Transcript Shape evolution - Kingston University

Wroclaw University of Technology
Kingston University, Dept. Computing, Information
Systems and Mathematics
Electro-nanopores in the lipid
membrane. Computer modeling vs
experiments
Malgorzata Kotulska
Department of Biomedical Engineering & Instrumentation
Wroclaw University of Technology, Poland
Wroclaw University of Technology
Wroclaw
Wroclaw University of Technology
Wroclaw
University of
Technology
Wroclaw University of Technology
Membrane reorganization under electric
field
E
ions
molecules
lipid bilayer with no pore
hydrophilic nanopore
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Cell electroporation
Rapid-freezing electron microscopy of red blood cells before and after brief
electric pulses (protoplasmic membrane face). Pore diameter 20-120 nm.
DC. Chang and TS. Reese, Biophysical J. 58 (1990 )
Hypo-osmolar conditions – hemolysis (?)
ML. Escande-Geraud et al., BBA 939 (1988) 247
GV. Gass, LV. Chernomordik, BBA 1023 (1990) 1
Iso-osmolar  no effect
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Molecular Dynamics
Lipid bilayer (2304 lipids) tk = 3680 ps. Red headgroups and blue
chains; (yellow and green lipids - periodic images; water not shown)
Movie from Tieleman DP., BMC Biochem. 2004, 19; 5:10.
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Energetical profile
Free energy of the pore
Wp (r,U )  2 r   r 2  0.5CLW U 2 r 2
JC. Weaver and YA. Chizmandzhev, Bioelectrochem. Bioenerg. 41 (1996) 135
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Problems
Basic
• Mechanism of electroporation
• Shape of electropores (cylindrical or irregular ?)
Applications
• Stabilizing of electropore (other than mechanical stress)
• Size control in long-lived electropores
(e.g. big and stable electropores for DNA delivery)
• Control of the sensitivity to electroporation
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Monte Carlo simulations – modified Pink’s model
H=Hvdw + Hconf + Hdip + He
The rate of heads in
standing configuration show
rapid head reorientation if
E > 0.5 · 108 V/m (250 mV)
M. Kotulska, K. Kubica, Physical Review E 72 (2005) 061903
Kotulska M., Kubica K., Koronkiewicz S., Kalinowski S., Bioelectrochemistry 70 (2007) 64
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The rate of chains in gel (all-trans) and fluid conformations depends on
electric field E if E > 0.5·108 V/m (250 mV)
(NL – negative layer, PL – positive layer)
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Creation of a hydrophilic pore
Kotulska M., Kubica K., in Advances in Planar Lipid Bilayers and Liposomes, vol. 7. ed.
A. Leitmannova Liu, Elsevier, 2008
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Methods of electroporation
•
Pulses
•
Current clamp
(M. Robello, A. Gliozzi BBA 982 (1989) 173)
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Electroporation under current-controlled
conditions (chronopotentiometry - ChP)
pore
formation
membrane
charging
pore
fluctuations
Voltage fluctuations under current-clamp, I = 0.2 nA, egg lecithin
Kalinowski S., G. Ibron, K. Bryl, Z. Figaszewski. 1998., BBA 1369:204-212
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Applications of chronopotentiometry
Modelling ischemic electroporated cell
Kalinowski S, Koronkiewicz S,
Kotulska M, Kubica K,
Bioelectrochemistry 70 (2007) 83-90
Noise 1/f, exponent dependent on physico-chemical conditions
M. Kotulska, S. Koronkiewicz, S. Kalinowski, Physical Review E 69 (2004),
031920
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CACC electroporation
(Chronoamperometry After Current Clamp)
Electroporation at
current clamp I
Delay time;
mean potential Um
stabilized (at I)
Clamping
voltage at
constant Um
Data
acquisition
(at Um)
1.5 M AlCl3 (DAlCl3  1.3 nm)
&
2 M NaCl (DNaCl  0.9 nm)
M. Kotulska, Biophysical Journal 92 (2007), 2412-21
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Periodograms
Periodograms for 2 M NaCl, B = 1.38, Sl = 0.6 nA2/Hz, Dmean = 1.73 nm (crosses,
upper curve), 0.2 M NaCl, B = 1.37, Sl = 2.1 nA2/Hz, Dmean = 2.1 nm (diamonds,
middle curve), and 1.5 M AlCl3, B = 1.55, Sl = 3.0 nA2/Hz, Dmean = 1.3 nm
(squares, bottom curve).
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artificial nanopore / maltoporin channel
Siwy Z, Fulinski A., Phys Rev Lett. 2002;
89(15):158101
Bezrukov SM, Winterhalter M.
Phys Rev Lett. 2000; 85(1):202
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Models
 Self-similar process or 1/f noise
Hypotheses:
 One long-term process
 Sums of Markovian processes
 Self-Organized Criticallity
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-stable probability density function (MLE)
(Left) Probability density function
of the conductance dynamics
approximated by MLE as a
long-tailed -stable distribution
( = 1.78) and the smoothed data
(stars). Confidence interval 0.95
(Right) Tail region in log-log .
Data obtained for 1.5 M AlCl3
(B = 1.64, G = 2.4 nm)
Statistical tests with STABLE
program by JP. Nolan.
(MLE, sample characteristic
function and quantile methods,
  [0.03, 0.1])
Kotulska M., Biophysical Journal 92 (2007), 2412-21
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fractional Levy stable motion tends to fractional
Brownian motion
Stability index 
depends on the
nanopore size.
(Data for 2 M NaCl)
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Shape evolution (?)
Images generated by Fractal Explorer
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Memory of the process
d = H  1/
(if d > 0 then the memory is long)
Memory current-clamp < Memory CACC
Feedback effect
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Electroporation in
medical applications
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Heart Defibrillation
ELECTROCHEMOTHERAPY
(ECT)
ELECTROGENETHERAPY
(EGT)
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Molecular transport into the cell
Mir L.M, S. Orlowski,
Adv.Drug Deliv. Rev.
35(1999) 107-118
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Electroporation in the cell
Dev S.B. et al.. IEEE Trans. Plasma Sci. 28 (2000) 206-223
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ECT of a squamous cell carcinoma
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Mechanisms of anti-cancer effect
 Enhanced transport of cytostatic drugs
 Radiosensitizing effect of bleomycin
 Vascular block
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Other pores/channels
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Modelling ionic flow through channels
Collaboration:
Witek Dyrka, Andy Augousti
Enhanced algorithm for Poisson-Nernst-Planck model
ze 

