Cell Membrane Potential Resting Membrane Potential

• Resting membrane potential: for quiescent cells The genesis of resting potential is mainly the result of • Action (membrane) potential: excited cells • The concentrations of diverse ions which prevail inside and outside of the cell close to the surface of the Both resting and action potentials are produced by temporary changes in the current flow across the membrane. membrane, namely, in the ionic flow through the resting and gated channel proteins in the membrane. • The selective permeability of the cell membrane to particular ions.

Each and every biosignal has its origin in a brief imbalance of the resting membrane potential, irrespective of the biosignal’s type. Basic Biophysics Tools and Relationships Resting Potential of a Membrane Permeable to One Ion

11.4.1 Basic Laws J   J (diffusion)  J (drift)  0 -Fick’s Law: diffusion Einstein Relationship K kT [K  ] d[I] D kT o  E   vi  vo  ln EK+: Nernst potential J  D K q [K  ] dx  q i Same for Na+ and Cl- -Ohm’s Law: drift (: mobility, Z: ionic valence, [I] ion concentration) dVm Donnan Equilibrium J  Z[I] - Suppose a membrane is permeable to both K+ and Cl-. dx   [K ]o [Cl ]i E  E  K  Cl    [K ]i [Cl ]o

Goldman Equation

- The Goldman equation describes the relationship between Vm and permeable ions. - Valid when the membrane potential or electric field is constant. (good for resting potential)

qV   V KKe kT K oi J   qV K   kT e 1

qV   V Na Na e kT Na  o i J   qV Na   kT e 1

qV   V Cl ekT   Cl Na  o  i J   qV Cl   kT e 1

Goldman Equation

- Space-charge neutrality: J   J   J  K Na Cl kT  P [K  ]  P [Na ]  P [Cl  ]  V  ln K o Na o Cl i  m      q  PK [K ]i  PNa[Na ]i  PCl [Cl ]o   kT D P , P , P Permeabilities, eg. P K K K Na Cl K  q  : membrane width Ion Pumps - Assuming an active K+ pump, passive channels for K+ and Cl- dK[] dv JJ D  ZK[] K  pump Kdx K K dx dCl[] dv JD  ZCl[] Cl Cldx Cl Cl dx

2kT  J  K [K  ] [K  ] pump q o i Membrane Potentials Resting Membrane Potential - Selective permeability of the membrane to ions: membrane potential - For neurons, 60 ~ 90 mV Significant ions determining the resting potential are K+, Na+, and Cl- ions: K+ ions and large immobile anions - By convention, V(out) = 0; the resting potential Vm = V(in) – V(out) = -60 mV. prevail in the intracellular space while Na+ and Cl- ions prevail in the extracellular space. Active mechanisms - Hyperpolarization: Vm < -60 mV are required to maintain the above concentration gradients across the membrane; for instance, the gradients of K+ and Na+ ions are due to the active sodium–potassium pump. - Depolarization: Vm > -60 mV • Inward electrical driving force on the permeable K+ ions, since these ions carry a positive electric charge. This electrical force opposes the •Outward chemical driving force (diffusional force) and thus limits the diffusional efflux of K+ ions. Graded Response An equilibrium is attained when the diffusional force driving K+ out of the cell is balanced by the electrical ∆Vm at the post-synaptic membrane force driving K+ into the cell. The Nernst equation gives - Due to a transformation from neurotransmitter chemical energy to electrical energy - Varies with the amount of neurotransmitter received The membrane is also slightly permeable to other ions such as Na+ and Cl- through (resting, nongated) - Sum or integration + - channel proteins in the membrane: UNa = 61 mV for Na ions and UCl = -68 mV for Cl ions. UK, UNa, UCl indicate the net driving force on the particular ion type.

The Goldman–Hodgkin–Katz equation predicts the equilibrium voltage U with contributions of each ionic species.

