NSCI 175 Lecture 5 Notes: Resting Membrane Potential, Bioenergetics, and Equilibrium Potentials

Chapter 5: Resting Membrane Potential, Bioenergetics, and Equilibrium Potentials

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Section 1: Course Logistics, Student Resources, and Academic Milestones

Succeeding in advanced neuroscientific training requires a combination of mastering complex cellular biophysics and navigating the administrative structures and resources provided by the department [103, 105]. This section outlines the academic deadlines, digital platforms, and support networks established for NSCI 175 [103, 104, 105].

1.1 Weekly Problem Sets and Interactive Worksheets

To facilitate active learning, the professor assigns specialized homework sheets designed to give students practical experience working with the mathematical models of cellular excitability [103, 104]:

• The Quantitative Focus: The homework focuses on calculations utilizing the Nernst Equation (to determine equilibrium potentials for individual ions) and the Goldman Equation (to determine the overall resting membrane potential based on multiple ionic permeabilities) [104, 136].

• Grading and Submission: Unlike other assessments, these worksheets are graded strictly for completion rather than correctness, allowing students to practice and make mistakes without academic penalty [104]. They are due on Wednesday, September 9th (9/9) [104].

• The Simulator Worksheet App: One of the assignments is a simulator worksheet that traditionally utilizes an interactive app [104]. Because this app is older and currently lacks a modern replacement, some students may experience compatibility issues [104]. The professor explicitly notes that if the app fails to load, students do not need to use it; they can fully complete the worksheet by executing all equations and calculations manually [104].

1.2 Office Hours and the Canvas Navigation Protocol

The instructional team hosts multiple weekly office hours for students seeking conceptual clarity or professional mentorship [105]:

• Scheduling Protocol: Sign-ups are managed through the Canvas Calendar Tool, which is a global platform feature located on the far-left global navigation panel (rather than within the specific course shell itself) [105].

• Visibility Troubleshooting: To view available office hour blocks, students must ensure that they have actively checked the box next to their specific course section (NSCI 175.01 Fall 2026) on the right-hand sidebar [105].

• The Invisible Slot Issue: The professor notes a current Canvas system bug: once an office hour slot is fully booked, it becomes completely invisible to other students rather than showing up as "taken" [105]. Students facing scheduling issues or invisible blocks are instructed to contact the team [106].

1.3 Writing Milestone and Roster Adjustments

The class continues to experience drop/add roster adjustments [106]. Students are urged to welcome new team members and help them integrate into their established working groups [106].

• Writing Assignment #1: The first formal writing assignment is officially due on Monday, September 14th [106].

• Piazza Instructions: The complete rubric and detailed instructions are published on Canvas and Piazza [106]. Students are instructed to review these guidelines immediately and post any general questions on Piazza so that the entire class can access the clarification [106].

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Section 2: Scientific Synthesis: Astrocyte Primary Cilia and Motor Learning

Before diving into resting potentials, the class reviewed the quantitative data from the "Ticket Out the Door" (TOD) case study analyzing how astrocytic dysfunction impacts synaptic structure and mammalian behavior [106]. This research used a genetic mouse model comparing Control mice (wild-type, in blue) and Knockout mice (lacking primary cilia on their astrocytes, in pink/red) [106, 107, 108].