J   D  n  n   

kT 

Nernst-Planck (Smoluchowski)
 0   r  r   e z n (r )   ex

Poisson
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Characteristics
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Optimization
 Adaptive gradient-based optimisation of step size:
super relaxation
 Adjustable relaxation coefficient
 Space segmentation
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Reducing computational cost
Dyrka W., Augousti A.T., Kotulska M.:
Ion flux through membrane channels – an enhanced algorithm for PoissonNernst-Planck model, submitted to J. Comp. Chemistry.
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Ryanodine receptor calcium channel
Collaboration:
Jean-Christophe Nebel
FKBP12.6
RyR2
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Ca dependent electromechanical coupling in cardiac myocyte
T-tubule
myocyte sarcolemmal membrame
Na/Ca exchanger
RyRs
L-type
channel
Efflux
Influx
SR Ca reuptake pump
Ca
Ca
Ca
Contrac
t
Relax
M. Scoote, A.J. Williams, Cardiovascular Research 56 (2002) 359-372
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Diseases resulting from channelopathies
1. Malignant Hyperthermia (MH),
2. Central Core Disease (CDD)
3. Catecholaminergic Polymorphic Ventricular Tachycardia (CPVT).
Hypotheses
• Mutations increase Ca2+ leak.
• Abnormal cardiac RyR phosphorylation and dissociation of FKBP12.6
may play a role in the pathogenesis of some forms of heart failure (HF),
but this presumption needs more experimental support.
Kania M. Kotulska M., A system for modeling the cooperativity of ryanodine
receptors in cardiac myocytes, Proc. IFMBE 11 (2005) 1727-83,
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What is the pore structure?
AJ. Williams, Q. Rev. Bioph. 34, 1 (2001), pp. 61–104.
Y. Wang et al. Biophys. J. 89 (2005) 256-265
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Thank you for your attention