Resting Potential, Ionic Concentrations, and Channels - Resting potential: approximately -70 mV (the negative sign signifies excess negative Resting Membrane Potential charge inside the cell relative to the outside) • The factor pk quantifies the respective - Associated with ion transport and selective permeability of the membrane to ions permeability of the membrane to the k-th - Extracellular fluid: primarily Na+ and Cl- ion type; i.e., the ease with which the k-th + - ion type crosses the membrane. The typical - Cytoplasm: K and A (amino acids and proteins). ratios of permeabilities for the resting state - Ions pass through a channel. have been determined, being especially - Passive channels: always open and ion-specific (Na+, K+, Ca2+, and Cl-). applicable for the squid axon, as - Active channels: open in response to neurotransmitters and an appropriate change in membrane potential

• U ~ -70 mV. The resulting electric field in the thin membrane of the cell (with the field magnitude U/d) is very high. The level of U

determines the electrical force while UK, UNa, and UCl determine the respective electrochemical diffusional force.

• A potential imbalance of the involved ionic concentrations in the cell, e.g., due to a slow depletion of ional gradients across the cell membrane in the course of the steady state, is prohibited by diverse active transport mechanisms in the membrane. These mechanisms maintain the ional gradients: K+ and Cl- ions are pumped back into the cell while Na+ ions back out of the cell.

Equivalent Circuit Model for the Cell Membrane Equivalent Circuit Model for the Cell Membrane Equivalent Circuit Model for the Cell Membrane Neurons in Bioelectric Phenomena Introduction - Neurons - Hodgkin and Huxley model

History - Galvani’s experiments with frog’s legs: action potential

Neurons - nerve cells - neuroglial cells (10-50 times more, support) - cell body, dendrites (receiver), axon, and pre-synaptic terminals (transmitter) myelin sheath node of Ranvier (signal jump) -Signal velocity in the axon: 0.5 ~ 120 m/s

http://stemcells.nih.gov/info/scireport/chapter8.asp

GFP-tagged protein Dissociated culture in a rat hippocampal of rat hippocampal neuron neurons Université Laval, Canada Université Laval, Canada

Dissociated culture of rat hippocampal neurons Université Laval, Canada Neurons

• Numerous short cellular extensions, known as dendrites, which branch out in a tree-like fashion and provide a receptive area. The receptive area serves as a cellular input for graded inputs from other neurons (over neuronal synapses), from a physical stimulus (direct impact), or even from a nonneuronal receptor cell (over synapses). A membrane imbalance, known as the (electric) graded potential, is generated in this receptive area in response to any of the cellular inputs. •The cell body, known as soma, serves primarily as the metabolic center of the cell. • A single long tubular extension (from 0.1mm up to 3 m in length), known as the axon, conducts nongraded action potentials (all-or-none events). • At the end of the axon, a presynaptic terminal resides which releases a chemical transmitter in a graded manner (though in quantal steps). The transmitter release serves as a cellular output toward another neuron or a muscle cell.

Types of neurons: • Sensory neurons, i.e., afferent neurons, include (or are interconnected with) sensory receptors located in the body or body’s periphery. The sensory neurons convey sensory information toward the central nervous system. Namely, sensory inputs such as light, sound, pressure, chemicals, or heat activate the corresponding receptors on the cellular level, e.g., activate gated channels for ions in the membrane of the dendrites. The resulting graded output of a receptor is converted into all-or-none action potentials which then propagate along the axon toward the neuronal synapses (as communication units with other neurons). Arriving in the central nervous system, an appropriate response is provoked, e.g., as a conscious perception or an involuntary reflex action. • Association neurons (interneurons) interconnect other neurons via synapses and ensure functional integrity of the central nervous system; These neurons comprise by far the largest class of neurons. • Motor neurons, i.e., efferent neurons, conduct action potentials from the central nervous system toward effector organs as muscle cells or glands. Namely, series of action potentials are converted into a graded release of a neurotransmitter (acetylcholine) in the neuromuscular synapses that triggers muscular contraction.

Neurons

• Neurons build specific (but not random) synaptic connections to other neurons, forming densely interconnected networks for functional processing, e.g., of incoming sensory information from the sensory neurons. The particular function of an embedded neuron in the network is greatly determined by its anatomical relationships to other neurons. On the input side, the neuron receives inputs either from sensory receptors (residing in the same neuron or in a receptor cell synaptically connected to this neuron, see below) or from other neurons (up to many thousands) via neuronal synapses located on dendrites and the cell body. On the output side, the axon branches out and builds collaterals (up to thousand) with the respective synapses in their terminal regions. These collaterals output a train of action potentials from the relevant neuron to numerous other neurons. In fact, the neuron is confronted with the task of decision- making based on prevailing inputs, to fire or not to fire action potentials on the output side—the very task of the nervous system.

