In Class Lecture 9/10/25: Synaptic Integration: Dendrites, PSPs, and Modulation

Overview: dendritic integration and the postsynaptic side

• The first weeks focus on piecing together how neurons function together and signal, moving from the presynaptic axon terminal to the postsynaptic dendritic side.

• Typical neuron receives 5,000 to 10,000 inputs on its dendrites; all must be integrated to determine whether an action potential fires at the axon hillock.

• Resting context from previous sessions: resting membrane potential, the molecular basis of the action potential, propagation, and the presynaptic release of neurotransmitter via vesicle fusion at the terminal.

• Today’s emphasis: how postsynaptic receptors on the dendritic side convert chemical messages into membrane potential changes (via ligand-gated ion channels and GPCRs) and how those changes summate to reach threshold for an action potential.

• Important framing: dendritic structure is diverse and can greatly affect integration; modeling synaptic integration is an active computational research area; the talk connects basic biology to computation and real-world relevance.

Quick analogy and real-world example used in class

• A Quiet Place example to illustrate top-down modulation of reflexes:

  • Descending input from cortex (contextual decision-making) can suppress reflexive actions (e.g., stepping on a nail while laboring).

  • The motor neuron must integrate input about pain from sensory/interneuron signals with higher-order information about survival and safety, leading to a controlled, non-reflexive action.

• Takeaway: motor output results from integration of multiple inputs, including high-level decisions, not just raw sensory input.

Postsynaptic receptors: LGICs vs GPCRs

• Two main receptor types on the postsynaptic side discussed:

  • Ligand-gated ion channels (LGICs): direct, fast gating by a neurotransmitter, leading to ion flux (e.g., Na+ entry -> depolarization).

  • G protein–coupled receptors (GPCRs): indirect, slower modulation via intracellular signaling cascades that can alter many ion channels and other targets.

• Example receptors shown (as described):

  • An excitatory receptor (purple) where binding of the neurotransmitter opens a pore, allowing sodium influx (EPSP).

  • A different receptor that binds a neurotransmitter (also shown in purple) leading to chloride influx via a channel (IPSP).

• Key concepts to remember:

  • Excitatory postsynaptic potentials (EPSPs) are depolarizing, bring the membrane potential toward threshold.

  • Inhibitory postsynaptic potentials (IPSPs) are hyperpolarizing, moving the membrane potential away from threshold.

  • Different postsynaptic receptors produce different PSP shapes, amplitudes, and durations.

• Practice prompt (from class): draw or identify which PSP is excitatory vs inhibitory and what they look like on a voltage vs time graph.

Key properties of EPSPs and IPSPs

• EPSPs (excitatory postsynaptic potentials)

  • Usually involve excitatory cation influx (e.g., Na+) through LGICs when glutamate or similar transmitter binds.

  • Result: depolarization of the postsynaptic membrane toward the action potential threshold.

• IPSPs (inhibitory postsynaptic potentials)

  • Often involve chloride influx through GABAergic receptors (e.g., GABA_A) or potassium efflux through other channels, depending on receptor type.

  • Result: hyperpolarization or stabilization away from threshold, reducing likelihood of firing.

• Resting vs reversal potentials (examples discussed):

  • Chloride equilibrium potential (ECl): approximately $E</em>{Cl} \approx -60 \text{to}\ -65 \text{mV}$, which is near the resting membrane potential.

  • In the chloride case, opening Cl− channels tends to maintain resting potential or push toward E_Cl, producing an inhibitory effect.

  • Glutamate (EPSP) context: the text notes an equilibrium potential for glutamate around $E_{Glu} \approx -65 \text{mV}$, close to resting in their example, underscoring how context and receptor type shape PSP direction and magnitude.

• Summary difference: EPSPs are excitatory and tend to depolarize toward threshold; IPSPs are inhibitory and tend to hyperpolarize or stabilize at negative potentials.

Spatial and temporal summation of inputs

• Neurons receive inputs from multiple presynaptic neurons, and PSPs must sum to reach threshold at the axon hillock.

• Spatial summation

  • Inputs from different parts of the dendritic tree arrive at roughly the same time and sum to produce a larger depolarization at the soma/axon hillock.

  • Example: five inputs (three excitatory, two inhibitory) can combine to determine if threshold is reached.

• Temporal summation

  • Multiple inputs from a single synapse arrive in quick succession; closer timing leads to greater summation because the individual EPSPs/IPSPs overlap and add before decay.

• Combined reality: spatial and temporal summation occur simultaneously with many inputs (5,000–10,000), making integration highly complex.

• Threshold concept: depolarization must exceed a threshold near the axon hillock to trigger voltage-gated Na+ channels and generate an action potential (typical display uses a threshold around $V_{th} \approx -40 \text{mV}$ in class examples).

• Visual takeaway: the postsynaptic neuron fires only if the integrated input crosses threshold; otherwise, no action potential.

Action potentials vs EPSPs: differences and implications

• Action potentials

  • All-or-none event; amplitude and duration are relatively consistent and do not scale with input strength.

  • Triggered when the membrane potential at the axon hillock reaches threshold due to summed PSPs.

• EPSPs/IPSPs

  • Graded potentials: size and duration vary depending on receptor type, neurotransmitter, and number of channels opened.

  • Mediated by neurotransmitter-gated channels (LGICs) or GPCRs with downstream effects.

• Behavioral implications

  • The neuron’s decision to fire is based on the integrated sum of multiple PSPs rather than a single input.

  • Complex dendritic structures and channel distributions can modulate how these sums occur, affecting excitability and information processing.

Dendritic length constant and passive cable properties

• Concept: how far depolarization travels along a dendrite before decaying to a small fraction of its initial value.

