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==Reference==

'''''Bacillus subtilis'' spreads by surfing on waves of surfactant'''

Angelini T.E., Roper M., Kolter R., Weitz D.A., Brenner M.P.

PNAS '''106''':   18109-18113 (2009)
PMID: 19826092 ([http://pubget.com/search?q=spreads+by+surfing+on+waves+of+surfactant Pubget])

==Motivation==
[[Image:Bacillus subtilis Gram.jpg|thumb|Gram-stained ''B. subtilis'']]

In times of stress ''Bacillus subtilis'' differentiate into spores, which helps them survive but at a significant energy cost. ''B. Subtilis'' try to keep this by three known mechanisms: 1) a sub-population of cells differentiations into cannibal cells, which selectively lyse non-cannibal cells; 2) the cells form a dense mat of exopolysacharides, called a biofilm; and 3) the cells spread out in search of a more hospitable environment. All three mechanisms appear to be controlled by the same regulatory protein, Spo0A.  This protein is part of a quorum sensing system. The lipopetide surfactin secreted by the bacteria activates the membrane kinase KinC, which, in turn, phosphorylates and thereby activates Spo0A. It has been shown that surfactin activates both biofilm-building matrix production and cannibal differentiation in the same cells.

How cannibalism and biofilm formation work is now broadly understood, but the mechanism by which colonies migrate outwards remains an open question. This paper proposes that surfactin gradients lead to gradients in surface tension, which leads to the colony spreading.

==Experimental Observations==

[[Image:Angelini2009 fig2c.jpg|thumb]]

Bacteria were inoculated into 4 mL of medium that is conducive to biofilm formation, and grown in a humidified chamber at 30 C. Cells formed a biofilm on the surface of the medium once the diffuse oxygen in the medium had begun to be depleted. About 12 hours after biofilm formation the biofilm began to climb the walls of the tube. The surface tension at the base of the climbing film was measured by placing a capillary tube sealed with a dialysis membrane.  The height of the fluid in the capillary tube reached an equilibrium when the capillary and hydrostatic pressures were equal:

<math>
\gamma \cos{\theta} = \frac{\rho g d h_r}{4}
</math>

The results showed that:
* The linear phase of biofilm wall climbing corresponds to a rate of ~1.4 mm/hr
* The surface tension dropped from <math>\gamma_0</math> = 53 mN/m at a rate of <math>\dot{\gamma}</math> = -0.18 mN/m*hr.
* Spreading occurs simultaneously with a drop in surface tension.

Experiments also showed that surfactin is necessary for biofilm spreading, while a flagellum is not. This suggests that the film migrates by a surfactin-dependent mechanism rather than by cell motility.

[[Image:Angelini2009 fig4.jpg|thumb|upright=1.2|center|Biofilm spreading. Black squares: wild-type; red circles: hag<sup>-</sup> (flagellum knockout); green triangles: srfAA<sup>-</sup> (surfactin knockout).]]

==Hypothesis==

===Conceptual Explanation===
Imaging the 'B. subtilis' biofilm shows that the colony is thicker in the center that at the edges. It has also been previously shown that 90% pure surfactin can reduce water surface pressure from 72 mN/m to 27 mN/m.

We assumed that:
* Biofilm density is linearly related to biofilm concentration.
* All cells secrete surfactin at the same rate.
* The bacteria are homogeneously distributed throughout the film.
* Surfactin concentration is controlled entirely by local film thickness.

These facts suggest that the variability in biofilm thickness leads to a gradient of surfactin. The surfactin gradient, in turn, leads to a gradient of surface tension.  The colonies are thinnest at the edges, so the surface tension increases outward from the colony center, which effectively drags the cells outwards.

===Scaling Analysis===

The surface tension gradient of the climbing film <math>\tau_\infin</math> is balanced by viscous stresses:

<math>
\tau_\infin \sim \frac{\eta U}{h_\infin}
</math>

where <math>\eta</math> is the film viscosity, U is the spreading velocity, and <math>h_\infin</math> is the film thickness. The units on both sides are Pa.

Next it is necessary to relate the curvature of the meniscus with the curvature of the moving film:

<math>
\frac{h_\infin}{l^2} \sim l_c^{-1}
</math>

<math>
l \sim 
\sqrt{h_\infin l_c} =
\left( \frac{h_\infin^2 \gamma_0}{p g cos{\alpha}} \right) ^{1/4}
</math>

where <math>l_c</math> is the capillary length. The equations can be combined to give the following scaling law:

<math>
h_\infin = \alpha_\tau \frac{\tau_\infin^2 l_c^3}{\gamma_0^2}
</math>

Fitting the scaling law to simulation experiments gives <math>\alpha_\tau</math> = 3.5.

==Relationship to Soft Matter Physics==

This paper suggests that the spreading of biofilms is caused by a surface tension gradient, which is a phenomenon that has been widely studied in thin films. In fact, a similar quantitative analysis of a thin film climbing out of a reservoir onto a vertical wall due to a temperature gradient-induced surface tension gradient led to the same scaling law - which is unsurprising, as both studies made the same physical assumptions.

==References==
López D, Vlamakis H, Losick R, Kolter R., '''Cannibalism enhances biofilm development in Bacillus subtilis'''. ''Mol Microbiol'' (2009). [http://pubget.com.ezp-prod1.hul.harvard.edu/search?q=Cannibalism+enhances+biofilm+development+in+Bacillus+subtilis.+ Pubget]

Yeh MS, Wei YH, Chang JS., '''Enhanced Production of surfactin from Bacillus subtilis by addition of solid carriers'''. ''Biotechnol Prog'' (2005). [http://pubget.com/search?q=Enhanced+Production+of+surfactin+from+Bacillus+subtilis+by+addition+of+solid+carriers Pubget]