A NUMERICAL MODEL FORELECTROPORATION IN BACTERIA

J.L. Moran, P.A. Garcia, N.N. Dingari, C.R. BuieDepartment of Mechanical EngineeringMassachusetts Institute of Technology

October 8, 2015

Electroporation

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J.C. Neu, W. Krassowska, Phys. Rev. E, 1999.

Hydrophilic Lipid heads

Hydrophobic pores

Hydrophobic tails

Hydrophilic pores

~5 nm

~5 nm

Schwan 1957, Tsong, Biophysical Journal, 1990.

1.5 cosmV ER θ=

1 VmV <

1 VmV ≥

Electroporation is governed by the Transmembrane Voltage (TMV)

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Our Focus: Transformation of Bacteria

• Electroporation protocols exist for a tiny fraction of bacteria on earth

• Goal: understand the principles governing successful DNA transfer into bacteria

• Here: COMSOL model to understand effect of bacterial physiology on electroporation

Microbial Fuel Cell SchematicCredit: Logan, B. Nature Rev. Microbio. 2009

Deepwater Horizon Oil SpillCredit: Getty Images

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Bacterial Physiology

www.daviddarling.info/encyclopedia/P/pilus.html

micro.magnet.fsu.edu/cells/procaryotes/images/procaryote.jpg

Pili on the surface of an Escherichia coli bacterium

• Outside the (inner) plasma membrane, most bacteria exhibit a “soft layer” consisting of (e.g.) fimbriae, sex pili, capsules, flagella, etc.

• The soft layer generally carries a net charge• Charge distribution in the soft layer affects polarizability (Dingari &

Buie, 2014) 4

• Electric potential inside/outside cell (σ = conductivity)

• Transmembrane voltage (TMV)

• Pore creation/destruction rate

• Pore radius evolution

• Membrane current density

( )β πγ πσ

= + − + + +

42max * 14 2 2

1 /m

effh t

V F rdr D rdt kT r r r r r

Electrical energy Steric repulsion of lipid heads Line tension

Effective membrane/liquid interfacial tension

Governing Equations

σ ε ε φ∂ ∇ ⋅ + ∇ = ∂ 0 0r t

( )φ φ≡ −m inside soft membraneV

( ) ( )α

= −

2exp / 1m ep

eq m

dN NV Vdt N V

Pore density [#/cm2]

Characteristic voltage for electroporation

Capacitive chargingProtein channels Current through electropores

( ) ( )σ πσ ∂= + +

∂

2,0 m p pm m m

m

V N t r AV VJ t Ch h t

DeBruin & Krassowska, Biophys. J. 1999 (Part I)Pucihar, Miklavcic & Kotnik, IEEE Trans. Biomed. Eng. 2009

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Numerical Implementation• COMSOL Multiphysics • 2D axisymmetric geometry• 36,353 mesh elements• Time-dependent solve (through

pulse duration)

SEM of E. coli (Wikimedia commons)

2 µm

12.5 kV/cmE =

0.5 µm

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Imposed Conductivity Profile in Soft Layer

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Induced Transmembrane VoltageNo Soft Layer 100-nm Soft Layer

All data shown at t = 1 ms (pulse truncated)Insets show TMV vs. time at positive-facing pole

E ( )φ φ≡ −m inside soft membraneV

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Pore Density vs. Position

All data shown at t = 1 ms (pulse truncated)Insets show mesh used for each case

No Soft Layer 100-nm Soft Layer

E

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Pore Radius vs. Position

All data shown at t = 1 ms (pulse truncated)Insets show mesh used for each case

No Soft Layer 100-nm Soft Layer

E

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Total Pores, Average Radius

membraneavg

membrane

NrdAr

NdA≡

∫∫

∫∫pores

membrane

N NdA= ∫∫

All data shown at t = 1 ms (pulse truncated)

Both the number and the size of pores created depend more strongly on buffer concentration when the soft layer is present

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Conclusions• The presence of a soft layer tends to amplify the

effect of varying background conditions (e.g. conductivity) on the pore size and number

• This work elucidates the effect of buffer concentration on bacterial electroporation

Ongoing Work• Enhance model of soft-layer transport to include

• Dissociation of pH-dependent ionogenic groups• Donnan potential

• Explore correlation between electroporation amenability and cell envelope properties (e.g. polarizability)

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Thank you

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Simulation Details

• Customized Mesh

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