closes.
• channels: Have a single slower activation gate (n); open on depolarization to allow efflux and repolarization.

Role in action potential:

• Rapid channel opening → depolarization.
• inactivation + channel opening → repolarization.
• The time- and voltage-dependence of these gates gives the AP its characteristic shape and the refractory periods.

The -ATPase (sodium-potassium pump) is an integral membrane protein that actively transports ions against their concentration gradients using ATP.

Mechanism:

• For each cycle it pumps 3 out and 2 in.
• Uses energy from hydrolysis of 1 ATP molecule.
• Undergoes conformational changes (E1 ↔ E2) with phosphorylation/dephosphorylation.

Functions:

• Maintains ionic gradients: High inside and high outside — essential for resting potential.
• Electrogenic contribution: Since it moves 3 positive charges out for 2 in, it contributes a small negative potential ( mV) directly.
• Restores gradients after action potentials.
• Cell volume regulation by controlling intracellular solute concentration.
• Secondary active transport: The gradient powers cotransporters (e.g., glucose– symport).

Significance: Without this pump, gradients would dissipate and excitability would be lost. It consumes a large fraction of the cell's resting energy.

Threshold:

• The threshold is the critical membrane potential (about mV in neurons) at which enough voltage-gated channels open to make influx exceed efflux, triggering a self-regenerating depolarization.
• Sub-threshold stimuli produce only local graded potentials that decay.

All-or-none principle:

• Once the threshold is reached, an action potential of fixed amplitude and shape is produced, regardless of how much the stimulus exceeds threshold.
• If threshold is not reached, no action potential occurs.
• Thus the AP is either fully present or completely absent — analogous to a switch.

Consequences:

• Stimulus intensity is coded not by AP size, but by the frequency of APs (frequency coding) and the number of fibres recruited.
• Ensures faithful, non-decremental signal propagation along the axon.

Example: A strong and a barely-threshold stimulus both generate identical AP spikes; the stronger one merely generates them at higher frequency.

Propagation is the movement of the action potential (AP) along the axon without loss of amplitude.

In unmyelinated fibres (continuous conduction):

• The AP at one point causes local circuit currents that depolarize the adjacent membrane to threshold.
• New APs are generated sequentially at each point along the axon.
• Slower because every patch of membrane must be depolarized.

In myelinated fibres (saltatory conduction):

• The axon is insulated by a myelin sheath (from Schwann cells/oligodendrocytes), broken at nodes of Ranvier.
• Voltage-gated channels are concentrated at the nodes.
• The AP 'jumps' from node to node — saltatory conduction.
• This is faster and more energy-efficient (less area to repolarize).

Direction of propagation:

• The refractory period behind the AP ensures it moves in one direction only (away from the point of origin).

Factors affecting velocity:

• Axon diameter: larger → faster.
• Myelination: myelinated → much faster.
• Temperature: higher → faster (within limits).

During and after an action potential, the membrane passes through refractory periods during which its excitability changes.

Functional importance:

• Ensures unidirectional propagation of the AP.
• Limits the maximum firing frequency of the neuron.

Ion movement across cell membranes is governed by fundamental electrochemical rules:

1. Concentration (chemical) gradient:

• Ions diffuse from a region of high concentration to low concentration (Fick's law).

2. Electrical gradient:

• Ions are attracted to regions of opposite charge and repelled from like charge (Coulomb's law).

3. Electrochemical gradient:

• The net driving force on an ion is the sum of chemical and electrical gradients.
• Movement continues until the electrochemical equilibrium (Nernst potential) is reached.

4. Electroneutrality:

• Bulk solutions remain approximately electrically neutral; only a tiny amount of charge separation near the membrane produces the potential.

5. Selective permeability:

• Ion flux depends on the permeability/conductance of specific channels.

6. Ohm's law for ionic current:

where is the driving force and the conductance.

7. Independence principle:

• Each ion's flow is independent of others (Hodgkin–Huxley), so total current is the sum of individual ionic currents.

Ion channels are classified by the stimulus that opens (gates) them.

Common features:

• All are integral membrane proteins forming ion-selective pores.
• Possess a selectivity filter and a gate.

Contrast:

• Voltage-gated respond to electrical changes, ligand-gated to chemical signals, and mechanically-gated to physical force — reflecting their specialized roles in signal generation, transmission, and reception.

Electrochemical equilibrium:

• A state in which the chemical driving force (concentration gradient) on an ion is exactly balanced by the electrical driving force (membrane potential).
• At this point, there is no net movement of the ion, though individual ions still cross randomly in both directions equally.
• The membrane potential at this state is the ion's equilibrium (Nernst) potential.

Calculation for :

Using the Nernst equation at (with ):

Substituting values:

Interpretation: The equilibrium potential for is about mV, which is close to (and helps set) the resting membrane potential, confirming the dominant role of permeability at rest.

Synaptic transmission is the process by which a signal is transferred from a presynaptic neuron to a postsynaptic cell across a synapse (mostly chemical).

