Biophysical Methods in Neuroscience · Biophysical Methods of Neurobiology (Dieter Braun) GFP - a fluorescent Protein Green fluorescent protein is also present in the jellyfish A

Biophysical Methods of Neurobiology (Dieter Braun)

Biophysical Methods in Neuroscience


The Fluorescence ProcessStage 1 : ExcitationA photon of energy hνEX creates an excitedelectronic singlet state (S1'). In chemilumi-nescence, S1’ is populated by a chemicalreaction. Stage 2 : Excited-State LifetimeFor finite time (typ. 1–10 ns), the fluorophoreundergoes conformational changes and issubject to interactions with its molecular envi-ronment. (a) the energy of S1' is partially dissipated,yielding a relaxed singlet excited state (S1). (b) not all excited molecules return to theground state (S0) by fluorescence emission:possibilties are collisional quenching, Fluores-cence Resonance Energy Transfer (FRET) andintersystem crossing.Stage 3 : Fluorescence EmissionA photon of energy hνEM is emitted, returningthe fluorophore to ground state S0. Due toenergy dissipation (S1’ to S1) the energy ofthe emission photon is lower (longer wave-length). Difference is called the Stokes shift,making it possible to detect emission photonsagainst the huge background of excitationphotons.

Fluorescein


Fluorescence Microscope

http://www.olympusmicro.com/


GFP - a fluorescent ProteinGreen fluorescent protein is also present in the jellyfish A. victoria,and absorbs blue light (488 nm) emitted by aequorin before re-emit-ting it as green light (512 nm)

4nm

2.5 nm

Chromophore after reaction of serine 65 - tyrosine 66 - glycine 67

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Chromophore entsteht erst durch Faltung des Proteins Bild: grüner „Käfig“ soll vor schädlichen Reaktionen schützen, die beim Ausbleichen des Farbstoffes entstehen können. GFP ist deshalb ein günstiger Farbstoff, weil man Zellen durch Implementierung von DNA zur Produktion von GFP bringen kann man kann einzelne Zellen einfärben


GFP - a fluorescent ProteinGreen fluorescent protein is also present in the jellyfish A. victoria,and absorbs blue light (488 nm) emitted by aequorin before re-emit-ting it as green light (512 nm)

4nm

2.5 nm

Staining of cells which activate a specific protein


Imaging of Neuronal Activity

Calcium Indicators to detect Neuronal activity


Fura-2 Ca-Dye

RatiometricallyExcitation at 365nm vs 380nm

=> ∆[Ca]free

Chromophore Ca-Binder


Calibration in Neurons

Ca-stores (S) (b) Ca-dye (B)

κDBCa[ ]∆Ca[ ]∆

-------------------B[ ]Kd

Ca[ ]before Kd–( ) Ca[ ]peak Kd–( )----------------------------------------------------------------------------------= =κS

SCa[ ]∆Ca[ ]∆

-------------------=

Binding Ratio Binding Ratio

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Fura-2 bindet an Kalzium, dadurch ändert sich allerdings auch die Zellchemie. Bei zunehmender Fura-2 Konzentration wird Kalzium-Concentration kleiner.





-------------------B[ ]Kd


SCa[ ]∆Ca[ ]∆

-------------------=

Binding Ratio

d Ca[ ]dt

--------------- d SCa[ ]dt

------------------ d BCa[ ]dt

-------------------+ +jin jout–

V-------------------=Total:

d Ca[ ]dt

--------------- 1 κS κB+ +( ) Ca[ ]totalδ t( )∆ γ Ca[ ] Ca[ ]before–( )–=

=> Ca[ ]∆ Ae t τ⁄–= τ1 κS κB+ +

γ----------------------------= A

Ca[ ]total∆1 κS κB+ +----------------------------=with ,

Binding Ratio

Administrator





Measure [Ca] transients to infer A,τ depending on [B] , kBInfer kS and [Ca] without dye

d Ca[ ]dt

--------------- d SCa[ ]dt

------------------ d BCa[ ]dt

-------------------+ +jin jout–

V-------------------=Total:

d Ca[ ]dt

--------------- 1 κS κB+ +( ) Ca[ ]totalδ t( )∆ γ Ca[ ] Ca[ ]before–( )–=

=> Ca[ ]∆ Ae t τ⁄–= τ1 κS κB+ +

γ----------------------------= A



-------------------B[ ]Kd


SCa[ ]∆Ca[ ]∆

-------------------=

Binding Ratio Binding Ratio

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Ca[ ]∆ Ae t τ⁄–= τ1 κS κB+ +