                +------------------------------------------+
                |        Astrocyte Primary Cilia           |
                |  (Acts as an antennal sensory organelle) |
                +--------------------+---------------------+
                                     |
                     +---------------^---------------+
                     |                               |
       +-------------v-------------+   +-------------v-------------+
       |   GENETIC KNOCKOUT MICE   |   |        CONTROL MICE       |
       |  (Ablated Primary Cilia)  |   |    (Intact Primary Cilia) |
       +-------------+-------------+   +-------------+-------------+
                     |                               |
       +-------------v-------------+   +-------------v-------------+
       |  Failed Synaptic Pruning  |   | Normal Synaptic Pruning & |
       |     By Astrocytes         |   |    Structural Maturation  |
       +-------------+-------------+   +-------------+-------------+
                     |                               |
       +-------------v-------------+   +-------------v-------------+
       | Excess of Weak, Thin      |   | Refined, Strong Synaptic  |
       | Dendritic Spines          |   |       Connections         |
       +-------------+-------------+   +-------------+-------------+
                     |                               |
       +-------------v-------------+   +-------------v-------------+
       | Severely Impaired Motor   |   | Robust Motor Learning on  |
       | Learning (Flat Rotarod)   |   |   Accelerating Rotarod    |
       +---------------------------+   +---------------------------+

2.1 Behavioral Analysis: The Rotarod Assay

To evaluate motor learning, researchers subjected both groups of mice to the Rotarod test [107]:

• The Mechanism: Mice are placed on a horizontally rotating cylinder that accelerates over time [107]. Initially, all mice are uncoordinated and fall off almost immediately [107]. Over successive trials, healthy animals learn the motor coordination required to balance on the accelerating cylinder [107].

• Quantifying the Behavior: This learning is measured as the latency to fall (the number of seconds a mouse successfully remains on the rod before falling) [107].

• The Divergent Data: Control mice (blue) exhibited a classic, steep learning curve—their latency to fall increased significantly with each trial [107]. Conversely, knockout mice (pink) showed a significantly flat learning curve [107, 108]. They failed to learn the task, demonstrating a profound motor learning deficit directly tied to astrocyte dysfunction [107, 108].

2.2 Cellular and Synaptic Quantifications

To determine the cellular mechanisms driving this behavioral deficit, researchers used fluorescent imaging to visualize dendrites (the receiving structures of neurons) and dendritic spines (the specialized physical protrusions where individual synaptic inputs occur) [108, 109].

1. Dendritic Spine Density: Knockout mice exhibited a statistically significant increase in the absolute number of dendritic spines per 10 microns of dendrite length compared to controls [109]. While having "more" synapses might intuitively sound beneficial, it actually represents a severe pathological failure of synaptic pruning [109]. Astrocytes are responsible for engulfing and pruning away unnecessary or inactive connections during learning and development [109]. A failure in this mechanism results in a cluttered, unrefined circuit, a phenotype closely mirrored in human neurodevelopmental disorders like autism and schizophrenia [109].

2. Spine Head Volume: Although the knockout mice had an excess of spines, high-resolution imaging revealed that the volume of individual spine heads was significantly smaller and thinner than in control animals [109, 110]. In neurobiology, a smaller spine head is a structural marker of a weak, immature, and unstable synapse [110].

2.3 Comprehensive Scientific Conclusion

Ablating the primary cilia on astrocytes disrupts their ability to prune and mature neural connections [109, 110]. This leaves the brain cluttered with an excess of weak, immature synapses, which directly prevents the neural circuits from consolidating new motor pathways—causing the severe behavioral deficits observed on the Rotarod [107, 110].

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Section 3: The Foundations of Neurophysiology: Hodgkin, Huxley, and the Squid Axon

Neurophysiology (or electrophysiology) is the scientific study of the electrical signals and biophysical properties that govern how neurons communicate [110].

3.1 The Nobel Breakthrough

The foundation of modern electrophysiology was laid by Alan Hodgkin and Andrew Huxley, who were awarded the 1963 Nobel Prize in Physiology or Medicine [110].

• The Work: They published a series of five fundamental papers that mathematically characterized the biophysical laws of the action potential [110].

• The Contribution: They defined the precise physical laws that dictate how ions move across cell membranes under the influence of both electrical and chemical forces [111].

3.2 The Model System: The Squid Giant Axon (Loligo)

Hodgkin and Huxley’s breakthroughs provide a classic textbook example of choosing the ideal model system for a specific research question [111, 112].

