Biophysics of Cell Motility

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By Dhruv Kumar Vig

Overview of Cell Motility

Cells are the primary building blocks of all living organisms and at a basic level their functions consist of growing, replicating, and dividing (Wolgemuth 2011). In order for a cell to complete these functions, they must produce force (Wolgemuth 2011). This force is produced by molecular motors that exist in the cell for example, in our muscles, myosin binds to actin filaments, thereby exerting forces (Wolgemuth 2011). These types of forces are able to be modeled using Brownian motion (link out to Wikipedia); however, this kind of modeling fails to address the molecular binding energies that are used by these molecules (Wolgemuth 2011). For instance, the binding and hydrolysis of ATP to a molecule completes a cycle of rotation that generates force; therefore, these molecules can be viewed as motors which can then be described by their force velocity relationship (Wolgemuth 2011). These forces also contribute to the movement of cells movement by gliding, swimming, twitch, or crawling (Wolgemuth 2011).

Input in figure 1. to the right...

In terms of cell motility, an organism is defined as a “swimmer” if it moves by creating a periodic change in the shape of its body (Lauga and Powers 2008) (Figure 1). Bacteria and Archaebacteria use ionic flux channels to drive their molecular motors that power the motion of their filamentary objects (Wolgemuth 2011). For example, E. coli use flagella that rotate counterclockwise and form bundles in order to push the bacteria forward (Armitage and Schmittt 1997) (Figure 1a). When the bacteria switch to counterclockwise rotation the bundles are broken apart and the cell tumbles (Figure 2b); after the bundles reform the bacteria is facing a new direction in which it can move (Armitage and Schmitt 1997). Calobacter crescentus’ filaments turn a clock wise motion to pushes the bacterium forward, while counter-clockwise motion pulls the bacterium backward (Lauga and Powers 2008) (Figure 1b); Rhodobacter sphaeroides’ filaments only turn one direction (Lauga and Powers 2008) and periodically stop to re-orient itself (Armitage and Schmidt 1997) (Figure 1c and Figure 2a). In a similar manner, Sinorhizbium meliloti, has several right-handed flagella that allow for quick forward swimming when the flagella form bundles and directional changes in which the flagella rotate at different rates (Figure 2c) (Armitage and Schmidt 1997). Other examples of bacteria with external flagella include sperm that use their flagella to produce a whip-like motion because its molecular motors are present throughout its filament (Figure 1e and 1f) (Lauga and Powers 2008). Furthermore, some bacteria do not need external flagella to move; Spiroplasma, doesn’t have flagella, but instead swims by circulating the kinks that are throughout its body (Figure 1d) (Lauga and Powers 2008).

Eukaryotes, on the other hand, have larger flagella cilia than bacteria (Lauga and Powers 2008) and these structures are powered by dynein motors that are located along the length of the filaments (Wolgemuth 2011). Additionally, other organisms have multiple flagella, such as Chlamydonmonas reinhardtii, an algae that exhibits ciliary and flagellar beat patterns (Lauga and Powers 2008) and recent studies have shown that is uses a “run and tumble” swimming mechanism that is powered by the oscillations of its flagella (Wolgemuth 2011) (Figure 1g); Paramecium on the other hand uses the coordinated beat patterns of their cilia to move (Figure 1h).

New technological advances in the field microcopy have led an increase in the study and experimentation of cell motility. Brownian motion models are being replaced by more complex physical equations that have been derived to model avenues that range from bacterial turbulence, swarming dynamics and wound healing to Lyme disease and Syphilis.

Technological Advances

Light-microscopy has normally been used to observe and track cells as they are moving. Now, however, fluorescent dyes can be used to stain a bacterium’s flagella, thus illuminating the key cellular structures are required for a bacterium to swim (Lauga and Powers 2008). Additionally, a technique known as “optical trapping” uses a laser beam to generate a change in momentum in cells that results in generation of force (Koning et al. 1996); measuring this change in force allows for the recording of the interactions between molecules that contain single motor proteins (Nabiev et al. 2008). Atomic force microscopy, on the other hand, can directly measure the force generated by cilia (Lauga and Powers 2008).

Reynolds Number

The world of microscopic organisms involves fluids that are highly viscous in nature and dominate any inertial forces that may be present (Happel and Brenner 1991); therefore, given these conditions the physics that governs the movements of these organisms at a microscopic scale can be described by a low Reynolds Number (Equation for Reynolds number, in caption describe Re = (ρ*L*U)/n) (Lauga and Powers 2008). The Reynolds Number is a dimensionless quantity that is based on the Navier-Stokes equation (link wiki), which describes the motion of an incompressible Newtonian fluid. The Reynolds number is the ratio of inertia to viscosity of a fluid (Wolgemuth 2008); therefore it allows for a qualitative description of the flow regime from the Navier-Stokes equation (Lauga and Powers 2008); examples of Reynolds numbers for swimming organisms shown in Table 1.

Insert in table 1...

Biophysical Studies

Bacterial Turbulence

It is suspected that as the concentration of bacteria increases in a given area should lead to a decrease in the Reynolds number because increasing the concentration of bacteria, increases the fluid flow between neighboring bacteria will feel drag due to the velocity difference between each bacterium (Wolgemuth 2008). However, bacteria such as Bacillus subtilis (wiki link), shows an increase in Reynolds number when there bacteria are found in dense colonies (Wolgemuth 2008). In these areas, a jet-like fluid motion is observed that has speeds which are faster than the speed of each bacterium; these jet-like motions are similar to fluid dynamics known as von Karman vortex street (wiki link), in which the Reynolds is greater than fifty (Wolgemuth 2008). It is these swimming patterns which have high Reynolds numbers for their fluid dynamics that are known as “bacterial turbulence” (Wolgemuth 2008). Wolgemuth (2008) developed a two-phase model that analyzed the group swimming dynamics of dense colonies of bacteria i.e. “bacterial turbulence.” Wolgemuth’s model treats the fluid and bacteria independently, and is based off of rod-like bacteria, like Bacillus subtilis, in which entropic forces will favor the restricted alignment of the bacteria (Wolgemuth) (Figure 1). Wolgemuth (2008) defined a series of equations and parameters that make up his two-phase group swimming model (Diagram 1); these parameters reproduce the behavior that is observed by in regions that “bacterial turbulence” are present (Figure 2 and 3). Understanding the behavior associated with “bacterial turbulence” has industrial and medical applications. Large concentrations of bacteria are found in filtration systems, like dead-end filtration (see wiki), in which water containing bacteria forced through a microfilter (Wolgemuth 2008). Additionally, biofilms (see wiki) are produced by an aggregation of bacteria to a single area and are known to cause infections and corrosion (Wolgeumuth 2008).