🔬Biophysics Unit 9 – Neurobiophysics: Cellular Electrical Signaling

Fundamentals of Cellular Electricity

• Cells maintain an electrical potential difference across their membrane called the membrane potential
• Membrane potential arises from the unequal distribution of ions (charged particles) between the intracellular and extracellular spaces
• The main ions involved in generating the membrane potential include sodium (Na+), potassium (K+), calcium (Ca2+), and chloride (Cl-)
• Ion concentrations are maintained by active transport mechanisms, such as the sodium-potassium pump (Na+/K+ ATPase), which moves Na+ out of the cell and K+ into the cell against their concentration gradients
• Passive transport mechanisms, like ion channels, allow ions to move down their electrochemical gradients across the membrane
• The resting membrane potential of a typical neuron ranges from -60 mV to -70 mV, with the inside of the cell being more negative relative to the outside
• The Nernst equation describes the equilibrium potential for a specific ion based on its concentrations inside and outside the cell: $E_{ion} = \frac{RT}{zF} \ln \frac{[ion]_{outside}}{[ion]_{inside}}$
  • R is the gas constant, T is the absolute temperature, z is the ion's valence, and F is Faraday's constant

Membrane Potential and Ion Channels

• Ion channels are specialized proteins embedded in the cell membrane that allow specific ions to pass through
• Ion channels can be gated (opened or closed) by various stimuli, such as voltage changes (voltage-gated channels), ligand binding (ligand-gated channels), or mechanical forces (mechanically-gated channels)
• Voltage-gated sodium (Nav) and potassium (Kv) channels play a crucial role in generating and propagating action potentials in neurons
• Ligand-gated ion channels, such as the nicotinic acetylcholine receptor (nAChR), are important for synaptic transmission
• The Goldman-Hodgkin-Katz (GHK) equation describes the membrane potential as a function of the permeabilities and concentrations of multiple ions: $V_m = \frac{RT}{F} \ln \frac{P_{K}[K^+]_{outside} + P_{Na}[Na^+]_{outside} + P_{Cl}[Cl^-]_{inside}}{P_{K}[K^+]_{inside} + P_{Na}[Na^+]_{inside} + P_{Cl}[Cl^-]_{outside}}$
  • P represents the permeability of the membrane to each ion
• The relative permeabilities of the membrane to different ions determine the resting membrane potential and the shape of the action potential
• Ion channel disorders, such as channelopathies, can lead to various neurological and neuromuscular diseases (epilepsy, myotonia)

Action Potentials: Generation and Propagation

• Action potentials are rapid, transient changes in the membrane potential that allow neurons to transmit signals over long distances
• The generation of an action potential involves the sequential opening and closing of voltage-gated sodium (Nav) and potassium (Kv) channels
• The action potential has several distinct phases:
  1. Resting state: The membrane potential is at its resting level (around -70 mV)
  2. Depolarization: When the membrane potential reaches the threshold (around -55 mV), Nav channels open, allowing Na+ to enter the cell and causing rapid depolarization
  3. Overshoot: The membrane potential briefly becomes positive due to the influx of Na+
  4. Repolarization: Kv channels open, allowing K+ to exit the cell, while Nav channels inactivate, causing the membrane potential to return to its resting level
  5. Hyperpolarization: The membrane potential briefly becomes more negative than the resting potential due to the continued efflux of K+ before returning to the resting state
• The refractory period is the time during which a neuron cannot generate another action potential, ensuring unidirectional signal propagation
  • Absolute refractory period: Nav channels are inactivated, and no new action potential can be generated
  • Relative refractory period: A stronger stimulus is required to generate an action potential due to the increased K+ conductance
• Action potentials propagate along the axon through the regenerative opening of Nav channels in adjacent regions of the membrane
• Myelination of axons by Schwann cells (in the peripheral nervous system) or oligodendrocytes (in the central nervous system) increases the speed of action potential propagation by enabling saltatory conduction

Synaptic Transmission and Neurotransmitters

• Synapses are specialized junctions between neurons or between neurons and other cells (muscle cells, gland cells) that allow for the transfer of information
• Synaptic transmission can be electrical or chemical
  • Electrical synapses: Direct communication between cells through gap junctions, allowing for rapid and bidirectional signal transmission
  • Chemical synapses: Communication through the release of neurotransmitters from the presynaptic neuron, which bind to receptors on the postsynaptic cell
• The process of chemical synaptic transmission involves several steps:
  1. Action potential arrives at the presynaptic terminal
  2. Voltage-gated calcium (Cav) channels open, allowing Ca2+ to enter the presynaptic terminal
  3. Ca2+ triggers the fusion of synaptic vesicles containing neurotransmitters with the presynaptic membrane
  4. Neurotransmitters are released into the synaptic cleft
  5. Neurotransmitters bind to receptors on the postsynaptic cell, causing changes in the postsynaptic membrane potential or intracellular signaling cascades
• Neurotransmitters can have excitatory (depolarizing) or inhibitory (hyperpolarizing) effects on the postsynaptic cell, depending on the type of receptor they bind to
  • Excitatory neurotransmitters: Glutamate, acetylcholine (ACh), serotonin (5-HT), norepinephrine (NE)
  • Inhibitory neurotransmitters: Gamma-aminobutyric acid (GABA), glycine
• Neurotransmitter action is terminated by reuptake into the presynaptic terminal or glial cells, enzymatic degradation, or diffusion away from the synaptic cleft
• Synaptic plasticity, the ability of synapses to strengthen or weaken over time, is the basis for learning and memory
  • Long-term potentiation (LTP): Persistent strengthening of synaptic transmission
  • Long-term depression (LTD): Persistent weakening of synaptic transmission

