Volker Steuber Biocomputation Research Group University of Hertfordshire UK vsteuberhertsacuk HodgkinHuxley Model 60 years and one Nobel Prize later The HodgkinHuxley model is phenomenological rather than mechanistic ID: 930591
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Slide1
LASCON 2020
Ionic Currents and their Effects
Volker
Steuber
Biocomputation
Research Group
University of Hertfordshire
UK
v.steuber@herts.ac.uk
Slide2Hodgkin-Huxley Model
Slide360 years (and one Nobel Prize) later
The Hodgkin-Huxley model is phenomenological rather than mechanistic.
“Certain features of our equations [are] capable of
physical interpretation, but the success of our
equations is no evidence in favour of the mechanism
of permeability change that we tentatively had in mind
when formulating them.”
(Hodgkin & Huxley, 1952)
What have we learnt about the underlying mechanisms?
Slide4Current methods to study ion channels
Electrophysiology
Pharmacology
X-ray crystallography
NMR (nuclear magnetic resonance)
ESR (electron spin resonance)
FRET (fluorescence energy transfer)
Site-directed mutagenesis
Heterologous
expression (
Xenopus
oocytes
, cell lines)
Immuno-histochemistry
(LM and EM)
Optogenetics
(Nature’s Method of the Year 2010)
Slide5Gigaseal and Patch clamp
Neher & Sakmann (1976)
Hamill et al. (1981)
Slide6Stochastic opening of single Na and K channels
Rapid opening and closing of single channels results in unitary current steps.
Na
K
Slide7Pharmacology
Narahashi et al. (1964): tetrodotoxin (TTX) from puffer fish selectively
blocks Na current in lobster giant axon.
Tasaki & Hagiwara (1957): selective K channel block with
tetraethylammonium (TEA).
Slide8Characterising individual channels with blocking agents
Pharmacological dissection of Na and K currents (Hille 1966).
Other channel blockers: Cs
+
, Ba
2+
, 4-aminopyridine, amiloride,
apamin, many local anesthetics.
Slide9Many local anesthetics block ion channels
Lidocaine stabilises the inactivated state of the Na channel.
A
Slide10Toxins block ion channels by binding to receptor sites
Simplest case: toxin T binds reversibly to receptor R to form inactivated
complex TR.
Fraction of free receptors (available channels) depends on toxin concentration [T] and dissociation constant K
d
:
relative peak Na current
Slide11Gates are located at the cytoplasmic side
Armstrong (1966): intracellular TEA (C9) only blocks open K channels.
Slide12Suggested location of gate and selectivity filter
TEA
TEA block can be dislodged by adding K
+
to extracellular medium and
stepping to hyperpolarised potentials, which suggests a pore.
Slide13Diversity of K channels
First evidence for existence of diverse K channels: discovery of slow
K currents in frog heart muscle.
Slide14Many K channels inactivate
Slow inactivation of K currents in frog muscle (Adrian et al.1970).
Slide15Fast and slow K channels coexist
Dubois (1983): pharmacological isolation of different K currents in frog axons.
The functional role of the different K channels in frog axons is still not clear.
They are not required for action potential repolarisation.
Slide16Na channels are less diverse
Kinetic differences between fast Na channels affect action potential width.
But there are also persistent (non-inactivating) and resurgent components.
Slide17Ion channel diversity due to gene duplications and mutations
Comparison of amino acid sequences of mammalian Na channels:
Slide18Dendrogram of K channels
Slide19Na, K and Ca channels form a gene superfamily
Slide20Structure of ion channels
Pore-forming unit is composed of four times six
transmembrane
segments.
Many K channels are formed from a tetramer
Na and Ca channels consist of 4
homologous domains
One monomer
of a K channel
Ca channel
Na channel
Slide21Channel opening depends on movement of voltage sensors
One of the six transmembrane segments (S4) contains several positively charged arginine residues and acts as voltage sensor.
The movement of the voltage sensors results in a small gating current.
Slide22Ion channel structure revisited
Channels are heavily glycosylated and anchored by intracellular proteins.
Slide23X-ray crystallography confirms channel structure
Doyle et al. (1998), MacKinnon lab: 3D structure of bacterial
KcsA
channel revealed by X-ray crystallography.
Tetramer with central pore and selectivity filter.
Slide24Some ion channels deviate from the 4x6TM motif
Slide25Subunit compositions
Hetero-
oligomers
(
ACh
receptor)
Homo-oligomers
(connexins)
Single protein with
transmembrane repeats
(Na
+
, Ca
2+
channels)
Pore-forming unit+auxiliary subunits(Na+
, Ca2+ channels)
Slide26Opening mechanisms
Ligand: neurotransmitter (glutamate
acetylcholine, GABA)
Phosphorylation by PKA increases
Ca
2+
channel opening in the heart
Ca
2+
, Na+, K+ channels
Monitor changes in cell fluidregulation, muscle tension
Slide27Inactivation mechanisms
Slide28Functions
Leak channelsSet the input resistance, allow/prevent spontaneous firing.