• The Evolutionary Pressure: Squids rely on rapid jet-propulsion to escape predators [111]. To execute this propulsive escape behavior, they require a rapid electrical reflex pathway [111].

• The Physics of Cable Theory: In biophysics, the speed of an electrical signal down an axon is directly proportional to its diameter—a larger diameter reduces internal resistance, allowing the action potential to travel significantly faster [111]. To maximize escape speeds, the squid evolved a "giant axon" with a diameter hundreds of times wider than any mammalian axon [111].

• The Experimental Advantage: In the 1940s and 50s, recording microelectrodes were relatively large and fragile [111]. It was technically impossible to poke an electrode into a microscopic mammalian axon [111]. However, the massive squid giant axon was so large that Hodgkin and Huxley could easily isolate it and insert a recording electrode directly down its length, unlocking the biophysics of neural excitability [111, 112].

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Section 4: The Physiology and Clinical Significance of the Resting Potential

At its most fundamental level, the brain's computational vocabulary is electrical [113]. Changes in the voltage across the neuronal membrane away from its baseline rest state are the primary means by which neurons collect, integrate, and distribute information [113]. Therefore, understanding how the baseline "rest" state is established is the first step in understanding all brain function [113].

4.1 Defining the Resting Membrane Potential (RMP)

The resting membrane potential is the stable difference in electrical charge (voltage) across the plasma membrane of a neuron when it is not actively receiving inputs or firing action potentials [113, 116, 121, 122].

4.2 Pathophysiological and Clinical Relevance

Maintaining a stable, negative resting membrane potential is an incredibly energy-intensive process [115]. Disruptions to this homeostatic state underlie several severe neurological conditions [114, 115]:

• Epilepsy and Seizure Disorders: A seizure represents an abnormal "electrical storm" in the brain where populations of neurons fire action potentials in massive, pathological synchrony [114]. This hypersynchrony occurs when a neuron's resting membrane potential becomes unstable or chronically depolarized (too close to zero) [114]. This state of hyperexcitability causes the cells to fire action potentials uncontrollably and synchronously [114]. Recurring seizures are the defining characteristic of the neurological condition known as epilepsy [114].

• Anesthetics: General anesthetics, such as isoflurane, work by changing the activity of specific ion channels in a way that stabilizes and hyperpolarizes the resting membrane potential [114]. By keeping the membrane potential negative and stable, it prevents sensory neurons from firing the action potentials that convey pain signals to the brain, producing effective anesthesia [114].

• Stroke and Oxygen Deprivation: Although the human brain represents only 2% of total body weight, it consumes 20% of the body's total oxygen [115]. This massive bioenergetic demand is driven by the need to synthesize Adenosine Triphosphate (ATP), which is required to fuel the active molecular pumps that maintain the resting potential [115]. During a stroke (caused by a ruptured blood vessel or a clot), a region of brain tissue is deprived of oxygen and blood [115]. Without oxygen, ATP synthesis ceases [115]. Lacking ATP, the molecular pumps fail, the resting membrane potential breaks down, electrical signaling halts completely, and the neurons suffer rapid, irreversible metabolic death [115].

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Section 5: Experimental Measurement of the Resting Potential

To physically measure the resting membrane potential of a neuron, electrophysiologists require a specialized three-part experimental setup [116].

                 [Recording Voltmeter] (Reads -65 mV)
                   /               \
                  /                 \
  [Recording Microelectrode]     [Reference Electrode]
         |                                |
         | (Inserted inside)              | (Placed in bath)
  +------v--------------------------------v------+
  |  Intracellular Space (Cytosol)               |
  |  - - - - - - - - - - - - - - - - - - - - -   |  <-- Net Negative Charge
  |==============================================|  <-- Phospholipid Bilayer
  |  + + + + + + + + + + + + + + + + + + + + +   |  <-- Net Positive Charge
  |  Extracellular Fluid (Bath Solution)         |
  +----------------------------------------------+

5.1 The Electrophysiological Toolkit

1. A Neural Preparation: Live neurons maintained in cell culture, a living slice of brain tissue in a chamber, or an intact brain in an anesthetized animal [116].