γ----------------------------= A


Results interpolated for no Ca-Dye:- 150-300nM Ca influx- Kinetics <100ms- 0.5-1% of Ca of an Action Potential is free=> Measurement of [Ca] in many physiological situations

Helmchen F., Imoto K. & Sakmann B. Ca2+ buffering and action potential-evokedCa2+ signaling in dendrites of pyramidal neurons. Biophys. J. 70, 1069-1081 (1996)


Clark, W., 1934. "Infrared photography," J. Biol. Photogr. Ass.2 (3):119-129

Seeing through in infrared


Clark, W., 1934. "Infrared photography," J. Biol. Photogr. Ass.2 (3):119-129

Seeing through in infrared

Ti-S Laser:- 700-1100nm- 100-400fs- €120.000


2-Photon Fluorescence Imaging

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Infrarot: der Farbstoff wird mit 2 Photonen nur im Fokus angeregt.


2-Photon Fluorescence Imaging

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Infrarot: der Farbstoff wird mit 2 Photonen nur im Fokus angeregt.


Ca-Imaging in Dendrites

Active Backpropagationof Action Potentials

Only in some Branches

Voltage sensitiveCa-Channels

NMDA Receptors


Measurements with Ca-Dyes

Quantal Analysisof single spines

Correlate Action Potentialswith Ca-Influx


Fluorescent Voltage-Sensitive DyesHigh fields inside Membranes

4nm

100mV / 4nm = 250kV/cmField Strength:

In

Out

E

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Die Farbstoffe liegen direkt in der Membran, sie sind spannungsabhängig.


Fluorescent Voltage-Sensitive DyesHigh fields inside Membranes

4nm

100mV / 4nm = 250kV/cmField Strength:

In

Out

E

Fluorescent Dyes: Charge relocation

E

+

-

+

Excitationblue shift

Emissionblue shift

+

Solvatochroism

Messungen von Aktionspotentialen in Dendriten von kultivierten und gentechnisch veränderten Hippocampusneuronen mit spannungssensi-tiven Farbstoffen, Dissertation Bernd Kuhn, 2001, http://tumb1.biblio.tu-muenchen.de/publ/diss/ph/2001/kuhn.pdf

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Die Farbstoffe liegen direkt in der Membran, sie sind spannungsabhängig.


Two-Dimensional Spectrum

Excitation λ

Em

issi

on

Change after100mV Depol.

Spectral Shift

Fluorescent Voltage-Sensitive Dyes

Fluorescent Dyes: Charge relocation

E

+

-

+

Excitationblue shift

Emissionblue shift

+

Solvatochroism

Messungen von Aktionspotentialen in Dendriten von kultivierten und gentechnisch veränderten Hippocampusneuronen mit spannungssensi-tiven Farbstoffen, Dissertation Bernd Kuhn, 2001, http://tumb1.biblio.tu-muenchen.de/publ/diss/ph/2001/kuhn.pdf


AP Backpropagation in Dendrites (cultured neurons)

Fluorescent Voltage-Sensitive Dyes

Bro

aden

ing

In Vivo detection of Whisker Sensing

Interaction of sensory responses with spontaneous depolarization in layer 2/3 barrel cortex.Proc Natl Acad Sci U S A. 2003 Nov 11; 100(23): 13638-43


Second Harmonic Generation (SHG)

ExcitationSHG TPF

P χ 1( )E1 χ 2( )E2 χ 3( )E3 …+ + +=



ExcitationSHG TPF

High-Resolution Nonlinear Optical Imaging of Live Cells by Second Harmonic GenerationBiophys. J. 1999 77: 3341-3349.