Two types of receptors cells • Primary receptors: specialized sensory neuron which exposes specific membrane regions in its bare dendrites. The free sensorial endings respond to a particular external stimulus by a corresponding graded change. The stimuli can be of thermal, mechanical, or chemical origin. Primary receptors include olfactory sensory neurons for the sense of smell. • Secondary receptors: separate nonneuronal receptor cell which is synaptically connected to an afferent sensory neuron. The receptor cell is usually highly specialized and converts the sensory stimulus (e.g., of acoustical, optical, or gustatory origin) into a graded change in its membrane potential, i.e., into its receptor potential. The receptor potential then activates synaptical transmission. Secondary receptors include hair cells connected to afferent sensory neurons via synapses for the sense of hearing. Action Membrane Potential

• If an excitable cell, such as a nerve cell or muscle cell, is stimulated, its transmembrane voltage u shows inevitable changes with respect to the resting state. As long as the resulting u does not reach a specific value, i.e., u does not exceed the stimulation threshold, the subthreshold stimulation is given. The membrane responds passively to this stimulation.

• Provided that the threshold is reached, the above-threshold stimulation occurs and the membrane responds actively. The stimulation triggers the excitable membrane to generate an action membrane potential in terms of a time-dependent electrical action impulse u(t). As an approximation, the voltage rapidly rises from the resting potential to positive values (u > 0) and then slowly recovers back. Equivalent Circuit Model for the Cell Membrane Action Membrane Potential

•The origin of an action potential is a local excitatory stimuli, in the course of which local membrane potential begins to increase and the membrane depolarizes above threshold. The excitatory stimuli may be of a different origin:

• Artificial excitation, as given by an injected positive current crossing the membrane from inside to outside

• Outward local currents that originate in the already excited proximal areas; for instance, spatial propagation of action potentials is based on such local currents.

• Opening of gated channels in the membrane that induces an inflow of positive cations into the cell, i.e., induces an inward current. For instance, receptors in the sensory nerve cell respond to a specific physical stimulus by activation of specific gated channels in the cell membrane. In consequence, outward currents 1. A capacitor corresponds roughly to the inner and outer faces of the plasma are induced in proximal areas close to the location of the gated channels. membrane. The capacitance is formed by the polar head groups of the constituent phospholipids that comprise the bilayer structure of the membrane.

