lecture tuesday 8/26
Overview
This lecture introduces neurophysiology, focusing on a single neuron to build foundational concepts for how neurons generate and conduct electrical signals. It builds on prior membrane transport ideas (diffusion for nonpolar molecules, channels/transporters for polar particles) and emphasizes charged particles and gradients.
Quick setup you should reproduce on paper
Draw a neuron with: dendrites, cell body (soma), axon. Include a rough outline, then add:
Sodium-potassium pumps (Na⁺/K⁺-ATPase) showing 3 Na⁺ pumped out for every 2 K⁺ pumped in.
Regions: extracellular fluid (ECF) outside the cell and intracellular fluid (ICF) inside.
Indicate gradients: where sodium and potassium are high/low.
Calcium (Ca²⁺) gradient: high outside, small amount inside.
Intracellular anionic proteins (negatively charged) inside the cell; label as anionic proteins.
Key visual cue: Na⁺ and K⁺ are generally cations (positively charged); Ca²⁺ is also a cation; intracellular proteins are anions.
Add a few potassium leak channels (always open, “leak” channels) drawn as simple openings in the membrane; indicate that potassium leaks out, down its gradient.
Note: glucose transporters (GLUTs, SGLTs) are present in real cells, but not the focus yet. They exist but are not drawn in detail here.
Core concepts introduced
Chemical gradients vs electrical gradients: different kinds of gradients across the membrane that influence ion movement.
Anionic intracellular proteins bias the inside to be more negative (negatively charged inside).
The outside (ECF) is biased toward being more positive due to the higher concentration of cations (Na⁺, Ca²⁺).
Potassium leak channels contribute to the negative interior by allowing K⁺ to exit.
The combination of these factors creates an electrochemical gradient across the membrane, i.e., a membrane potential.
Key ions and their distribution (as discussed in the lecture)
Sodium (Na⁺): higher outside (ECF), lower inside (ICF); flow direction if a Na⁺ channel opens: into the cell (down its chemical gradient, aided by electrical gradient).
When a Na⁺ channel opens, the inside becomes more positive (depolarization).
Potassium (K⁺): higher inside (ICF), lower outside (ECF); flow direction if a K⁺ leak channel opens: out of the cell (down its chemical gradient, aided by the outside being more positive).
When K⁺ leaks out, the inside becomes more negative (hyperpolarization).
Calcium (Ca²⁺): higher outside (ECF); small amount inside (ICF); tends to flow into the cell when a Ca²⁺ channel opens.
Ca²⁺ influx is foundational for neural signaling.
Intracellular proteins (anionic): negative charge inside; cannot cross membrane; contribute to internal negativity.
Extracellular and intracellular sides: ECF (outside) vs. ICF (inside).
Three core contributors to the resting membrane potential (RMP)
1) Anionic proteins inside (negative charge) – increase inside negativity.
2) Excess cations outside (Na⁺, Ca²⁺) – creates a positive outside, contributing to a negative inside when compared across the membrane.
3) Potassium leak channels – allow continuous outward flow of K⁺ (positive charge leaving the inside), driving the inside toward more negative values.
Result: The resting membrane potential (RMP) is typically about V_{rest} \,\approx \, -70\ \text{mV} with a common range of -60\ \text{to}\ -80\ \text{mV}. This is written as a difference of charge inside relative to outside (inside is negative).
Important related potentials and concepts
Potassium equilibrium potential (E_K): around -90\ \text{mV}, the voltage at which K⁺ diffusion out of the cell is balanced by the opposing electrical gradient.
If only Na⁺ channels were open, the membrane would depolarize toward the Na⁺ equilibrium potential, roughly up to about +60\ \text{mV}.
Sodium pump details: the Na⁺/K⁺-ATPase pump maintains gradients by actively transporting 3 Na⁺ out and 2 K⁺ in per cycle, contributing to the overall ion distribution and resting potential.
