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Mathematical modeling of bacterial flagellar behavior
supported by National Science Foundation Grant DMS-0815751 & DMS-1410886

How do bacteria move? Understanding the swimming mechanism of bacteria using mathematical models is a challenging subject in sciences. Bacteria such as Escherichia coli and Salmonella typhimurium swim in an aqueous environment by means of rotating their helical flagella. Each flagellar filament is driven by a rotary motor embedded in the cell surface. The motor can turn either clockwise (CW) or counterclockwise (CCW) when viewed from outside the bacteria. The rotation of motors leads the cell to either run or tumble. The runs are directed swimming driven by flagellar bundling; all of the flagellar motors turn CCW and coalesce into a superflagellum. When the motor changes the direction of rotation from CCW to CW the flagella unravel and fly apart; the cell tumbles.



Animated Gif movies - Click to play


NG=128^3, del-4, f1=f2=100Hz



bundling:(L,CCW), (L,CCW)
tumbling: (L,CCW), (L,CW)



NG=128^3, del-4, f1=f2=100Hz



(L,CW), (L,CW)
(R,CW), (R,CW)


(L,CCW), (R,CCW)
(L,CCW), (R,CW)
(L,CW), (R,CCW)
(L,CW), (R,CW)



Two flagella, (L,CCW), (L,CCW) f1 = 100Hz

f2=102Hz


NG=128^3, del-4, f1=f2=100Hz

a left-handed helix, CCW
a left-handed helix, CW




Polymorphic transformation

By motor reversal
Under steady flow