2. Variable conductances, g, represent voltage-gated or passive ion channels specific to each ion transport.

3. Electromotive forces -- the electrochemical gradients driving the flow of ions are modeled as batteries.

Note that each ion, in this case Ca2+, Na+, K+, and Cl-, is represented by its own component of the circuit. Each of these consists of a variable conductance and an emf. Also note that all of these ion circuit components are in parallel with each other. Action Potential Sequence of events to excite action potential - A large depolarizing signal of up to 100 mV that travels along the axon Equilibrium potential of potassium : EK=−80 mV - All/none signal without decreasing in amplitude Equilibrium potential of sodium :ENa=+60 mV - At the end of the axon, the change in potential causes the release of a packet of neurotransmitter. 1. Resting potential: At resting potential some potassium leak channels are open but the voltage-gated sodium channels are closed. Even though no net current flows, potassium, the major ion species, moves A. Schematic of an electrophysiological recording of an across the membrane, thus pulling the resting potential close to the K+ equilibrium potential. action potential showing the various phases which 2. Stimulation: A local membrane depolarization caused by an excitatory stimulus causes some voltage- occur as the wave passes a point on a cell gated sodium channels in the neuron cell surface membrane to open, allowing sodium ions to diffuse in through the channels along their electrochemical gradient. Because they are positively charged, they begin a membrane. reversal in the potential difference across the membrane from a positive-outside to a negative-inside. Initially, B. An actual action potential (blue trace) recorded from the inward movement of sodium ions is also favored by the negative-inside membrane potential. a mouse hippocampal pyramidal neuron. In this case, 3. Depolarization ("Rising phase"): As sodium ions enter and the membrane potential becomes less the action potential was stimulated by a prolonged negative, more sodium channels open, causing an even greater influx of sodium ions. This is an example of pulse of current (brown trace; approx. 2 micro positive feedback. As more sodium channels open, the sodium current dominates over the potassium leak Amps)passed into the cell through the recording current and the membrane potential becomes positive inside. electrode. This method of stimulation distorts the AP 4. Peak: By the time the membrane potential has reached a peak value, time-dependent inactivation gates compared to the schematic, in that the "real" action on the sodium channels have already started to close, reducing and finally preventing further influx of potential is sitting atop a voltage offset caused by the sodium ions. While this occurs, the voltage-sensitive activation gates on the voltage-gated potassium channels current pulse. Thus, for example, the "undershoot" is begin to open. offset from the resting potential, although it would dip 5. Repolarization ("Falling phase"): As voltage-gated potassium channels open, there is alarge below rest if the offset were not present. The slow outward movement of potassium ions driven by the potassium concentration gradient and initially favored by the positive-inside electrical gradient. As potassium ions diffuse out, this movement of positive decline of the membrane potential back toward rest charge causes a reversal of the membrane potential to negative-inside and repolarization of the neuron back upon the termination of the current pulse reflects the towards the large negative-inside resting potential. long time constant of the neuronal membrane.

Sequence of events to excite action potential

Equilibrium potential of potassium : EK=−80 mV Equilibrium potential of sodium :ENa=+60 mV

6. Hyperpolarization ("Undershoot"): Closing of voltage-gated potassium channels is both voltage- and time-dependent. As potassium exits the cell, the resulting membrane repolarization initiates the closing of voltage-gated potassium channels. These channels do not close immediately in response to a change in membrane potential; rather, voltage-gated potassium channels (also called delayed rectifier potassium channels) have a delayed response, such that potassium continues to flow out of the cell even after the membrane has fully repolarized. Thus the membrane potential dips below the normal resting membrane potential of the cell for a brief moment; this dip of hyperpolarization is known as the undershoot. 7. Refractory Period: During the next ~ 1 msec, the Na+ and K+ Channels cannot be opened by a stimulus. The Na+/K+ Pump actively pumps Na+ out of the neuron and K+ into the neuron. This reestablishes the initial ion distribution of the resting neuron (the voltage returns to the resting potential due to leak currents, however, not due to the pump's action). The refractory period is important because it ensures unidirectional (one way) propagation of the action potential. http://www.wikipedia.org

Threshold for initiation • Action potentials are triggered when an initial depolarization reaches the threshold. This threshold potential varies, but generally is about 15 millivolts more positive than the cell's resting membrane potential, occurring when the inward sodium current exceeds the outward potassium current. The net influx of positive charges carried by sodium ions depolarizes the membrane potential, leading to the further opening of voltage- gated sodium channels. These channels support greater inward current causing further depolarization, creating a positive-feedback cycle that drives the membrane potential to a very depolarized level.

•Theaction potential threshold can be shifted by changing the balance between sodium and potassium currents. For example, if some of the sodium channels are in an inactivated state, then a given level of depolarization will open fewer sodium channels and a greater depolarization will be needed to trigger an action potential.

Action Membrane Potential Action Membrane Potential

• The duration of the action potential is about 1ms and is limited (fixed) by both the gradual inactivation of the voltage-gated Na+ channels and delayed opening of the voltage-gated K+ channels. The maximum amplitude of the action potential is nearly constant because the concentration gradient of Na+ ions across the membrane is relatively constant. • The beginning of the action potential is followed by a period of diminished excitability. •An absolute refractory period during which another depolarizing stimulus—no matter how great the stimulus is—can not trigger another (subsequent) action potential in the already excited area, i.e., the net inflow of Na+ ions cannot exceed the outflow of KC ions because the voltage-gated Na+ channels are in the nonactivable state. •A relative refractory period immediately follows the absolute refractory period, during which a larger stimulus— i.e., larger than normally required to reach the threshold—is needed to initiate another action potential. However, if the subsequent action potential is initiated, it is lower in both ascending slope and peak amplitude. A reduced magnitude of the total Na+ inflow flattens the ascending slope of the membrane potential. In addition, the elevated (delayed and hyperpolarizing) outflow of K+ ions in the second half of the ongoing action potential period partly compensates the second depolarizing stimulus, impedes a prompt release of a subsequent action potential, and thus reduces the peak amplitude of the subsequent action potential. • Usually, the absolute refractory period lasts about 1ms while the relative refractory period lasts approximately another 2–4 ms. • The refractoriness of the membrane prevents temporal overlap of action potentials (or action impulses) and excludes the possibility of back-propagation of action potentials along an excitable membrane.

