wroclaw university of technology electro-nanopores in the lipid membrane. computer modeling vs...

Wroclaw University of Technology

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

Wroclaw University of Technology

Wroclaw

Wroclaw University of Technology

Wroclaw University of Technology

Wroclaw University of Technology

Membrane reorganization under electric field

lipid bilayer with no pore hydrophilic nanopore

E

ionsmolecules

Wroclaw University of Technology

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

Wroclaw University of Technology

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.

Wroclaw University of Technology

Energetical profile

222 5.02),( rUCrrUrW LWp

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

Free energy of the pore

Wroclaw University of Technology

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

Wroclaw University of Technology

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

Wroclaw University of Technology

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)

Wroclaw University of Technology

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

Wroclaw University of Technology

Methods of electroporation

• Pulses

• Current clamp (M. Robello, A. Gliozzi BBA 982 (1989) 173)

Wroclaw University of Technology

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

Wroclaw University of Technology

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

Wroclaw University of Technology

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

Wroclaw University of Technology

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).  

Wroclaw University of Technology

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

Wroclaw University of Technology

Models

Self-similar process or 1/f noise

Hypotheses: One long-term process Sums of Markovian processes Self-Organized Criticallity

Wroclaw University of Technology

-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

Wroclaw University of Technology

Stability index depends on the nanopore size.

(Data for 2 M NaCl)

fractional Levy stable motion tends to fractional Brownian motion

Wroclaw University of Technology

Shape evolution (?)

Images generated by Fractal Explorer

Wroclaw University of Technology

Memory of the process

Memory current-clamp < Memory CACC

Feedback effect

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

Wroclaw University of Technology

Electroporation inmedical applications

Wroclaw University of Technology

Heart Defibrillation

ELECTROCHEMOTHERAPY(ECT)

ELECTROGENETHERAPY(EGT)

Wroclaw University of Technology

Molecular transport into the cell

Mir L.M, S. Orlowski, Adv.Drug Deliv. Rev. 35(1999) 107-118

Wroclaw University of Technology

Electroporation in the cell

Dev S.B. et al.. IEEE Trans. Plasma Sci. 28 (2000) 206-223

Wroclaw University of Technology

ECT of a squamous cell carcinoma

Wroclaw University of Technology

Mechanisms of anti-cancer effect

Enhanced transport of cytostatic drugs

Radiosensitizing effect of bleomycin

Vascular block

Wroclaw University of Technology

Other pores/channels

Wroclaw University of Technology

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

Wroclaw University of Technology

Characteristics

Wroclaw University of Technology

Optimization

Adaptive gradient-based optimisation of step size: super relaxation

Adjustable relaxation coefficient

Space segmentation

Wroclaw University of Technology

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.

Wroclaw University of Technology

Ryanodine receptor calcium channel

Collaboration:

Jean-Christophe Nebel

FKBP12.6

RyR2

Wroclaw University of Technology

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

Wroclaw University of Technology

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,

Wroclaw University of Technology

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

Wroclaw University of Technology

Thank you for your attention