2. A Reference Electrode: Placed in the extracellular bath solution surrounding the neurons to serve as a ground [116].

3. A Recording Electrode (Microelectrode): A glass pipette with an extremely fine tip filled with an electrically conductive salt solution, designed to penetrate the neuronal membrane [116].

5.2 Step-by-Step Measurement Protocol

1. Extracellular Baseline: When both the recording microelectrode and the reference electrode are placed outside the neuron in the extracellular bath, they are in the same electrical compartment [116]. Because there is no charge difference between them, the voltmeter reads exactly 0 millivolts (mV) [116].

2. Membrane Penetration: The electrophysiologist carefully drives the recording microelectrode through the hydrophobic phospholipid bilayer of the axon or cell body into the intracellular cytosol [116, 117].

3. The Voltage Drop: The instant the electrode penetrates the membrane, the voltmeter detects a sharp drop in voltage, revealing that the inside of the neuron is strictly more negative than the outside [116, 117].

4. Quantifying the Resting Value: While different cell types among the brain's 3,000+ populations exhibit variations in their exact resting state, the average resting membrane potential of most neurons is between -60 mV and -75 mV (typically cited in textbooks as -65 mV) [117, 121].

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Section 6: The Biophysical Mechanics Establishing the Resting Potential

The cell interior maintains a permanent negative charge at rest because of the precise coordination of three biophysical components: the lipid bilayer, selective ion channels, and active molecular pumps [118, 119, 122].

6.1 The Phospholipid Bilayer

The plasma membrane is a highly hydrophobic lipid bilayer [118]. Because water-soluble ions (like $Na^+$, $K^+$, and $Cl^-$) carry electrical charges, they cannot dissolve in the hydrophobic core of the bilayer [118]. The membrane acts as an absolute physical barrier that separates the intracellular cytosol from the extracellular fluid, preventing charges from freely diffusing and neutralizing [118].

6.2 Ion Channels and Gating Mechanisms

Ion channels are specialized protein complexes that span the full width of the phospholipid bilayer, forming an aqueous pore through which ions can pass [119].

• The Selectivity Filter: Each channel class features a microscopic selectivity filter made of amino acids that restricts passage to only one specific ion class (e.g., allowing only $K^+$ to pass while excluding $Na^+$) [119].

• Leak Channels: These channels are passively open at rest, meaning they are ungated and allow constant, unregulated diffusion of their target ion across the membrane [119, 120]. At rest, neuronal membranes possess an exceptionally high number of open Potassium ($K^+$) leak channels [119, 120, 136].

• Gated Channels: These channels are closed at rest but open instantly in response to specific physical triggers [120]. Gating mechanisms include:

  • Voltage-Gating: Opens in response to changes in the membrane's electrical potential [120].

  • Chemical/Ligand-Gating: Opens when a chemical neurotransmitter binds to a receptor [120, 129].

  • Thermal Gating: Opens in response to temperature changes [120].

  • Mechanical Gating: Opens in response to physical stretch or pressure (e.g., sensory neurons in the skin that open when you step on a sharp tack) [120].

6.3 The Sodium-Potassium Pump ($Na^+$/$K^+$ ATPase)

The sodium-potassium pump is an active enzyme embedded in the membrane that hydrolyzes ATP to move ions against their steep concentration gradients [122, 123, 124].

• The Stoichiometry: The pump exchanges 3 Sodium ($Na^+$) ions OUT of the cell for every 2 Potassium ($K^+$) ions IN [124].

• The Electrogenic Gradient: Because the pump moves 3 positive charges out of the cell for every 2 positive charges it brings in, it creates a net deficit of positive charge inside [124, 125]. This electrogenic exchange directly contributes to making the inside of the cell negative [124, 125].