• Changes in the membrane voltage are caused by substantial changes in the membrane’s permeabilities pk to different ions (dominating around the membrane) but not by changes in the concentrations of the ions. The bulk concentrations of Na+, K+, Cl- ions inside and outside the cell remain constant undermost physiological conditions and also during the action potential. - This is because the relative number of ions crossing the membrane is very small and amounts to only about 0.001% of all intracellular ions. - Original resting ionic gradients across the membrane are restored and maintained by diverse active mechanisms in the cell membrane.

Propagation of Action Potential Propagation of Action Potential

• The transient electric signal of the taction potential travels along nerve and muscle cells to carry time-sensitive • Action potentials propagate in two ways without being attenuated. information throughout the human body. - Along unmyelinated axons: every patch of its membrane contains voltage-gated Na+ and K+ channels. Thus • The depolarizing imbalance spreads passively in the axial direction of the sensorial ending towards the trigger action potentials can be produced along the entire length of the axon. The action potential in one patch serves zone and experiences a particular attenuation over distance. Arriving at the trigger zone, an action potential can as a stimulating source for the action potential further in adjacent regions. The action potentials are regenerated be released if the graded local imbalance exceeds the local level of the membrane threshold. Then the action along the entire length of the unmyelinated axon with the same amplitude and duration of the action potential. potential actively propagates without any attenuation along a myelinated axon of the sensory neuron. The Ion channels have to be opened along the entire length of the axon in the course of the regeneration. synapse transmits excitatory information towards the motor neuron with the use of chemical substances. In analogy, the action potentials propagate without failure and without attenuation along an unmyelinated axon of the - The passive spread of the depolarization along the axon is relatively fast compared to the time it takes to open motor neuron towards the nerve–muscle synapse. voltage-gated channels and to generate an action potential. In other words, for a higher conduction speed fewer action potentials need to be produced per axon length. In addition, the very thin membrane of the unmyelinated • There should be active propagation in axon because typical spatial distances in human exceeds a meter while the axon shows a high capacitance, slowing down the conduction of changes in the membrane potential. size of  (decay length) is in the range of a few mm. - Along myelinated axons: the layer consists of tightly wrapped Schwann cells forming sheets of insulating membrane (myelin sheath) interrupted every 1–2 mm by bare patches of axon membrane about 1–2 m in length; the gaps are known as the nodes of Ranvier. Because of the isolation preventing (depolarizing) current flow across the membrane, action potentials can be triggered only at the nodes. The isolation increases the transverse membrane resistance and strongly reduces the current through the internodal surface. In other words, myelinated axons offer fewer sites for an active regeneration of action potentials, which speeds up the propagation of action potentials. The myelination significantly decreases local capacitance because the axonal membrane is about 100 times thicker. Also, the reduced area of the membrane tends to reduce capacitance of the nodal area, which speeds up nodal discharging and allows the membrane threshold to be reached more quickly in order to regenerate an action potential further down the myelinated axon. The propagation of action impulses is accelerated in comparison with unmyelinated axons.

Propagation of Action Potential Propagation of Action Membrane Potential

• The internodal distance is in the range of , for the passive spread of depolarization is spatially limited to values similar to .

