CN C2 Biophysics of Neural Computation

history

• Early times of neural electricit
  In 1868, Bernstein first recorded the electrical properties of a neuron, termed as action potential (AP). AP does not change over the distance, the shape keeps the same:

  sharp rise,
  rapidly decrease,
  slowly recover to its normal value.

  

• 20th century of the neural electrophysiology

  In 1900s, Louis Lapicque found that higher voltage, the quicker the neuron respond, the lower voltage the slower respond. A mathematic equation about the neural electricity based on Ohm’s law and the integrate-and-fire model of the neuron was established.

  In 1920s, Edgar Adrian found the “all-or-nothing” principle: a neuron either emits an action potential or it does not.

  If stronger stimulation is applied: The neuron emits more of the exact the same action potentials.

  The neural system cares more about quantity than quality (analogy value).

• 21st century of neurophysiology

  The rapid and precise signaling of synapses forms the basis for all information.

Characteristics of Neural Computation Systems

• 基本计算单元：Neurons
• 信号传递：Signaling is organized in the same way in all neurons
• 神经元的多样性：Neurons differ most at the molecular level
• 神经可塑性：
  • Neuron carefully selects to connect each other;
  • Neural connections can be modified by experience

Some Facts about Cortex(皮层)

The neocortex is the seat of human reasoning.

Its 30 billion or so neurons,forming columns, are organized in six layers. The layers of the column are indicated by

• L1, at the surface of the brain;
• through L6, the deepest cortical layer.
• L5, where Cell bodies are.

Human Brain is of 78 billion neurons, having 1000 trillion synapse(突触). Human brain is of low power($\approx 20 watts$) in a low volume($ \approx 1.5L$).

Example Retinal Neurons

a multi-layered network:

• Photoreceptors-bipolar cells-ganglion cells in feedforward pathway;
• Horizontal cells and amacrine cells in lateral pathway.

The action potentials arising from the ganglion cells is the sole source of output from the retina to the rest of the brain.

Olfactory Neuron

• Neurons have different structures and functions
• Neurons differ most at the molecular level
• Signaling is organized in the same way
• Neural connections can be modified by experience

Neural Morphology 神经元形态

The nervous system has two classes of cells: Neurons and glial cells.

Neurons

Neurons are excitable cells which can transmit the impulses, signaling units of the nervous system.

Classification

• By Morphology:

  1. unipolar neurons

     single nerve fiber extends from cell body then branching into one axon(轴突) and one dendrite(树突).

     

  2. bipolar neurons

     one axon and one dendrite from cell body; found in special sensory areas (eyes, ears, nose).

     

  3. multipolar neurons

     one axon and many dendrites from cell body; carrying information in cerebral cortex,CNS.

     

• By Function:

  1. sensory(感觉) neurons
  2. motor(运动) neurons
  3. inter(中间)neurons

• By Synapses:

  1. excitatory(兴奋) neurons
  2. inhibitory(抑制) neurons

There are also other classifications such as patterns of local and long-range connectivity, developmental history, gene expression profile, intrinsic physiology, and strategies to encode information.

Glial cells(胶质细胞)

Glial cells are nonexcitable cells which can support nourishment and protect the neurons.

Why different types of neurons?

To form neurons’ architecture.

Neural Structure 神经元结构

The neural structures decide the expression and transmission of neural signaling.

Signaling of all neurons is organized in the same way.

Dendrites

Input component, produces graded local signals.

Soma(胞体)

The integrative zone, makes the decision to generate an AP.

Axon

Conductive component, propagates an all-or-none AP .

Axon-end (轴突终端)

Output component, releases neurotransmitter, interact with other neurons.

Most neurons have the four functional regions to signal: Input Component, Trigger or Integrative Component, Conductive Component, Output Component.

Neurons differ most at the molecular level

• Different molecular composites: Distinctive proteins, enzymes, neurotransmitters, receptors
• Different combination of ion channels: Various thresholds, excitability, firing properties (Modeling studies only consider)

Brain Works via AP (or Spikes)

1. Direction (方向性, 沿轴突向下游传递)
2. All-or-nothing (on-off) 神经脉冲
3. Non-degrading(一致性, 沿轴突传递的活动强度一致)

Ion channels 离子通道

Ion channels are proteins that span the cell membrane (跨膜蛋白质).

membrane: two-layers structure

• two-layers structure consisting of well-insulated phospholipids(磷脂) which act as a barrier to water-soluble molecules

• Resting membrane potential: ***Selective permeability(选择性渗透)***to some ions and the concentration gradients formed by active pumping lead to a difference in electrical potential across the membrane.

  The concentration gradient for K+ forces K+ out of the cell, developing a net negative charge inside the neuron.

Properties

• Recognize and select specific ions
• Open and close in response to specific electrical, mechanical and chemical signals
• Conduct ions through the membrane

1. Rapid signaling in the neuron depends on ion channel.
2. Currents through single ion channels can be recorded.

shared characteristics

• The flux of ions through a channel is PASSIVE, which meas no energy comsumption and electrochemical driving force - determined.

  Electrochemical driving force

  Determined by two factors:

  • The electrical potential difference across the membrane
  • The concentration gradient of the permeate ions across the membrane

• The opening and closing of ion channels involve onformational(形态与结构) changes. Three models of changes:

  localized	conformational	in one region
  generalized	structural	along the length
  	blocking particle swing into and out	channel mouth

Four types of ion channels

• Voltage-gating （电压门控）
• Phosphorylation-gating（磷酸化门控）
• Ligand-gating （配合基门控）
• Stretch/pressure-gating （机械门控）

Electrical properties and Membrane Potential 电学特性及膜电位

Membrane potential

Membrane potential is a difference of electrical potential across the membrane.

$$V_m = V_{in} - V_{out}$$

Cell Polarization

• depolartization(去极化）: a less negative $V_m$
• Hyperpolarization(超极化): a more negative $V_m$

Resting membrane potential

Resting membrane potential is the membrane potential of a cell at rest without any stimulus.

$$V_r = V_{in} - V_{out} \overset{\small{V_{out} = 0}}{=} V_{in}$$

• results from the separation of charges across the cell membrane (positive ~ negative);
• determined by resting ion channels.

1. Unequal distribution of ions inside and outside
2. The permeabilities of ion channals: open/close, selectivity

Equilibrium potential

Equilibrium potential is the membrane potential for one single ion when its chemical and electrical gradients are equal in magnitude.

$$V_{Eq} = \frac{RT}{zF}\ln{(\frac{[X]_{out}}{[X]_{in}})}$$

Electrogenic pumps 电力泵

Here is the workflow of Sodium – Potassium pump.

Equivalent circuit

The functional properties including Membrane and ion channels of the neuron can be represented in an electrical equivalent circuit.

Electrical properties

Passive

Passive properties refer to the capacitative and resistive aspects inherent in neuronal membrane.

• The resting membrane resistance
• The membrane capacitance
• The intracellular axial resistance along axons and dendrites

Active

Active properties mean that the electrical potentials across the plasma membrane may be affected by the activation of voltage, ligand(配对基), or second messenger(第二信使) gated transmembrane ionic channels.

神经递质 （Neurotransmitter