• Establishing the Concentration Gradients: By working constantly, the pump establishes and maintains the standard chemical gradients of the brain: high sodium outside / low sodium inside, and high potassium inside / low potassium outside [124].

6.4 Intracellular Proteins (Anions)

The intracellular cytosol is packed with a high concentration of large proteins and organic molecules that carry heavy net negative charges [125]. Because these proteins are massive, they are physically trapped inside the cell and cannot pass through any ion channels [125]. They remain permanently anchored inside, providing a constant baseline of negative charge [125].

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Section 7: Intracellular vs. Extracellular Ionic Concentrations

To predict how ions will move across the membrane, we must map their relative distributions at rest [124, 125]. At rest, the membrane is highly organized, maintaining distinct concentrations of four primary ions [124, 125]:

The Role of Active Chloride Pumps: To keep chloride ($Cl^-$) highly concentrated on the outside of the cell, neurons express specialized active chloride transporters that pump $Cl^-$ out against its gradient [126].

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Section 8: The Dual Physical Forces Driving Ionic Movement

Once an ion channel opens, the movement of ions across the membrane is not random; it is governed by the simultaneous action of two independent physical forces [127]:

8.1 Concentration (Diffusional) Forces

Diffusion is the passive, thermal movement of molecules from an area of high concentration to an area of low concentration [128].

• The Principle: Molecules naturally spread out down their chemical gradient [128].

• Application: Because potassium ($K^+$) is highly concentrated inside the cell, opening a potassium-selective channel causes $K^+$ to diffuse out of the cell [131, 133]. Because chloride ($Cl^-$) is highly concentrated outside, opening a chloride-selective channel causes $Cl^-$ to diffuse into the cell [128, 129].

8.2 Electrostatic (Electrical) Forces

Electrostatic force is driven by the physical law of charges: like charges repel one another, while opposite charges attract [130].

• The Principle: Positive charges move toward negative areas, and negative charges move toward positive areas [130].

• Application: Because the inside of the neuron is negative at rest ($-65$ mV), positive ions (cations like $Na^+$ and $Ca^{2+}$) are heavily attracted to the intracellular space [130].

8.3 The Convergence of Forces

For certain ions, these two physical forces act in the same direction, creating an immense biophysical drive [130]:

• Sodium ($Na^+$) and Calcium ($Ca^{2+}$): For both cations, the concentration gradient drives them inward (from high outside to low inside), and the electrical gradient also drives them inward (attracted to the negative cell interior) [130]. When a sodium or calcium channel opens, these ions flood into the cell with extraordinary speed [130].

• Chloride ($Cl^-$): For chloride, the forces conflict [126, 127]. The concentration gradient drives chloride inward (high outside), but the negative charge of the cell interior repels the negative chloride ion, driving it outward [126, 127].

• Potassium ($K^+$): For potassium, the concentration gradient drives it outward (high inside), but the negative interior of the cell exerts an electrical pull trying to keep the positive $K^+$ ion inside [131, 134].

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Section 9: The Biophysics of Equilibrium Potentials

The concept of an equilibrium potential is one of the most challenging, yet crucial, principles in cellular neurobiology [131, 132].

9.1 Defining the Equilibrium Potential ($E_{ion}$)

The equilibrium potential of an individual ion class is the specific membrane voltage at which there is no net movement of that ion across the membrane [131, 132]. This state of equilibrium is reached when the outward diffusional force is perfectly equal in magnitude and opposite in direction to the inward electrical force acting on that specific ion [132].

9.2 Correcting the Concentration Misconception

Students frequently harbor a major misconception: they assume that when an ion is at its equilibrium potential, there are equal concentrations of that ion on both sides of the membrane [131]. This is false. [131] Even at equilibrium, the steep concentration gradients established by active pumps remain completely intact [134]. Equilibrium simply means that the net flow of the ion has stopped because the electrical force prevents further chemical migration [131, 132].