Electrical Signaling in Neural Networks

• Neural networks are complex systems of interconnected neurons that process and transmit information
• The connectivity and organization of neural networks determine their functional properties and the behaviors they control
• Neurons can be classified based on their morphology, neurotransmitter content, or functional role within a network (sensory neurons, interneurons, motor neurons)
• Neural circuits are composed of multiple neurons connected in specific patterns, such as feedforward or feedback loops, to perform specific functions
• Convergence occurs when multiple presynaptic neurons synapse onto a single postsynaptic neuron, allowing for the integration of information from multiple sources
• Divergence occurs when a single presynaptic neuron synapses onto multiple postsynaptic neurons, allowing for the distribution of information to multiple targets
• Lateral inhibition is a common motif in sensory systems, where the activation of one neuron leads to the inhibition of its neighbors, enhancing contrast and sharpening the representation of stimuli
• Oscillations and synchronization of neural activity play important roles in information processing, attention, and memory
  • Gamma oscillations (30-120 Hz) are associated with cognitive processes and sensory binding
  • Theta oscillations (4-8 Hz) are involved in memory formation and spatial navigation
• Neuronal population coding refers to the idea that information is represented by the collective activity of groups of neurons rather than individual cells

Experimental Techniques in Neurobiophysics

• Patch-clamp recording is a powerful technique for measuring the electrical activity of individual neurons or isolated ion channels
  • Whole-cell recording: Measures the electrical activity of an entire neuron
  • Single-channel recording: Measures the activity of individual ion channels
• Voltage-clamp and current-clamp are two main configurations used in patch-clamp recordings
  • Voltage-clamp: Allows for the measurement of ionic currents while holding the membrane potential constant
  • Current-clamp: Allows for the measurement of changes in membrane potential while injecting current
• Extracellular recording techniques, such as single-unit or multi-unit recordings, measure the electrical activity of neurons in intact neural circuits
• Optogenetics is a technique that uses light-sensitive proteins (opsins) to control the activity of specific neurons or neural circuits with high temporal and spatial precision
  • Channelrhodopsin-2 (ChR2): Light-gated cation channel used for depolarizing neurons
  • Halorhodopsin (NpHR): Light-driven chloride pump used for hyperpolarizing neurons
• Calcium imaging uses fluorescent calcium indicators (GCaMP) to measure changes in intracellular calcium concentration, which serves as a proxy for neuronal activity
• Functional magnetic resonance imaging (fMRI) and positron emission tomography (PET) are non-invasive techniques for measuring brain activity and metabolism in humans and animals
• Connectomics aims to map the complete wiring diagram of neural circuits using techniques such as electron microscopy and viral tracing

Computational Models of Neuronal Activity

• Computational models are mathematical descriptions of neuronal and neural network behavior that help understand and predict their function
• The Hodgkin-Huxley model is a seminal model that describes the generation of action potentials based on the dynamics of voltage-gated sodium and potassium channels
  • The model consists of four differential equations describing the changes in membrane potential and the gating variables of the ion channels
• Integrate-and-fire models are simplified models of neuronal activity that treat neurons as point processes, summing inputs until a threshold is reached and an action potential is generated
• Cable theory describes the propagation of electrical signals along the dendrites and axons of neurons, taking into account the passive properties of the membrane (resistance and capacitance)
• Synaptic plasticity models, such as the Bienenstock-Cooper-Munro (BCM) model, describe the activity-dependent changes in synaptic strength that underlie learning and memory
• Neural network models, such as feedforward and recurrent neural networks, simulate the behavior of interconnected populations of neurons
  • Artificial neural networks (ANNs) are inspired by biological neural networks and are used in machine learning applications
• Spiking neural networks (SNNs) incorporate the temporal dynamics of neuronal activity and are more biologically realistic than traditional ANNs
• Computational models are used in conjunction with experimental data to test hypotheses, make predictions, and guide further research

Applications and Current Research

• Neuroprosthetics and brain-machine interfaces (BMIs) aim to restore lost sensory, motor, or cognitive functions by interfacing the nervous system with artificial devices
  • Cochlear implants restore hearing by directly stimulating the auditory nerve
  • Retinal implants provide visual information by stimulating the retina or visual cortex
  • Motor prosthetics decode neural activity to control robotic limbs or paralyzed muscles
• Neuromodulation techniques, such as deep brain stimulation (DBS), are used to treat neurological and psychiatric disorders by modulating the activity of specific brain regions
  • DBS is used to treat Parkinson's disease, essential tremor, and dystonia by stimulating the subthalamic nucleus or globus pallidus
  • Transcranial magnetic stimulation (TMS) and transcranial direct current stimulation (tDCS) are non-invasive neuromodulation techniques used to study and treat various neurological and psychiatric conditions
• Neuromorphic engineering aims to design artificial systems that mimic the structure and function of biological neural networks
  • Neuromorphic chips, such as IBM's TrueNorth and Intel's Loihi, implement spiking neural networks in hardware for energy-efficient computing
• Optogenetics and chemogenetics are being used to dissect the neural circuits underlying behavior, cognition, and disease
  • Designer Receptors Exclusively Activated by Designer Drugs (DREADDs) are engineered G protein-coupled receptors that can be activated by specific ligands to modulate neuronal activity
• The Human Connectome Project and similar initiatives aim to map the structural and functional connectivity of the human brain at multiple scales
• Research in neurobiophysics is advancing our understanding of neurodegenerative diseases (Alzheimer's, Parkinson's), psychiatric disorders (schizophrenia, depression), and developmental disorders (autism, ADHD)
• Advances in neurobiophysics are also contributing to the development of more efficient and brain-inspired artificial intelligence systems