The Dependence of Bacterial Cell Growth on Turgor Pressure

Rico Rojas

Goal: To measure and understand how expansion of the bacterial cell wall depends on

mechanical force.

Vibrio

The osmotic pressure within bacteria is much higher than atmospheric pressure.

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P ~ (Cin − Cout )Morse Equation

Gram negatives: P ~ 1 atmGram positives: P ~ 10 atm

The bacterial cell wall is a cross-linked polymeric gel that encloses the cell.

Polysaccharides Polypeptides

Gan et al., 2008

Bacillus

Mechanical stress the in cell wall balances the turgor pressure and stretches the wall.

Does stress also determine strain rate of the cell wall, i.e., growth rate of the cell?

Bacillus - w/Gaurav

ε = strain =Δl/le

This growth in size of the cells appears to be the result of the progressive effect of endosmosis. They distend under the influence of the liquid, and gradually expand like soap bubbles expand under the influence of air which distends them. Cell walls themselves are composed of molecules, and also experience development, particularly the trend of expansion.

ξ Mesh Size

χ Cross-Link Conc.

Spring Constant

Rate of Cross-Link Dissociation

Ball-and-Spring Model of the Cell Wall

Rojas, et al. 2011

Strain Rate

Furchtgott et al., 2011

Jen Hsin

Ball-and-Spring Simulation Platform

B. mycoides

Growth rate depends on the osmolarity of the medium.

Scott, 1953; Christian and Scott 1955

Conc. of Sucrose or Salt

Growth rate vs. medium osmolarityof Salmonella in different media

Christian, 1955

Measures, 1975

Bacteria have a number of mechanisms for regulating their turgor.

Wood, 2006

Characterizing the response of cells to changes in osmolarity

Single cell measurements

Dye tracing concentration of mannitol in LB

Raw Data: length vs. time

T=30 s

Strain rate vs. time

n=32

Turgor pressure modulates growth rate

T=30 s

The frequency-dependent waveform response of growth rate elucidates the time scale of osmoregulation

The phase is constant across a range of driving frequencies

A simple model

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P = RT(Cin − Cout )

€

˙ C in = −α P − P0( )

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˙ ε ~dPdt

+ kd P ⎛ ⎝ ⎜

⎞ ⎠ ⎟I. Constitutive Equation

II. Morse Equation

III. Osmoregulation

{ {

GrowthElasticity

€

P = RT(Cin − Cout )

€

˙ C in = −α P − P0( )€

˙ ε ~dPdt

+ kd P ⎛ ⎝ ⎜

⎞ ⎠ ⎟I.

II.

III.

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Cout = Asin(ωt) + C0

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˙ ε = η ω 2

1+ω 2

⎛ ⎝ ⎜

⎞ ⎠ ⎟sin(ωt) −

ω1− μ

μ +ω 2

1+ω 2

⎛ ⎝ ⎜

⎞ ⎠ ⎟cos(ωt) + ρ

⎛

⎝ ⎜

⎞

⎠ ⎟

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μ =kd

αRT=

growthosmoregulation

A simple solution

Model

Data

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˙ ε = η ω 2

1+ω 2

⎛ ⎝ ⎜

⎞ ⎠ ⎟sin(ωt) −

ω1 − μ

μ +ω 2

1+ω 2

⎛ ⎝ ⎜

⎞ ⎠ ⎟cos(ωt) + ρ

⎛

⎝ ⎜

⎞

⎠ ⎟

€

μ =kd

αRT

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ϕ =arcsin −ω 2 − μ

1− μ( )2

+ ω 2 − μ( )2

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

Things to do: test and refine the model

1. Ion channel knockouts2. Deprive cells of compatible solutes3. Knockout/over-express/purify endopeptidase

ω

?

ampl

itude

B. subtilis

To do: comparative study

Things to do: address the relationship between synthesis and mechanics

Garner et al., 2011

MreB Motion

Things to do: apply external mechanical force

Other ideas:1. Functionalized microcapillary2. MEMS device

Optical Trap – w/Tim Squashed Cells - Kian

Thanks!