Calcium gradient: Ca²⁺ tends to be kept at very low intracellular levels; external high Ca²⁺ supports signaling when Ca²⁺ channels open.
The membrane potential is an emergent property of both chemical gradients and the electrical charges across the membrane, i.e., the electrochemical gradient.
Translating gradients into voltage: the concept of equilibrium potentials
If you consider a single ion type and its gradient, the equilibrium potential for that ion (Eion) can be estimated by the Nernst equation: E{\text{ion}} = \frac{RT}{zF} \ln\left(\frac{[\text{ion}]{\text{out}}}{[\text{ion}]{\text{in}}}\right)
In simple terms, this is the voltage where the chemical gradient for that ion is exactly opposed by the electrical gradient for that ion.
In neurons, because multiple ions are present, the resting potential is not equal to any single E_ion but is determined by a balance of several ions and channels.
The Goldman-Hodgkin-Katz (GHK) equation extends this idea to multiple ions and varying permeabilities (PK, PNa, PCl, etc.). A schematic form is: Vm = \frac{RT}{F} \ln\left(\frac{PK[K^+]{out} + P{Na}[Na^+]{out} + P{Cl}[Cl^-]{in}}{PK[K^+]{in} + P{Na}[Na^+]{in} + P{Cl}[Cl^-]{out}}\right)
These equations are introduced conceptually; you won’t be required to memorize them, but you will understand that channel permeability and ion gradients together set the resting potential and responses to stimulation.
Resting membrane potential in context of membrane structure (cellular diagram ideas)
A membrane sketch can show:
Sodium-potassium pump moving Na⁺ out and K⁺ in (3 Na⁺ out per 2 K⁺ in);
Potassium leak channels widely distributed; sodium leak channels present but less abundant (e.g., ~1 Na⁺ leak channel per ~10 K⁺ leak channels);
Anionic proteins trapped inside (negative charge);
Sodium, potassium, calcium distributions highlighting high outside (Na⁺, Ca²⁺) and high inside (K⁺) tendencies;
Outer surface (ECF) mostly positive relative to inner surface (ICF).
How gradients produce an electrical gradient (the battery analogy)
Differential charges across the membrane create a voltage difference similar to a battery with a positive outside and a negative inside.
This voltage difference is the membrane potential and stores electrochemical energy that can drive ion flow when channels open.
A simple mental model: when positive and negative charges are separated across the membrane, they tend to flow to re-establish balance (opposites attract, like charges repel).
In neurons, creating local charge differences (via gradients and selective permeability) provides the energy for electrical signaling.
What opens channels and what happens then
Stimuli can open or close channels, changing membrane permeability and thus the membrane potential.
Types of stimuli leading to channel opening:
Chemical stimuli via ligand-gated (receptor) channels: neurotransmitters or other chemicals bind receptors and open ion channels (e.g., sodium channels opening to depolarize).
Electrical stimuli via voltage-gated channels: channels open when the membrane potential reaches a threshold (introduced as a topic to be explored later).
Mechanical stimuli via mechanically gated channels: physical deformation of the membrane (e.g., touch receptors) opens channels.
Consequences of opening specific channels:
Sodium channels open → depolarization (inside becomes more positive).
Potassium leak channels open → hyperpolarization (inside becomes more negative) due to outward positive current.
Calcium channels open → depolarization/recruitment of signaling cascades (Ca²⁺ influx).
At rest, there are more potassium leak channels than sodium leak channels, so resting permeability is biased toward K⁺, pulling the resting potential closer to the potassium equilibrium potential (approximately −90 mV) but not all the way there because there are also small sodium leak and active pumping that maintain the −70 mV rest.
Depolarization vs hyperpolarization (conceptual recap)
Depolarization: membrane potential moves toward zero (less negative), e.g., opening Na⁺ channels causes the inside to become more positive.
Hyperpolarization: membrane potential becomes more negative, e.g., opening K⁺ leak channels causes outward positive current.