Steps in chemical synaptic transmission:

• 1. Arrival of AP: The action potential reaches the presynaptic terminal.
• 2. influx: Depolarization opens voltage-gated channels; enters.
• 3. Vesicle fusion: triggers fusion of synaptic vesicles with the membrane, releasing neurotransmitter into the synaptic cleft.
• 4. Receptor binding: Neurotransmitter diffuses and binds ligand-gated ion channels on the postsynaptic membrane.
• 5. Postsynaptic potential: Channel opening changes ionic permeability.

Role of ligand-gated channels — postsynaptic potentials:

• Excitatory postsynaptic potential (EPSP): e.g., influx via ACh receptors → depolarization.
• Inhibitory postsynaptic potential (IPSP): e.g., influx or efflux via GABA receptors → hyperpolarization.

Integration:

• Multiple EPSPs and IPSPs summate (spatial and temporal). If the summed potential reaches threshold at the axon hillock, an AP is generated.

Termination: Neurotransmitter is removed by degradation, reuptake, or diffusion.

Membrane capacitance ():

• The membrane behaves like a capacitor because the lipid bilayer separates charges (ions) on either side.
• It stores charge; measured per unit area ().

Membrane resistance ():

• The resistance to ion flow through the membrane, determined by the number of open ion channels.
• High = few open channels; low = many open channels.

Time constant ():

• Governs how fast the membrane potential changes in response to a current.
  
• It is the time to reach of the final voltage change.
• A larger = slower voltage change; smaller = faster response.

Length (space) constant ():

• Describes how far a graded potential spreads passively before decaying to of its value.
  
  where = internal (axial) resistance.

Influence on signaling:

• High and low give a larger , allowing signals to spread further — important for efficient conduction and synaptic integration.
• Capacitance slows the rate of potential change, affecting conduction velocity.

The voltage clamp is an experimental technique developed by Cole, and used by Hodgkin and Huxley, that holds (clamps) the membrane potential at a chosen constant value while measuring the ionic currents flowing across the membrane.

Principle:

• A feedback amplifier injects current equal and opposite to the ionic current needed to keep fixed.
• The injected current is a direct measure of the membrane ionic current at that voltage.

Procedure:

• Two electrodes are used: one to measure and one to pass current.
• By stepping the voltage and using ion substitution or channel blockers (e.g., TTX blocks , TEA blocks ), individual ionic currents are isolated.

Significance:

• Allowed separation of the and currents underlying the action potential.
• Demonstrated that ionic conductances are voltage- and time-dependent.
• Provided the data for the Hodgkin–Huxley mathematical model.
• Formed the foundation for later techniques like the patch clamp (studying single channels).

Conclusion: The voltage clamp confirmed the Ionic Hypothesis and revolutionized electrophysiology.

Since every action potential has the same amplitude (all-or-none), information about stimulus strength cannot be carried by AP size. The nervous system uses other coding strategies:

1. Frequency coding (rate coding):

• A stronger stimulus produces action potentials at a higher frequency (more spikes per second).
• Weak stimuli produce low-frequency firing.
• This is the primary way intensity is encoded in single neurons.

2. Population (recruitment) coding:

• Stronger stimuli recruit more neurons/receptors with different thresholds.
• Low-threshold fibres fire first; high-threshold fibres join as intensity rises.

3. Temporal pattern coding:

• The timing and pattern of spikes (bursts vs regular firing) can carry additional information.

4. Labelled-line coding (quality):

• The type of stimulus (modality) is coded by which specific pathway/neuron is active.

Role of refractory period:

• The refractory period sets an upper limit to firing frequency, preventing indefinitely high rates.

Summary: Stimulus intensity is represented by a combination of firing frequency and the number of active fibres, allowing rich information transfer despite fixed AP amplitude.

Membrane proteins are central to every aspect of a cell's electrical excitability. Their integrated roles are:

1. Ion channels — generating and shaping signals:

• Voltage-gated channels (Na, K, Ca) produce and propagate the action potential.
• Leak channels (mainly K) establish the resting membrane potential.
• Ligand-gated channels generate postsynaptic potentials.

2. Pumps — maintaining gradients:

• The -ATPase restores and maintains the Na/K gradients that store the potential energy for excitation.
• -ATPase and Na/Ca exchangers keep intracellular low.

3. Receptors — signal reception and modulation:

• Ionotropic receptors directly open channels (fast).
• Metabotropic receptors act via second messengers to modulate channel activity (slow, prolonged).

4. Transporters/exchangers:

• Use existing gradients for secondary active transport, indirectly supporting ionic balance.

Integrated significance:

• Pumps create the gradients → leak channels set the resting potential → voltage/ligand-gated channels use the gradients to generate and transmit signals → receptors allow communication and modulation.
• Together they convert stored electrochemical energy into rapid electrical signaling, making excitability possible.

Clinical relevance: Mutations or drugs affecting these proteins cause channelopathies (e.g., epilepsy, cardiac arrhythmias), highlighting their fundamental importance.