Download lecture 21 - Biological and Soft Systems

Lecture21:TowardsCharacterising
theBiophysicsofSingleNeurons
DrEileenNugent
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Fri 04/12/15 11:00-12:30
Fri 04/12/15 14:00-15.30
Mott Seminar room
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Richard Naud and Wulfram Ger
in Fig. 7. Here the voltage threshold measured from a current pulse is significa
different from the voltage threshold measured with a current step.
Real neurons have sodium ion channels that gradually open as a function of
membrane potential and time. If the channel is open, positive sodium ions flow
the cell, which increases the membrane potential even further. This positive fe
ThepredictivepowerofSingleNeuronModels
back is responsible for the upswing of the action potential. Although this str
positive feedback is hard to stop, it can be stopped by a sufficiently strong hyper
larizing current, thus allowing the membrane potential to increase above the act
Richard Naud and Wulfram Gerstner
tion threshold of the sodium current.
Sodium ion channels responsible for the upswing of the action potential r
ere the voltage threshold measured
from a current pulse is significantly
very fast. So fast that the time it takes to reach their voltage-dependent leve
om the voltage threshold measured
with aiscurrent
step.Therefore these channels can be seen as currents wi
activation
negligible.
rons have sodium ion channelsmagnitude
that gradually
open
as a function
of membrane
the
BuildingNeuralPlatforms:
depending
nonlinearly
on the
potential. This section explo
potential and time. If the channel
open,
positivewith
sodium
ions flow
Micropatterning,HighThroughputSingle-CellAnalysis
theisLIF
augmented
a nonlinear
terminto
for smooth spike initiation.
hich increases the membrane potential even further. This positive feedponsible for the upswing of the action potential. Although this strong
dback is hard to stop, it can be stopped by a sufficiently strong hyperpo4.1 The Exponential Integrate-and-Fire Model
rent, thus allowing the membrane potential to increase above the activald of the sodium current.
Allowing
the transmembrane
current to react
be any function of V , the membrane dyn
ion channels responsible for the
upswing
of the action potential
will follow an equation
of the type:
ControllingSingleNeurons:
o fast that the time it takes toicsreach
their voltage-dependent
level of
Optogenetics
s negligible. Therefore these channels can be seen as currents
dV with a
C
= F(V ) + I(t),
(
depending nonlinearly on the membrane potential. This sectiondtexplores
mented with a nonlinear14term for smooth spike initiation.
Richard Naud and Wulfram Gerstner
where F(V ) is the current flowing through the membrane. For the perfect IF it is z
(F(V ) = 0),
for the LIF it is linear with a negative slope (F(V ) = gL (V E0 )).
Fig. 9 Generalizations
of the
LIF includecan
either
refractorispeculate on the shape of the non-linearity. The simplest non-linearity wo
ness, adaptation, linearized
be the quadratic : F(V ) = gL (V E0 )(V VT ) (Latham et al, 20
currents, orarguably
smooth spike
Exponential Integrate-and-Fire
Model
initiation. Various
regroupHowever this implies that the dynamics at hyperpolarized potentials is non-lin
ments have various names.
which
conflicts with experimental observations. Other possible models could
For instance,
the refractorye transmembrane current
to
be
any
function
of V
the membrane
dynamExponential-Integrate-andmade with cubic
or, even
quartic functions
of V (Touboul, 2008). An equally sim
Fire
(rEIF)
regroups
refracow an equation of the type:
non-linearity is the exponential function:
AllowthetransmembranecurrenttobeanexponentialofV:
toriness,
smooth spike initiation and the features of a LIF
✓
◆
V VT
dV(Badel et al, 2008b).
F(V ) = gL (V E0 )(28)
+ gL DT exp
(
C
= F(V ) + I(t),
DT
dt
AdaptiveExponentialIntegrateand
FireModels
Addlinearizedcurrentwithcumulativespike-triggeredadaptationeachadditional
5.1 Thethe
Adaptive
Integrate-and-Fire
where
DT isExponential
called
slope
factorIFthat
the sharpness of the spike initiat
) is the current flowing
through
membrane.