• Definition: the dendritic length constant $\lambda$ is the distance over which the depolarization decays to about 37% of its original value.

• Basic formula (cable theory):

  • $\lambda = \sqrt{\frac{R<em>m}{R</em>i}}$

  • Where $R<em>m$ is the membrane resistance (per unit length) and $R</em>i$ is the internal (axial) resistance (per unit length).

• Factors that influence $\lambda$

  • Membrane resistance $R<em>m$: higher $R</em>m$ (fewer open channels) increases $\lambda$; lower leakiness -> longer spread of depolarization.

  • Internal resistance $R<em>i$: higher $R</em>i$ (thinner dendrite, more axial resistance) decreases $\lambda$; thicker dendrites reduce axial resistance and increase spread.

  • Dendritic geometry: tapering, diameter, and branching affect current spread. Wider parts allow easier current flow; narrow parts increase resistance.

• Practical implication: a longer $\lambda$ implies more distal inputs can influence the soma and potentially trigger an action potential; a short $\lambda$ limits distal influence, requiring more proximal inputs or more intense summation.

• Real-world caveat: real neurons have elaborate dendritic trees; passive cable theory (length constant) is a simplification, helpful for intuition but not a full model of synaptic integration.

Measuring and interpreting dendritic properties

• Dendritic length constant is a property of the individual neuron and can be measured via electrophysiology in a dish.

• Visualization analogy used in class: a hose with many small leaks (ion channels) represents how current can leak out along the membrane; more leaks (more open channels) reduce resistance and shorten the length constant.

• The dendritic cable behaves as a bidirectional conductor: injected current flows in both directions along the dendrite, decaying with distance due to membrane leaks and axial resistance.

• Example outcome: a thin dendrite has high internal resistance, leading to a shorter length constant; leaky dendrites (many open channels) have a shorter length constant due to low membrane resistance.

Practical modeling and limitations

• Dendritic length constant provides a useful, but simplified, framework for thinking about how synaptic inputs sum along a dendrite.

• In reality, neurons have highly branched and variable dendritic trees; integration depends on geometry, channel distributions, active properties, and neuromodulation.

• Researchers study how these properties shape information processing and neuronal excitability using both computational models and experimental measurements.

Modulation by norepinephrine: a practical application

• Class activity focused on how neuromodulators can alter dendritic processing and excitability:

  • Task: determine how norepinephrine (a neuromodulator) can influence the dendritic length constant and neuronal excitability.

  • Mechanistic hint given: norepinephrine initiates a cascade of intracellular events that leads to the closure of a potassium leak channel.

• Key questions to answer during the ticket-out-the-door exercise:

  • Which postsynaptic receptor type mediates this modulation? (Options discussed: LGIC vs GPCR)

  • How does this modulation change membrane resistance ($R_m$)?

  • How does the change in $R_m$ affect the dendritic length constant ($\lambda$)?

  • How does the resulting change in $\lambda$ influence neuronal excitability (likelihood of firing an action potential)?

• Expected conceptual answer (as guided in class):

  • norepinephrine acts on a GPCR (not an LGIC) on the postsynaptic side to trigger a signaling cascade that closes a potassium leak channel.

  • Closing K+ leak channels increases $R_m$ (higher membrane resistance).

  • Higher $R<em>m$ increases the dendritic length constant $\lambda = \sqrt{R</em>m/R_i}$, allowing depolarizations to spread farther along the dendrite.

  • A larger $\lambda$ increases the likelihood that distal inputs can contribute to reaching threshold at the axon hillock, thereby increasing neuronal excitability (greater chance of firing).

• Note on terminology used in class:

  • The two postsynaptic receptor types referenced are LGICs and GPCRs; modulation via norepinephrine is typically associated with GPCR signaling pathways.

• Final takeaway: neuromodulators can dynamically reshape synaptic integration by altering membrane resistance and dendritic signal spread, thereby tuning the excitability of neurons in context-dependent ways.

Recap: key terms and formulas to memorize

• EPSP: excitatory postsynaptic potential; depolarizing, graded response.

• IPSP: inhibitory postsynaptic potential; hyperpolarizing, graded response.

• LGIC: ligand-gated ion channel; mediates fast synaptic transmission.

• GPCR: G protein–coupled receptor; mediates slower, modulatory signaling.

• Axon hillock: site where membrane potential integration determines if an action potential is fired.

• Threshold: typically around $V_{th} \approx -40 \,\text{mV}$ in class discussions.

• Resting membrane potential: typically around $V_{rest} \approx -65 \text{ to } -70 \text{ mV}$.

• Dendritic length constant: $\lambda = \sqrt{\frac{R<em>m}{R</em>i}}$; distance over which depolarization decays to ~37% of initial value.

• Equilibrium potentials discussed: $E<em>{Cl} \approx -60 \text{ to } -65 \text{ mV}$, $E</em>{Glu} \approx -65 \text{ mV}$ (as used in the lecture examples).

• Spatial summation: inputs from different dendritic locations summing at the soma/axon hillock.

• Temporal summation: rapid succession of inputs from a single or nearby synapses summing in time.

• Modulation example: norepinephrine acting on a GPCR to close a potassium leak channel, increasing $R_m$, increasing $\lambda$, and increasing excitability.

Quick study prompts inspired by the lecture

• Explain how a set of mixed excitatory and inhibitory inputs arriving at different dendritic locations can either trigger or fail to trigger an action potential at the axon hillock.

• Describe how a higher dendritic length constant can change the influence of distal synapses on the neuronal output.

• Distinguish between EPSP and IPSP in terms of depolarization vs hyperpolarization, receptor types involved, and typical reversal potentials.

• Outline how norepinephrine modulation via a GPCR can alter membrane resistance and what that implies for neuronal excitability.