P χ 1( )E1 χ 2( )E2 χ 3( )E3 …+ + +=



Voltage-Sensitive SHG- tilting of the SHG-Dye- static E-Field contribution

P χ 1( )E1 χ 2( )E2 χ 3( )E3 …+ + +=

χ 2( ) χsurface2( ) χ 3( )EDC+=

influenced by Membrane Potential ?! PolarizationMechanisms of membrane potential sensing with second-har-monic generation microscopy, Journal of Biomedical Optics -- July 2003 -- Volume 8, Issue 3, pp. 428-431



Also: intrinsic SHG for Histology

Uniform polarity microtubule assemblies imaged in native brain tissue by second-harmonic generation microscopy.Proc Natl Acad Sci U S A. 2003 Jun 10; 100(12): 7081-6.

Voltage-Sensitive SHG- tilting of the SHG-Dye- static E-Field contribution

P χ 1( )E1 χ 2( )E2 χ 3( )E3 …+ + +=

χ 2( ) χsurface2( ) χ 3( )EDC+=

influenced by Membrane Potential ?! PolarizationMechanisms of membrane potential sensing with second-har-monic generation microscopy, Journal of Biomedical Optics -- July 2003 -- Volume 8, Issue 3, pp. 428-431


Gene expression of a few cells

RNA Chip


Functional Magnetic

Resolution: 1-3mm @ 3T fMRI: blood oxygenation level

Resonance Imaging (fMRI)


Positron Emission Tomography (PET)

1ns time window

3 mm

blood flowwith 15O-label

(rCBF)

dopaminergiccells withF18-dopa


Coupling Cells to Planar Electrodes

- Metal electrodes- Isolated electrodes

Cell

CleftSi02p-Si

VM

VE

VS

rJ

VJ(x,y)

Electrode / Sensor(no electrochemical reactions)

Basic Circuit

Search for (a) well-defined system(b) Neuronal Interfaces

Vorlesung Biophysik Braun - Methoden in der NeuroBiologie

High-pass filter characteristics 2D

Cell

CleftSi02p-Si

VM

VE

VS

rJ

VJ(x,y)

Electrode / Sensor

Core-Coat Conductor

Iohmic i,VJ∇R

---------- dx⋅=

Net Current:Iohmic

VJ∇R

----------∇ dxdy⋅=

Normalization of all currents to Area:

IohmicVJ∇rJ

----------∇=

R [Ohm/cm²] -> rJ [Ohm]

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Imaging Neuronal Seal Resistance on Silicon Chip using Fluorescent Voltage-Sensitive Dye, Dieter Braun and Peter Fromherz Biophysical Journal 87:1351-1359 (2004)

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Metallelektrode ist bei faradaysche Strömen giftig für die Zelle, deshalb Spannungsübertragung nur über Kapazität wünschenswert. Zwischen Zelle und Elektrode gibt es eine Lücke – Cleft – von ca. 50 nm

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Ströme werden normiert bezüglich Fläche der Platten.


High-pass filter characteristics 2D

Cell

CleftSi02p-Si

VM

VE

VS

rJ

VJ(x,y)

Electrode / Sensor

Current in Node:

Current through cell

Resulting PDE:

In frequency space with transfer functions:

Also:

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Imaging Neuronal Seal Resistance on Silicon Chip using Fluorescent Voltage-Sensitive Dye, Dieter Braun and Peter Fromherz Biophysical Journal 87:1351-1359 (2004)


High-pass filter characteristics 2DFrequency Space

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Bei sehr hohen Frequenzen der anliegenden Spannung ist der ohmsche Term zu vernachlässigen.

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Membrankapazität ca. 1 µF/cm², Siliciumkapazität bis 0,34 µF/cm² Die hohe Membrankapazität folgt aus Membran-double-layer mit ca. 4nm. Würde man eine Metallelektrode benutzen, ist auch die Kapazität der führende Faktor, bis zu 20 µF/cm², da sich eine Debyesche Doppelschicht der Ionen der physiologischen Lösung auf dem Metall absetzt. Hohe Kapazität wegen Dicke der Doppelschicht von ca. 1nm mit Dielektrizitätskonstante Epsilon(Wasser)=80).