Forthethe
perfect
it isregulates
zero Model
currentwicanbetuned
The Exponential
for the LIF it is -subthresholdcouplingconstantai
linear with a negative
slope (F(V )Integrate-and-Fire
= gL (V E0 )).(EIF;
We Fourcaud-Trocme et al (2003)) mo
The simplest
way
to
combine
all
the
features
is
to
add
to
the
a linearized
integrates
current according
to Eq. 28 EIF
andmodel
29 and
resets the dynamics to
te on the shape -itsspike-triggeredjumpsizebi
of the non-linearity.
Thethesimplest
non-linearity
current with cumulative
spike-triggered
adaptation: would
(i.e. produces
once the simulated potential reaches a value q . The ex
e the quadratic : F(V ) = gL (V
E0 )(V aVspike)
T ) (Latham et✓al, 2000).
◆
N D T . As in the LIF, we hav
value
matter, as long
V asVTq >> VT +
dV of q does not
is implies that the dynamics at hyperpolarized
potentials
is
non-linear,
C
= gL (V E0 ) + gL DT exp
+ I(t) Â wi
(30)
resetdtthe dynamics once we have detected
a spike.i=1The value
at which we stop
DT
flicts with experimental observations.
Other
possible
models
could
be
numerical
integration should not be confused with the threshold for spike initiat
dwi
cubic or even quartic functions We
ofti V
(Touboul,
simple
=
ai (Vdynamics
E0 ) wonce
i 2008).
i An equally
reset the
we are sure
the spike has been(31)
initiated. This can
dt
y is the exponential function: if V (t) > VT thenV (t) ! Vr
(32)
✓i (t) ! wi (t)◆+ bi
and w
(33)
V VT
F(V ) = gL (V where
E0 )each
+ gadditional
(29)
L D T exp current wi can be tuned by adapting
4
its subthreshold coupling
DT
constant ai and its spike-triggered jump size bi . The simplest version of this framework assumes N = 1 and it is known as the Adaptive Exponential Integrate-and-Fire
called the slope factor that
regulates the sharpness of the spike initiation.
(AdEx; Brette and Gerstner (2005); Gerstner and Brette (2009)). This model com-
C
= F(V ) + I(t),
(28)
dt by adapting its subthreshold coupling
where each additional current wi can be tuned
constant ai and
itsF(V
spike-triggered
bi . The
simplest version
of thisIFframewhere
) is the current jump
flowingsize
through
the membrane.
For the perfect
it is zero
work assumes
N=
and
is LIF
known
thewith
Adaptive
Exponential
(F(V
) =10),
foritthe
it is as
linear
a negative
slope (F(VIntegrate-and-Fire
) = gL (V E0 )). We
(AdEx; Brette
Gerstner
(2005);
and BretteThe
(2009)).
model comcanand
speculate
on the
shape Gerstner
of the non-linearity.
simplestThis
non-linearity
would
arguably
the quadratic
: F(Vneurons,
) = gL (V
)(V see
VT in
) (Latham
pares very well
with be
many
types of real
as weE0will
Sect. 7.et al, 2000).
However this implies that the dynamics at hyperpolarized potentials is non-linear,
which conflicts with experimental observations. Other possible models could be
made with cubic or even quartic functions of V (Touboul, 2008). An equally simple
non-linearity
is the exponential function:
5.2 Integrated
Models
✓
◆
V VT
F(V ) = g (V E ) + gL DT exp
(29)
For some neurons the spike initiation isL sharp 0enough
and can Dbe
T neglected. In fact,
GeneralisedLinearModels
if the slope factor D ! 0 in Eq. 30, then the AdEx turns into a linear model with
where InsomeinstancesspikeinitiationisverysharpandtheslopefactorΔ->0
DT is called the slope factor that regulates the sharpness of the spike initiation.
a sharp threshold.
As
we have seen in Sect. 2, the solution to the linear dynamical
TheAdaptiveExponentialisthenalinearmodelwithasharpthreshold
Exponential Integrate-and-Fire (EIF; Fourcaud-Trocme et al (2003)) model
system can be
cast in the
the current
form: according to Eq. 28 and 29 and resets the dynamics to Vr
integrates
(i.e. produces a spike)Zonce
• the simulated potential reaches a value q . The exact
value ofVq(t)does
as long ass)ds
q >>
DT . As
the LIF, we have
= Enot
k(s)I(t
+ VT h+a (t
tˆi ) inκ(s)istheinputfilter
(34)to
0 +matter,
η
(t)shapeofthespike
a
reset the dynamics once0 we have detected a spike.
