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Electro-nanopores in the lipid membrane. Computer modeling vs

experiments

Malgorzata KotulskaDepartment of Biomedical Engineering & Instrumentation

Wroclaw University of Technology, Poland

Kingston University, Dept. Computing, Information Systems and Mathematics

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Wroclaw

Wroclaw University of Technology

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Membrane reorganization under electric field

lipid bilayer with no pore hydrophilic nanopore

E

ionsmolecules

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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 Iso-osmolar no effectGV. Gass, LV. Chernomordik, BBA 1023 (1990) 1

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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

222 5.02),( rUCrrUrW LWp

JC. Weaver and YA. Chizmandzhev, Bioelectrochem. Bioenerg. 41 (1996) 135

Free energy of the pore

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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

The rate of heads in standing configuration show rapid head reorientation if

E > 0.5 · 108 V/m (250 mV)

H=Hvdw + Hconf + Hdip + He

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 chargingpore 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

M. Kotulska, S. Koronkiewicz, S. Kalinowski, Physical Review E 69 (2004), 031920

Noise 1/f, exponent dependent on physico-chemical conditions

Modelling ischemic electroporated cell

Kalinowski S, Koronkiewicz S, Kotulska M, Kubica K, Bioelectrochemistry 70 (2007) 83-90

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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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Stability index depends on the nanopore size.

(Data for 2 M NaCl)

fractional Levy stable motion tends to fractional Brownian motion

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Shape evolution (?)

Images generated by Fractal Explorer

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Memory of the process

Memory current-clamp < Memory CACC

Feedback effect

d = H 1/ (if d > 0 then the memory is long)

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Electroporation inmedical 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

Enhanced algorithm for Poisson-Nernst-Planck model

kT

zennDJ

exrnzerr )(0

Nernst-Planck (Smoluchowski)

Poisson

Collaboration:

Witek Dyrka, Andy Augousti

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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 Poisson-Nernst-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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SR Ca reuptake pump

Na/Ca exchanger

Efflux

RyRs

L-type channel

Influx

Ca

Contract

Ca

Ca

Relax

T-tubule myocyte sarcolemmal membrame

M. Scoote, A.J. Williams, Cardiovascular Research 56 (2002) 359-372

Ca dependent electromechanical coupling in cardiac myocyte

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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