High-pass filter characteristics 2DFrequency Space Time Space

0DPoint

ContactModel

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Time Space: desto weiter außen, desto schneller kann die Spannung abfließen rj soll groß sein, Aj zu vergrößern ist schwierig, cM ist von der Membran vorgegeben


Imaging of Seal ResistanceLock-In Technique


Imaging of Seal ResistanceLock-In Technique

Cascade of transfer functions:

Chip: Volt.-Sens. Dye: Photomultiplier Tube:s

Total:

VSTIM Fluorescence

Cell

CleftSi02p-Si

VM

VE

VS

rJ

VJ(x,y)

Electrode / Sensor


Imaging of Seal ResistanceFrequency based Imagings

Cell

CleftSi02p-Si

VM

VE

VS

rJ

VJ(x,y)

Electrode / Sensor


Chip: Volt.-Sens. Dye: Photomultiplier Tube:s

Total:

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Mit Hilfe der spannungsabhängingen Fluoreszens wird die Aufladung der Zelle gemessen. Die Zelle ist asymmetrisch aufgeladen: die Membranspannung auf der Obseite hat ein anderes Vorzeichen als die der Unterseite. Wir messen die Unterseite der Zelle - am Rand ist allerdings die Membran der Oberseite zu sehen, welche nicht im Kontakt mit der Elektrode ist.


Imaging of Seal Resistance


Total:

Transient Imaging

Cell

CleftSi02p-Si

VM

VE

VS

rJ

VJ(x,y)

Electrode / Sensor

Fourrier-Based Calculation:

Transform VSTIM from time space -> frequency spaceCalculate Expectation VPM in frequency spaceBacktransform VPM from frequency space -> time spaces


Transistors

www.biochem.mpg.de/mnphys

Electrochemical clean and CMOS compatible neurointerface

MeasuringVJ-VB

Retzius cell from leech

Rat hipocampus neurons

Averageover 64 signals


Measuring of Cell-Surface DistanceIRM: RICM:

Reduction of

Interference Reflection Reflection Interference

d

stray light with λ/4 plates

Contrast MicroscopyMicroscopy


Evanescent field

Measuring of Cell-Surface Distance

http://www.olym-pusmicro.com/primer/techniques/fluorescence/tirf/olympusaptirf.html

High NAImplementation


TIRF

Evanescent field

Measuring of Cell-Surface Distance

TIRAFTotal InternalReflection Fluorescence

Total Internal ReflectionAquous Fluorescence

FluorescentmarkerExcitation

http://www.olym-pusmicro.com/primer/techniques/fluorescence/tirf/olympusaptirf.html

BuffermarkerExcitation

cell cell

High NAImplementation


FLIC:

Measuring of Cell-Surface DistanceFluorescence InterferenceContrast Microscopy

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Die Zelle liegt auf Silizium-Oxid mit Stufen. Die Membran folgt den Stufen. Mit einer stehenden Welle wird die Oberfläche abgetastet. Abhängig von der Höhe der Stufe d ist das Bild dunkler oder heller. Da die Stufenhöhe bekannt ist, weiß man, wie die Fluoreszenzintensität aussieht, wenn die Zelle direkt auf den Stufen liegt. Wenn sie einen zusätzlichen Abstand dJ hat, schiebt sich die gemessene Kurve im Vergleich zur erwarteten nach links. Dieser Shift kann durch die Messungen in den Flanken sehr genau bestimmt werden.


Measuring of Cell-Surface DistanceFLIC: Fluorescence Interference Contrast Microscopy


Fluorescence Interference Microscopy

rkup

rkdown

Transfer of electrical field due tointerference and multireflection

Situation in fluorescentlayer (i.e. membrane)

Polarizations at Surface

Probability of Excitation or of Emission accordingto Fermi’s Golden rule and dipole far field operator proportional to:

Transitiondipole of

fluorescentdye

Incomingor outgoingelectrical

field


Fluorescence Interference MicroscopyPex pEex

2

λex

∫NAex

∫Cyl∫

Layer∫=Integrated Probability of Excitation

Pem pEem2

λem

∫NAem

∫Cyl∫

Layer∫=Integrated Probability of Emission

Expected relative fluorescence Ifluorescence PexPem=


Fluorescence Interference MicroscopyNumerical implementation

- First program with fixed layer system, C(no complex numbers, no objects)

- Second program in Java: complex object, more sophisticated numerical methods, easy buffering

Used to check the numerics of first: found some errors

- Third program in LabView:easy to play around and to debug

(a) “Numerical recipes in C” helps a lot for speed

pEex2

λex

∫NAex

∫Cyl∫

Layer∫pE 2

Cyl∫

Layer∫

NAex

∫λex

∫

>105-fold slower

(b) Integration order is crucial

with garbage collection, free layer objects, multiple windows GUI.