The value at which we stop the
i
numerical integration should not be confused with the threshold for spike initiation.
where k(t) is
input
filter andonce
ha (t)
of the
with its This
cumulaWethe
reset
the dynamics
we is
arethe
sureshape
the spike
hasspike
been
initiated.
can be
Ifweallowarbitraryshapefittingforthesekernelsκ(s)andη
a(t)basedonmeasurements
Â
withadatasetfromtrainingneurons->Generalisedintegrateandfiremodel
tive tail. The sum
runs on all the spike times {tˆ} defined as the times where the
voltage crosses Addsomestochasticnoisetothethreshold(escapenoise)-GeneralisedLinearModels
the threshold (V > VT ). To be consistent with the processes seen in
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UsingExtracellularRecordingsto
PredictEncoding
6
PredictionforRetinalCellActivity
J.W.Pillow,J.Shlens,L.Paninski,A.Sher,A.M.Litke,E.J.ChichilniskyandE.P.Simoncelli(2008)
Spatio-temporalcorrelationsandvisualsignallinginacompleteneuronalpopulation.Nature
7
454,pp.995–999
IncludingCoupling
J.W.Pillow,J.Shlens,L.Paninski,A.Sher,A.M.Litke,E.J.ChichilniskyandE.P.Simoncelli(2008)
Spatio-temporalcorrelationsandvisualsignallinginacompleteneuronalpopulation.Nature
8
454,pp.995–999
ThepredictivepowerofSingleNeuronModels
BuildingNeuralPlatforms:
Micropatterning,HighThroughputSingle-CellAnalysis
ControllingSingleNeurons:
Optogenetics
SoftLithographyforControlledGrowth
ofLargenumbersofaddressablecells
Shin et al Nature Protocols 7, 1247–1259 (2012)
Pioneered by Whitesides Group, Harvard
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Valves:ControlofBiochemical
EnvironmentofNeurons
Quake Group: Science 7 April 2000: Vol. 288 no. 5463 pp.
113-116
Weitz Lab: Applied Physics letters 92 (24) 243509
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AxonDiodes:Directingthe
ConnectivityofNeurons
“Axon diodes for the reconstruction of
oriented neuronal networks in microfluidic
chambers” Peyrin et al (UPMC Paris)
Lab Chip, 2011,11, 3663-3673
Microfluidic device controls
Physiological conditions and enables
rapid medium and drug switching
Channel Asymmetry imposes controlled
Un-directional axon connectivity
Seeding of different cell populations
possible to mimic physiological
network development – populations
can be chemically addressed
ORIGINAL DEVICE “Microfluidic
Multicompartment Device for Neuroscience
Research.” Taylor et al (Irvine CA) Langmuir,
2003, 19, 1551-1556
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Hydrogels:Replicatingthe
MechanicalEnvironmentofNeurons
Made by crosslinking
polymer chains, readily
absorb water
Closely mimic gel-like
properties of the extra
Cellular matrix
Can be chemically
functionalized
Cryogels : Interconnected
macro porous structures
of interest in tissue
engineering
Soft substrates for neurons
(Gelatin, pore size 100 um)
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3DNeuronalScaffolds
“The performance of laminin-containing
cryogel scaffolds in neural tissue
regeneration”
Jurga el al (Lyon)
Biomaterials, 2011, 32, 3423-34
Neurons seeded in GelatinLaminin cryogels
Ø 
Ø 
Ø 
Ø 
Seeded with neural stem cells filling most small pores (100um)
Transplanted into hippocampal brain slices - neuroblast but not glial cell penetration
Rat cortex transplantation resulting in lower neuroblast density
Placed in 96 well plates, seeded with stem cells, observed differentiated neuron-like
cells (MAP2) and astrocyte-like (S100beta)
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Example:BiophysicalModelBuildingwith
SingleCellMicrofluidicPlatforms
E.ColiCellSizecontrol
Sizing
Timing
xf
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MechanismsofSizeControl
A
SIZER
B
TIMER
no control on size
only on
(fixed)
fixed final size
slope ~-1
log(initial size x0)
elongation ⇥⇤
elongation ⇥⇤
independent from x0
slope ~0
log(initial size x0 )
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HighThroughputSingleCell
Platforms
Growth Inlets
Channels
Outlets
Coverslip
1. 10000’sofcells
2. ControloverPhysiologicalState
•  Open ended Microfluidic
Cell Culture Platform
3. AutomatedDataCollection
Advantages
+ cells lost on both ends eliminate effects of ‘aging’
+ pressure controlled clamping prevents cell movement
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SizeControlinE.Coliisachievedbychanges
inthedoublinggme
Ref:ConcertedcontrolofEscheriacoli
celldivision,M.Osella,E.Nugent&M.
