Webpages about Smoldyn and spatial simulation

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The E. coli Min system


All of the core proteins in the Min system, MinC, MinD, and MinE, dimerize with dissociation constants that are roughly equal to their in vivo concentrations. Why? This is not part of any models of the Min system that I am aware of, and yet there's probably a reason for this dimerization. Spatial modeling might be a way to explore this issue. I found, in unpublished wet-lab research several years ago, that MinD only hydrolyzes ATP when MinD is a dimer; it is inactive when it's a monomer.

Filamentous cells

Long E. coli cells exhibit the same spatiotemporal oscillations as short cells, except that the spatial period is unchanged. That is, a cell that is twice as long as a wild type cell shows two concentration maxima, a cell that is three times as long shows three maximia, and so on. A classic Min system model paper, by Huang, Meir, and Wingreen, states that their model agrees with this observation, exhibiting stable multi-peak oscillations. I don't believe this result. When I test their model using either PDE or particle-based models, I find that one can start with multi-peak oscillations, but the oscillations eventually settle down to a single wave that goes back and forth the length of the whole cell. Thus, what's the correct model?

Spherical cells

The Min system has been investigated in spherical E. coli cells, with some interesting results. My recollection is that the division plane alternates axes at each generation (although I might be remembering it wrong). Can a model replicate the experimental observations?

Similarity to yeast polarization

A publication by Alexandra Jilkine, Altschuler, and others (see the Smoldyn publications page) investigated yeast cell polarization. They showed that recruitment of proteins to the membrane was an essential part of it. This is reminiscent of MinD recruitment in the Min system, so I wonder if there are other parallels between these two systems, and also how widespread these mechanisms are.

Macromolecular crowding

Diffusion in crowded environments

Lots of people have investigated diffusion in crowded environments using both experiments and simulations. For example, see Tatiana Marquez-Logo's work, on the Smoldyn publications page. Two papers that especially influence my thinking here are work by Ridgway et al. (Biophys. J. 94:3748, 2008), who showed that hydrodynamic influences are important, and a review on crowding experiments by Dix and Verkman (Ann. Rev. Biophys. 37:247, 2008), which says that crowding has much less influence on diffusion than is commonly believed. Smoldyn cannot simulate hydrodynamic influences, at least at present. Nevertheless, many aspects of Smoldyn are ideally designed to study crowding, so I expect that it could be used to investigate more questions in the field. For example, consider realistic systems, like the actual density of the nucleus, as Sam Isaacson recently did in a paper on diffusion in the nucleus (PNAS 108:3815, 2011).

Reaction rates in crowded environments

Whereas diffusion in crowded environments has been studied extensively, much less work has investigated reaction rates in crowded environments. The general picture is well known: with increasing crowding, reaction rates get faster at first, as the crowders reduce the effective volume of the system; reaction rates then peak and start declining due to slowed diffusion. The holy grail of this research project would be a simple equation that enabled one to accurately predict in vivo chemical reaction rates from in vitro chemical reaction rates. With such an equation, one could convert extensive in vitro data to apply to cells, and one could then build accurate kinetic models of cellular systems.

Reversible reactions in crowded environments

Reaction reversibility is substantially more complex than it seems at first due to the possibility of geminate recombinations. These recombinations are strongly affected by the details of molecular diffusion on very small length scales, which is where macromolecular crowding is likely to have the most interesting effects on diffusion. So, how does crowding affect geminate recombinations, and hence how does it affect the rates and equilibrium constants of reversible reactions?


Metabolic channeling

Metabolism has been modeled for a long time using coarse modeling methods, such as ODEs or stoichiometric methods. These seem to have led people to believe that metabolism can be treated accurately as a well-mixed system. In contrast, Paul Srere and others have shown experimental evidence for metabolic channeling, in which metabolites do not diffuse freely from one enzyme to the next, but they instead are "handed" off from one to the next. I find this latter view much more likely because there is increasing evidence in cell biology quite generally that scaffolds and other large protein complexes are the rule, rather than the exception. Smoldyn should be a good tool for simulating metabolic channeling, and for seeing if that leads models to agree better with experiments than well-mixed models.

Signaling systems

E. coli chemotaxis

The E. coli chemotaxis signaling system has been studied very thoroughly. See work by Karen Lipkow (some of which is on the Smoldyn publications page). Nevertheless, I suspect that there are many more open questions here. For example, how does cross-talk work between signals from different receptors (Tar, Tsr, etc.)?

E. coli motor switching

A classic paper by Duke and Bray (J. Mol. Biol. 308:541, 2001) shows that the E. coli motor may switch between clockwise and counter-clockwise rotation using a ring of FliM proteins that interact with each other via conformational spread. According to this model, proteins are biased to be in the same state as their neighbors. This positive feedback induces switch-like behavior. I built a Smoldyn model of the Duke and Bray model, using the exact same parameters as they used. However, I found substantially different behavior, including a much higher interaction threshold for switching. I never figured out what caused the difference, but thought that it was interesting and might be worth pursuing.

B. subtilis chemotaxis

B. subtilis chemotax in much the same way as E. coli do, but with some differences. See Rao et al., Phys. Biol. 2:148, 2005. I'm not aware of any spatial computer models of the B. subtilis chemotaxis system. Building one would be interesting, in part to see how the two systems compare, and how the two species have solved the same problem in different ways.