The bacteria Listeria monocytogenes is widely present in the environment and can cause serious infection in humans who consume contaminated vegetables or unpasteurized dairy products. The only current prevention against this bacterium is through proper food preparation; infections are treated with antibiotics. A better understanding of how Listeria spreads from cell to cell could lead to the development of new means of medical intervention for this and other related bacterial infections.
Figure 1: A stained view of Listeria moving within a cell. The red dots indicate the Listeria, and the green "comet tails" are the trailing actin filament network. (See http://cmgm.stanford.edu/theriot)
The transport of Listeria is rather remarkable. On the surface of the bacterium is a protein called ActA, which catalyzes the production of actin filaments. Actin is a cytoskeletal protein in eukaryotic cells, which can bind to other actin in a linear chain through a process called polymerization, thereby forming fairly stiff filaments. Experimental observations show that, upon entry into the interior of a cell (the cytoplasm), the ActA proteins on the surface of the Listeria stimulate a process which takes actin monomers (basic units) present in the host cytoplasm and assembles them into a gelatinous network of filaments. Because ActA is distributed asymmetrically on the surface of the Listeria, the cloud of actin filaments produced is also asymmetric. Once the cloud is sufficiently dense (which takes an hour or more), the continued actin polymerization pushes the bacteria away from the (relatively immobile) network of actin filaments in a direction determined by the underlying asymmetry. The actin polymerization continues at the surface of the Listeria as it moves, now generating a "comet tail" network of actin filaments in the direction opposite of its motion. This process allows the Listeria to propel itself across the cytoplasm until it reaches the cell membrane, at which point actin polymerization continues to push the bacteria into the membrane. The resulting protrusion in the cell membrane becomes a target for another cell to engulf the bacterium through phagocytosis, thereby effectively propagating the infection to a new host cell where the process can continue.
The actual physical mechanism by which actin polymerization occurs, however, is still under debate. In contrast with some other subcellular transport processes (managed by proteins such as myosin and kinesin), no clear motor mechanism is evident which converts chemical fuel (ATP) to the physical work needed to lengthen actin filaments, particularly under the resistive stress of the existing actin network. More precisely, ATP is involved in the binding of a new actin monomer to the actin filament but the energy is released (through hydrolysis) only after the monomer is already in place to be bound. Perhaps a more subtle motor mechanism is responsible for generating the force needed to extend the actin filament, or perhaps a more passive means of harvesting the energy available from thermal fluctuations is sufficient. Experimental results do not yet yield a conclusive picture of which mechanism is correct. One can see that the Listeria stays in close contact with the actin filament pushing it, and that the addition of actin monomers to the network occurs at the Listeria surface. Other quantitative information about the propulsion speed, binding force between the actin filament and Listeria, and length scales are also available.
Figure 2: A depiction of the buildup of the cloud of actin filaments around a latex sphere coated with ActA, followed by the escape of the sphere propelled by a "comet tail" of actin filaments in its wake. (See http://cmgm.stanford.edu/theriot)
Further insight into the actin polymerization process have emerged from recent experiments in which a polystyrene or latex bead is coated symmetrically with a few proteins (including ActA) and placed in an extract from a cell cytoplasm. A cloud of actin filaments is found to form on the surface of the bead, creating a sort of cage. But occasionally, the bead is found to get pushed out of the cage along an apparently unpredictable direction through a more directed actin polymerization process. That is, the phenomena observed in Listeria propulsion are also present even if the surface is symmetrically coated with ActA; the escape of the bead from the actin cloud is then a result of a spontaneous symmetry-breaking process. These experiments allow the exploration of how the actin polymerization process depends on other physical parameters, such as the size of the bead and the density of the surface protein coating, and provide further data with which to confront theoretical models.
The students at the Mathematical Modeling Camp will be invited to develop and explore physical models for the actin polymerization process which are motivated by the experimental observations and results. Work on this problem will likely draw from a blend of mechanics, differential equations, probability theory, and numerical simulations. No background in biology is required; the relevant details will be provided and discussed but the emphasis of the modeling problem is on physical mechanisms.
More general background reading:
á Hoppensteadt. Frank C. and Charles S. Peskin. Modeling and Simulation in Medicine and the Life Sciences. Second Edition. Springer, New York: 2002. (Chapter 5: Muscle Mechanics.)