9.3 Step-by-Step Walkthrough of Potassium Equilibrium

To understand how an equilibrium potential is physically generated, we can trace a step-by-step biophysical model [133]:

      [STAGE 1: Concentration Drive]                 [STAGE 2: Steady State Equilibrium]
    
       Inside Cell       Outside Cell                  Inside Cell       Outside Cell
      (High K+, An-)       (Low K+)                   (High K+, An-)       (Low K+)
      
      +------------+   +------------+                 +------------+   +------------+
      |  K+ ---->  |   |            |                 |  K+ <----> |   | + + +      |
      |  An-       |   |            |                 |  An-       |   | + + +      |
      +------------+   +------------+                 +------------+   +------------+
Membrane Potential: Vm = 0 mV                    Membrane Potential: Ek = -80 mV
(K+ flows out down concentration gradient)       (Electrical pull in balances chemical push out)

1. Initial State (No Permeability): We begin with a cell containing a high concentration of potassium ($K^+$) and large, negatively charged proteins (Anions, $An^-$) [133]. Outside the cell, $K^+$ is low [133]. Initially, there are no open channels, and the membrane potential ($V_m$) is 0 mV [133].

2. Channel Insertion: We insert potassium-selective leak channels into the membrane [133].

3. Outward Diffusion: Driven by the steep concentration gradient, potassium ions immediately begin diffusing out of the cell through the leak channels [133].

4. Charge Separation: As positive $K^+$ ions exit the cell, they leave behind their negatively charged counter-ions (the large anions), which are too big to pass through the channels [134]. This separation of charge occurs immediately at the membrane boundary [134]. The outer surface of the cell membrane gains a net positive charge, while the inner surface gains a net negative charge [134].

5. The Electrostatic Opposing Force: As the inside of the cell becomes progressively more negative, it begins to exert an electrostatic pull on the positive $K^+$ ions, pulling them back inward [134].

6. Dynamic Equilibrium: Eventually, as more potassium leaves, the negative charge inside the cell grows large enough that the inward electrical attraction perfectly balances the outward concentration drive [134]. At this exact voltage, net potassium movement halts [132, 134]. For potassium, this occurs when the inside of the cell is exactly -80 mV [135, 136].

9.4 Equilibrium Potentials of Major Ions at Body Temperature ($37^\circ C$)

By calculating the balanced electrical and chemical forces using the Nernst Equation, we find the following equilibrium potentials for the primary ions [104, 136]:

• Potassium ($E_K$): -80 mV [135, 136]

• Sodium ($E_{Na}$): +62 mV [136]

• Calcium ($E_{Ca}$): +120 mV [136]

9.5 The Fundamental Rule of Ionic Flow

An open ion will always flow across the membrane in the direction that pulls the overall membrane potential ($V_m$) closer to that ion's specific equilibrium potential ($E_{ion}$) [136].

• If Sodium channels open: $Na^+$ will flood into the cell, pulling the negative membrane potential up toward $+62$ mV [136].

• If Calcium channels open: $Ca^{2+}$ will flood into the cell, pulling the membrane potential toward $+120$ mV [130, 136].

• If Potassium channels open: $K^+$ will exit the cell, pulling the membrane potential down toward $-80$ mV [135, 136].

9.6 Why is the Resting Potential Closer to Potassium?

At rest, neuronal membranes are selectively permeable almost exclusively to potassium because potassium leak channels are passively open [136]. Because $K^+$ is the only ion moving freely, it pulls the resting membrane potential close to its own equilibrium potential of $-80$ mV [136]. The reason the actual resting membrane potential of a neuron (around $-65$ mV) is slightly more positive than $-80$ mV is because the membrane also has a tiny, minor baseline permeability to sodium [136]. A very small amount of sodium leaks into the cell at rest, pulling the voltage slightly positive away from $-80$ mV to the final resting baseline of $-65$ mV [136].

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