• The nodal area is very rich in voltage-gated Na+ channels. a high channel density contributes to the generation of an intense (depolarizing) inward Na+ current in response to the passive spread of depolarization—that periodically boosts the amplitude of the action potential. However, the mean density of the voltage-gated Na+ channels over the axon’s length is much lower than for unmyelinated axons, which highlights the metabolic benefits of myelinated axons. In addition, less current is needed to facilitate propagation of excitation, which results in a smaller ionic imbalance to restore, e.g., by the active sodium–potassium pumps. Consequently, the restoration of only small concentration gradients requires lower energy expenditure by the active pumps.

• Nervous systems have developed two mechanisms for large propagation speed: - Giant axons - Axons encased by the myelin sheath

• The typical values for v are in the range from 0.5 to 100 m/s for both types of axons and, in general, increase with the axon diameter. A small diameter of axons offers advantages in required biological space and metabolic efficiency. For thin axons with diameter of a few m, myelin sheath speeds up the impulse propagation by a factor of more than 10 compared to unmyelinated axons. Conversely, for a given propagation speed, myelinated axons are smaller, require less biological space, and are more energy efficient than their unmyelinated counterparts.

• The propagation of action impulses goes only in one direction. Back propagation is impossible because refractory periods prevent an immediate re-excitation of adjacent axonal regions (nodes). Propagation of Action Membrane Potential Synaptic Propagation of Action Potential Synaptic Propagation of Action Potential

• The synapse works as a mediating junction with chemical transmission so that electric action potentials can •In neuromuscular synapses, only excitatory postsynaptic potentials, known as endplate potentials, are generated. propagate from one nerve cell (presynaptic neuron) to another nerve cell (postsynaptic neuron). the synapse physiological information, carried by the action potentials, proceeds unidirectionally from the presynaptic basically consists of membrane of the axon terminal, over the synaptic cleft, up to the postsynaptic membrane, in which graded - A presynaptic terminal (bouton) at the end of the axon, which ends with a presynaptic membrane postsynaptic potentials are induced. - A very narrow gap (10–50nm in width in neuronal synapses and 100nm in neuromuscular synapses), known as the synaptic cleft • The synapses serve not only for information gating but also for physical amplification. A small presynaptic - An adjacent postsynaptic terminal, which begins with a postsynaptic membrane of the receiving nerve cell or terminal can depolarize a large postsynaptic cell over the synaptic amplification because the chemical muscle cell. In the case of the nerve cell, the postsynaptic terminal is usually located on its dendrites or its cell transmission involved is an active process in which many thousands of postsynaptic transmitter-gated channels body. are opened in response to presynaptic depolarization.

• The presynaptic ending contains synaptic vesicles (about 50 nm in size) which hold neurotransmitter molecules • The differences between action potentials and postsynaptic potentials (excitatory or inhibitory) : (e.g., acetylcholine) encapsulated in a membrane for chemical transmission across the cleft. Numerous vesicles - Unlike action potentials with their all-or-none behavior (typically ~ 100 mV with impulse duration of about 2 ms), are already docked to the internal face of the presynaptic membrane (active zones). After an action potential postsynaptic potentials are graded [~ 0.1–10 mV with duration from 5 ms up to 20 min in neuronal synapses]. arrives at the swelling of the axon terminal, the presynaptic membrane becomes depolarized. Depolarization - Unlike action potentials triggered at a certain threshold level, postsynaptic potentials have no threshold. opens voltage-gated Ca2+ channels which are abundant in this membrane. A rapid Ca2+ inflow follows because of - Unlike action potentials which propagate actively without failure and without attenuation over long distances (up a high electrochemical driving force. The entry of Ca2+ ions—as much as a thousand fold increase in the Ca2+ to 1–2 m in the human body), postsynaptic potentials spread passively and decrementally only over short concentration at the active zones—commands vesicles to merge with the presynaptic membrane. In the course of distances (up to 1–2 mm). the fusion, transmitter molecules are released into the synaptic cleft. The remaining vesicle membrane is recycled - Unlike action potentials showing absolute and relative refractory periods, postsynaptic potentials have no back into the cell. refractory period. - Unlike action potentials with no overlap, postsynaptic potentials are capable of summation. • Neurotransmitter molecules diffuse through the synaptic cleft, arrive at the postsynaptic membrane, and bind to highly specific receptors, namely, receptor sites of transmitter-gated channels. • The differences above are tightly interrelated with the differences between the voltage-gated channels (e.g., for Na+ ions) involved in the genesis of action potentials and transmitter-gated channels (e.g., acetylcholine-gated • The chemical transmitters involved in neuronal synapses may not only have a depolarizing effect but also a channels) involved in the genesis of postsynaptic potentials. An action potential can only be triggered by voltage- hyperpolarizing effect on the postsynaptic membrane. In the latter case, the synapse is called an inhibitory gated Na+ channels because these channels are regenerative. It means that a progressing depolarization of the synapse. membrane caused by Na+ influx opens even more voltage-gated Na+ channels, which accelerates this depolarization. In contrast, a depolarization produced by a dominant Na+ influx through the acetylcholine-gated channels does not lead to the opening of more acetylcholine-gated channels. Receptors Receptors Neurotransmitters Neurotransmitters