Net effect: small changes in channel openings can shift the membrane toward depolarization or hyperpolarization, setting the stage for action potentials and graded potentials.
Recap of the resting potential and its significance
At rest: inside is negative relative to outside due to combination of:
Anionic proteins inside (negative charge).
Higher extracellular positive ions (Na⁺ and Ca²⁺ outside).
Continuous outward leak of K⁺.
Na⁺/K⁺-ATPase maintaining gradients.
Resting potential is typically around V_{rest} \approx -70\ \text{mV} (range -60\ \text{to}\ -80\ \text{mV}).
The membrane behaves like a battery, and the energy stored in the electrochemical gradient powers neural signaling when channels open.
Preview of next steps in the course
We will move from resting potential to graded potentials in dendrites and soma, then to action potentials generated and conducted along axons.
We will explore how different channels contribute to signal propagation, including:
Graded potentials: small, localized changes at the dendrites/soma due to receptor-channel opening.
Action potentials: large, all-or-none spikes driven by voltage-gated channels; they propagate along the axon.
There will be a discussion of how neurons communicate with other neurons via neurotransmitters at synapses and how neurotransmitter receptors can open ion channels (ligand-gated) to influence post-synaptic membranes.
Practical notes from the lecture and learning activities
A core student activity is to create a poster-sized, hand-drawn neuron with all relevant channels and gradients to solidify understanding.
The instructor emphasizes that learning comes from drawing and manipulating the schematic, not just passively viewing the diagram.
The lecture uses analogies (e.g., battery, Rose Bowl gates) to explain permeabilities and flows.
The lecture explicitly sets up two PowerPoint sessions: this first focuses on a single neuron; the second will cover how one neuron communicates with another.
Ethical/philosophical/practical implications discussed (implicitly)
The content emphasizes learning through hands-on visualization and active engagement, which aligns with effective teaching practices in neuroscience.
Understanding cellular neurophysiology lays the groundwork for appreciating neural signaling in health and disease, with practical implications for medicine and neuroscience research.
Quick reference equations and numbers (LaTeX format)
Resting membrane potential (typical): V_{rest} \approx -70\ \text{mV}, range -60\ \text{to}\ -80\ \text{mV}
Sodium-potassium pump stoichiometry: 3\ Na^+\ \text{out} : 2\ K^+\ \text{in}
Potassium equilibrium potential (approximate): E_K \approx -90\ \text{mV}
Sodium equilibrium potential (illustrative when channels open): E_{Na} \approx +60\ \text{mV}
Single-ion equilibrium potential (Nernst):
E{\text{ion}} = \frac{RT}{zF} \ln\left(\frac{[\text{ion}]{\text{out}}}{[\text{ion}]_{\text{in}}}\right)Multi-ion membrane potential (Goldman–Hodgkin–Katz, schematic):
Vm = \frac{RT}{F} \ln\left(\frac{PK[K^+]{out} + P{Na}[Na^+]{out} + P{Cl}[Cl^-]{in}}{PK[K^+]{in} + P{Na}[Na^+]{in} + P{Cl}[Cl^-]_{out}}\right)
Key terms to remember
Resting membrane potential (RMP), electrochemical gradient, chemical gradient, electrical gradient, membrane permeability, leak channels, voltage-gated channels, ligand-gated (receptor) channels, mechanically gated channels, depolarization, hyperpolarization, graded potentials, action potentials (preview).
Study tips based on this lecture
Practice drawing a neuron with accurate distributions of ions and channels.
Label outside (ECF) vs inside (ICF) and mark where gradients exist.
Memorize the typical resting potential and the approximate equilibrium potentials for key ions (K⁺, Na⁺) as intuitive anchors.
Distinguish chemical vs electrical gradients and understand how both interact to set the membrane potential.
Be able to explain why opening K⁺ channels hyperpolarizes while opening Na⁺ channels depolarizes.
Prepare for the next lecture by reviewing stimulus types (chemical, electrical, mechanical) and how they influence channel opening and membrane potential.