Notes


’Optical’ Stimulation

FM1-43 uptake

Ca Detection

“Photoconductive”

Remodeling of Synaptic Actin Induced by Photoconductive Stimulation; Cell, Vol 107, 605-616, 30 November 2001

Stimulation


’Optical’ Stimulation

FM1-43 uptake

Ca Detection

“Photoconductive”

Remodeling of Synaptic Actin Induced by Photoconductive Stimulation; Cell, Vol 107, 605-616, 30 November 2001

Stimulation

Dark

Bright

low Si-field effect capacitance

high Si-field effect capacitanceVoltage across SiO2

Voltage across Si

=> break-through of SiO2

Probably:


Planar Patch-Clamp

Whole cell patch clamp recording performed on a planar glass chip., Biophys J. 2002 Jun;82(6):3056-62.

Automating Patch-Clamp on a Chip

Long holes essential for Gigaseal


Temperature FluorescenceImaging of Temperature Laser


Temperature FluorescenceImaging of Temperature

Locked Temperature Oscillations

Laser

d=5µm

Laser


Two-State Model under Temperature Oscillationswith Temperature

Sensitivity of Fluorescence Signal

Kinetics in Phase Space


Two-State Model under Temperature Oscillationswith Temperature

Sensitivity of Fluorescence Signal

Measurements near single molecule level:DNA Hairpins Transfer h in Amplitude and Phase with Fit



Kinetics in Phase SpaceImaging Fluorescence Lock-In

Excitation IEx

Modulation E

Phase lag α

Dye(e.g. Temp.)

I q E( ) IEx× td∫=

Slow Imaging

Modulation E(e.g. Temp.)

Excitation IEx



Excitation IEx

Modulation E

Phase lag α

Dye(e.g. Temp.)

Aeiϕ 4π---

I0° I180°–I0° I180° 2Iback–+--------------------------------------------- i

I270° I90°–I270° I90° 2Iback–+------------------------------------------------+=

IEx IExΘ ωt α–( )sin[ ] ωt α–( )sin∆ IEx0( )+=

q q0 A ωt ϕ+( ) 1+sin[ ]=

IαAπ IExq0∆

2------------------------- α ϕ+( )cos 2 IExq0∆ 2πq0IEx

0( )+ +=


Slow Imaging

Co-Modulation as follows

Leads to images with slow detector:

Infer Amplitude and Phase of q:

Iback 2πq0IEx0( ) Iconst+=

Modulation E(e.g. Temp.)

Excitation IEx



Excitation IEx

Modulation E

Phase lag α

Dye(e.g. Temp.)

Aeiϕ 4π---

I0° I180°–I0° I180° 2Iback–+--------------------------------------------- i

I270° I90°–I270° I90° 2Iback–+------------------------------------------------+=

IEx IExΘ ωt α–( )sin[ ] ωt α–( )sin∆ IEx0( )+=

q q0 A ωt ϕ+( ) 1+sin[ ]=

IαAπ IExq0∆

2------------------------- α ϕ+( )cos 2 IExq0∆ 2πq0IEx

0( )+ +=


Slow Imaging

Co-Modulation as follows

Leads to images with slow detector:

Infer Amplitude and Phase of q:

DNA Hairpin under Temperature Oscillation

10 µm 10 µm170Hz 170Hz

Amplitude Phase

Iback 2πq0IEx0( ) Iconst+=



10µm

Imaging of Kinetics at Each pixel

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Biophysical Methods in Neuroscience · Biophysical Methods of Neurobiology (Dieter Braun) GFP - a fluorescent Protein Green fluorescent protein is also present in the jellyfish A