Neurotransmitters Neurotransmitters

Function of Neurons and Receptors Function of Neurons and Receptors

• The input stimulation activates receptive fields in the sensorial ending; e.g., the stretch-gated channels in the • Beginning with an input stimulus, the graded input stimulus first affects membrane are opened. In consequence, a net influx of positive ions results into the sensorial ending. The local u - The receptive field of the sensory neuron and becomes encoded by drives toward more positive values, yielding a local depolarization of the membrane (or an imbalance of u related - The graded receptor potential which spreads in a lossy way over a short-range toward - The trigger zone, in which graded changes of the receptor potential are transformed into a digital train of action to the resting state with u = UR. The arising local difference u - UR, i.e., the graded receptor potential, is proportional to the intensity of the stretch. In fact, the stronger and longer is the mechanical stretch of the potentials (analog-to-digital converter). receptive field, the larger and longer is the resulting receptor potential in the sensorial ending. - Afterward, the all-or-none action potentials regenerate themselves along the axon, spread in a lossless way over • The local receptor potential induces axial currents inside and outside the sensorial ending flowing toward and a long-range, and arrive at from the resting membrane regions, respectively. The imbalance in the resting potential spreads passively along - The synapses, the secretory components, in which the digital train is transformed again into a graded signal, i.e., the sensorial ending and attenuates with increasing distance from the receptive field (site of origin). The into a graded release of neurotransmitter. imbalance cannot be conveyed much further than 1–2mm (short-range conduction). Arriving at the trigger zone of • Such electric signals in neurons usually propagate only in one direction the sensory neuron, namely, at the first node of Ranvier, action potentials can now be generated here provided • Immediately after release of an action potential, there is an absolute refractory period lasting for about 1 ms, during which another (subsequent) action potential cannot be generated. Consequently, there is no overlap of that the induced local depolarization (graded difference u - UR exceeds the local membrane threshold. • Then the action potentials actively propagate without any attenuation or waveform change along the axon of the action potentials in the time domain and a minimum time interval exists between successive action potentials. sensory neuron (long-range conduction). The action potentials reach the axon’s terminal region, a nerve–nerve The absolute upper limit for the instantaneous frequency of action impulses—or maximum firing frequency — synapse, in which a chemical neurotransmitter is released into the synaptic cleft as the information carrier. The results to less than 1 kHz. transmitter molecules interact with (e.g., open) the transmitter-gated channels in the postsynaptic membrane of • If the attenuated receptor potential at the trigger zone is only slightly larger than the (resting) threshold level— the downstream motor neuron. provided a relatively weak physical stimulus is present—the following action potential is generated only after the • Again, the local postsynaptical u becomes imbalanced; i.e., a graded postsynaptic potential arises which spreads relative refractory period. In contrast, a strong stimulus yields a large amplitude of the receptor potential, which passively and does not reach beyond the trigger zone of the motor neuron, namely, beyond the axon hillock. Here, helps to overcome the elevated threshold during the relative refractory period. That is, the large amplitude of the another action potential can be triggered if the local membrane threshold is exceeded. Afterward, the action receptor potential fires the following action potential earlier in comparison with the small amplitude given the weak potential propagates actively along the axon toward the nerve–muscle synapse. Likewise, a graded postsynaptic stimulus. Thus weak physical stimuli tend to yield weak receptor potentials and a relatively low firing frequency; in potential is induced in the membrane of the muscle cell. The latter potential spreads passively along this contrast, strong stimuli generate strong receptor potentials and a high firing frequency. Typically, there is a linear membrane and, in turn, generates action potentials in the muscle cell. Lastly, the action potentials cause the relationship between the amplitude of the receptor potential and the firing frequency. In other words, strong stimuli muscle cell to contract. generate a greater number of action potentials in a given time frame. • In summary, the four elementary types of information about a physical stimulus are coded as follows: - The stimulus strength (and temporal changes of the strength) is coded by the frequency of action potentials. - The stimulus duration is coded by the number of action potentials. - The stimulus type (e.g., mechanical, chemical, or optical) and the stimulus location (and its spatial dimensions) are coded by distinct receptors responding to only a particular stimulus type and by distinct neural pathways that carry the relevant action potentials towards the central nervous system. Function of Neurons and Receptors