ConsentinoLagomarsinoPNAS111
3431-3435(2014)
ln(birth length x0)
B
40
0.045
doubling
time ⇥ [min]
❖ Doubling time depends on initial size
INDIVIDUAL TIMER DEPENDING
ON INITIAL SIZE
elongation ⇥
❖ Single cell growth rate not correlated
with initial size
A
growth rate
[min -1]
❖ Anticorrelation between elongation
and initial size, slope -0.3
NOT PURE SIZE CONTROL
30
0.030
0.015
0.6
20
10
1.2
1.8
ln(birth length x0)
0.6
1.2
1.8
ln(birth length x0)
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SizeControl:Catastropheand
Recovery
❖ Strong control and saturation
approximated by Hill Function
(90 – 98% of cells)
hd (x) =
kxn
hn + xn
❖ Size Control Catastrophe as cells
enter filamentous regime
❖ Recovery of size control for even
longer cells
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ConcertedControlaccuratelydescribes
doublingtimedistributions
20
ThepredictivepowerofSingleNeuronModels
BuildingNeuralPlatforms:
Micropatterning,HighThroughputSingle-CellAnalysis
ControllingSingleNeurons:
Optogenetics
Optogenetics
© 2005 Nature Publishing Group http://www.nature.com/natureneuroscience
TECHNICAL REPORT
Millisecond-timescale, genetically targeted optical control
of neural activity
Edward S Boyden1, Feng Zhang1, Ernst Bamberg2,3, Georg Nagel2,5 & Karl Deisseroth1,4
Temporally precise, noninvasive control of activity in welldefined neuronal populations is a long-sought goal of systems
neuroscience. We adapted for this purpose the naturally
occurring algal protein Channelrhodopsin-2, a rapidly gated
light-sensitive cation channel, by using lentiviral gene delivery in
combination with high-speed optical switching to photostimulate
mammalian neurons. We demonstrate reliable, millisecondtimescale control of neuronal spiking, as well as control of
excitatory and inhibitory synaptic transmission. This technology
allows the use of light to alter neural processing at the level of
single spikes and synaptic events, yielding a widely applicable
tool for neuroscientists and biomedical engineers.
Neural computation depends on the temporally diverse spiking patterns of different classes of neurons that express unique genetic markers
and demonstrate heterogeneous wiring properties within neural networks. Although direct electrical stimulation and recording of neurons
Figure 1 ChR2 enables light-driven neuron
in intact brain tissue have provided many insights into the function of
circuit subfields (for example, see refs. 1–3), neurons belonging to a
specific class are often sparsely embedded within tissue, posing fundamental challenges for resolving the role of particular neuron types in
information processing. A high–temporal resolution, noninvasive,
genetically based method to control neural activity would enable
elucidation of the temporal activity patterns in specific neurons that
drive circuit dynamics, plasticity and behavior.
Despite substantial progress made in the analysis of neural network
geometry by means of non–cell-type-specific techniques like glutamate
uncaging (for example, see refs. 4–7), no tool has yet been invented
with the requisite spatiotemporal resolution to probe neural coding at
the resolution of single spikes. Furthermore, previous genetically
encoded optical methods, although elegant8–10,11, have allowed control
of neuronal activity over timescales of seconds to minutes, perhaps
owing to their mechanisms for effecting depolarization. Kinetics
roughly a thousand times faster would enable remote control of
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Light-GatedIonChannels
23
LightDrivenNeuralSpikingand
Inhibition
24
PulseTrains
25
ControlofBrainCircuits
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What’sNext
GuestLecturerSarahTeichmann(EBI/Sanger/
Cavendish)
Fri:Graphtheoryforanalysisofprotein
complexes
Mon:Topologyforcellcyclespeedestimation
insinglecelltranscriptomics
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