Voltage-gated channels
Signal processing.
Ligand-gated channels
Communication between neurons. Respond to transmitters.
Gap junction channels
Electrical synapses between neurons.Transporters and Pumps Re-establish needed ion concentrations.
Slide29Transporters vs true channels
Transporters and pumps
Ion channels
~10
2
ions / s
Can transport ions uphill,
against electrochemical gradient
(use a second ion or split ATP)
~10
6
ions / s
Ions always flow downhill
Slide30Some specific functions of ion channels
Fast Na and fast delayed rectifier K Action potential generation and termination.
Slow delayed rectifier / KCNQ channels
Decrease neuronal excitability. Mutations lead to convulsions.
ACh
and
muscarine inhibit KCNQ channels (M current) in sympathetic neurons
increased response to synaptic input.
Delmas & Brown (2005)
Slide31Specific functions of ion channels
A currentK channel that activates transiently on depolarization. Enables neurons to fire repetitively at low rates. Shaker mutation: flies shake their legs under anaesthesia.
Slide32Specific functions of ion channels
Ca dependent K channelsLarge conductance (BK, voltage dependent) and intermediate and small conductance (IK and SK, voltage independent).
Responsible for afterhyperpolarizations (AHPs), spike frequency adaptation and bursting.
Slide33Specific functions of ion channels
Ca dependent K channelsZador
et al. (1992):
dendritic
“cold spots” can implement XOR operations.
Slide34Specific functions of ion channels
Inward rectifiers Activated by hyperpolarization, depending on extracellular [K
+
]. Maintain
resting potential near E
K. Heterogeneous group of channels, some of whichexhibit voltage dependent block by Mg
2+ or spermine / spermidine. No intrinsic voltage sensors not considered voltage gated channels.
Slide35Specific functions of ion channels
High voltage activated Ca channelsProvide Ca influx for activation of Ca dependent K channels. Can
result in persistent depolarisation (e.g. cardiac pacemaker) and widen
action potentials (e.g. inferior olive).
Ca is an important second messenger and involved in a multitude of
intracellular processes (synaptic plasticity, muscle contraction, transmittersecretion, gene expression...).
Slide36Specific functions of ion channels
Low voltage activated Ca channelsDe-inactivated by hyperpolarization (like fast Na channels). This can lead to rebound responses after offset of hyperpolarising input.
Resurgent Na current
Activated by action potential repolarization. Can drive spontaneous activity and
enable neurons to fire rapidly.
Afshari et al. (2004
)
Slide37Specific functions of ion channels
h (HCN) current Mixed cation
current (E
h
≈ -20 mV)
that is activated by hyperpolarization.Supports rhythmic firing /
pacemaking and rebound responses after offset of hyperpolarising input. Activation is facilitated by cAMP. Can be identifiedby “sag” during hyperpolarising current injection.
Cl
channels:Stabilise cells near resting potential. Some can be activated by Ca,
which results in slow AHPs. Others are activated by cell volume changes,which protects against osmotic swelling. Mutations affect salt retention
and can lead to kidney stones.
Slide38When things go wrong: ion channels and disease
Mutations in over 60 ion-channel genes are currently linked to human diseases.
Common channelopathies include myotonias, Hereditary Ataxia,
Long QT Syndrome (Sudden Arrythmia Death Syndrome), some forms
of epilepsy, etc.
Slide39Beyond the Hodgkin-Huxley model: Markov models
Kinetic model with channel states that undergo first order transitions.
Hodgkin-Huxley models can be represented as Markov models, but usually not vice versa.
K channel model (n
4
gating kinetics):
Slide40Goldman-Hodgkin-Katz current equation
Hodgkin-Huxley model assumes linear instantaneous current-voltagerelations:
Calcium ions have an [Ca
2+
]
out
/[Ca2+]in concentration ratio of about 50,000/1, which introduces a non-linear instantaneous I-V relation. This
can be modelled by the GHK current equation (constant field equation):Calcium permeability changes can be treated in analogy to the
Hodgkin-Huxley formalism:p
Ca Ca permeability (m/s), zCa = 2 Ca valency, R Gas constant, F Faraday constant, T temperature, m and h activation and inactivation variables
Slide41Goldman-Hodgkin-Katz current equation
Slide42References
Principles of Computational Modelling in Neuroscience.
D. Sterratt, B. Graham, A. Gillies, D. Willshaw, Cambridge University
Press (2011).
Methods in Neuronal Modeling: from Ions to Networks
.
C. Koch and I. Segev eds., MIT Press (1998).
Computational Neuroscience: Realistic Modeling for Experimentalists.E. De Schutter
editor, CRC Press (2000).Ion Channels of Excitable Membranes.
B. Hille, Sinauer (2001).
Foundations of Cellular Neurophysiology.D. Johnston and S. Wu, MIT Press (1994).