• The trigger zone of the neuron deserves an extended functional description, for it not only serves as the place of origin of action potentials, but it also integrates inputs from other neurons into a single neuronal response. Typically up to ten thousands of axon terminals converge via synapses to the relevant neuron, with some of the synapses being excitatory and others inhibitory. The trigger zone has a high density of voltage-gated Na+ channels that account for a relatively low threshold (at about 50 mV) if compared with the thresholds in other Spatial and temporal summation regions of the neuron; e.g., at the cell body the threshold is much higher at about 35 mV. Therefore, a passively of excitatory and inhibitory spreading depolarization is more likely to generate an action potential at the trigger zone with the lowest threshold postsynaptic potentials within (or discharge first the trigger zone to the threshold level) in comparison with other regions of the neuron. The trigger zone is typically located at the axon hillock in motor neurons and association neurons, whereas in sensory the trigger zone. neurons this zone is located at the first node of Ranvier (of myelinated axons) or just beyond the receptive field. • If the sum level of all potentials, i.e., the total depolarization at the trigger zone, is at or above the threshold level by the time the potentials reach the trigger zone, an action potential is generated. Any further increase in the sum level increases the frequency of action potentials. • The translation of graded postsynaptic potentials into a pulse sequence of all-or-none action potentials is analogous to the discussed translation of receptor potentials into action potentials. In fact, spatial locations of synapses are critical for their effectiveness. - Excitatory synapses are usually located on dendrites. - Inhibitory synapses are usually found on the cell body near the axon hillock. •This integrative behavior is the quintessential action of the neuron which weights the different input information and then responds appropriately at the output side (as a triggering component).

•For amplification of the stimulus in the receptor cells, e.g., a single molecule of a chemical stimulus (substance) may activate a receptor protein (residing outside the cell membrane) in terms of a low energy complementary interaction; e.g., a scent molecule may activate an odorant receptor. This interaction triggers a chain reaction for the synthesis of numerous molecules which then act as secondary transmitters inside the cell. Consequently, the secondary transmitters begin to gate ion channels in the membrane (from intracellular site) or to vary the intracellular amount of Ca2+ ions.

Nervous systems Nervous systems

Measurement of the Cell Membrane Potential Measurement of the Cell Membrane Potential

Hodgkin-Huxley Model of the Action Potential - Empirical model of an action potential in a squid giant axon, Nobel Prize (1963) - Stimulation of the post-synaptic membrane;

1. Vm reaches threshold 2. active Na+ conductance gates open 3. an inward flow of Na+ ions 4. further depolarization 5. increases Na+ conductance; inducing more Na+ current

6. continues driving Vm to Ena 7. concludes with the closure of the Na+ gates

-K+ conductance: similar but slower FitzHugh-Nagumo Model for Neurons - A 2-D simplification of the Hodgkin-Huxley model of AP generation in squid giant axons - The motivation was to isolate the mathematical properties of excitation and propagation from the electrochemical properties of Na+ and K+ ion flow. It explains 1. Absence of All-or-None Spikes 2. Absence of Threshold 3. Excitation Block 4. Anodal Break Excitation 5. Spike Accommodation 6. Traveling Waves

-K+ conductance: similar but slower

Supplementary methods