Models of the diffusion of biological macromolecules

[Cincinnatus]

I'm wondering if anyone is aware of any computational/theoretical work on solving the problem of describing the motion of a biological macromolecule in a cellular microdomain? This would have to mean setting up and solving a stochastic partial differential equation with boundary conditions defined by the geometry/permeability of the microdomain in question.

I've seen various papers on anisotropic diffusion but most are considering the case where there is no boundary. As an example, this paper comes to mind: Brownian Motion of an Ellipsoid (2006) Science Han et al.
http://www.sciencemag.org/cgi/content/abstract/314/5799/626

 

[Andy Resnick]

There's no shortage of diffusion theory, data, and techniques: fluorescence correlation spectroscopy, fluorescence recovery after photobleaching, fluorescence anisotropy, 2-point microrheology, etc. etc. The main shortcoming is the lack of high-quality physiologically relevant data- cells have a cytoskeleton and directed transport, for example. Some sort of method to passively track a protein of interest as it is trafficked around the cell does not yet exist. Consequently, there is no way yet to rationally select one mathematical model over another.

 

[Cincinnatus]

There's no shortage of diffusion theory, data, and techniques: fluorescence correlation spectroscopy, fluorescence recovery after photobleaching, fluorescence anisotropy, 2-point microrheology, etc. etc. The main shortcoming is the lack of high-quality physiologically relevant data- cells have a cytoskeleton and directed transport, for example. Some sort of method to passively track a protein of interest as it is trafficked around the cell does not yet exist. Consequently, there is no way yet to rationally select one mathematical model over another.

Of course that's all true but people still publish these models. I'm explicitly looking for citations to papers that consider this as a stochastic boundary value problem. Almost everything I've seen treats only the unbounded case.

 

[atyy]

Kruk PJ, Korn H, Faber DS. The effects of geometrical parameters on synaptic transmission: a Monte Carlo simulation study. Biophys J. 1997 Dec;73(6):2874-90.

Coggan JS, Bartol TM, Esquenazi E, Stiles JR, Lamont S, Martone ME, Berg DK, Ellisman MH, Sejnowski TJ. Evidence for ectopic neurotransmission at a neuronal synapse. Science. 2005 Jul 15;309(5733):446-51.

Ridgway D, Broderick G, Ellison MJ. Accommodating space, time and randomness in network simulation. Curr Opin Biotechnol. 2006 Oct;17(5):493-8. Epub 2006 Sep 8. Review.

 

[Cincinnatus]

Thanks for the references atyy. It seems that none of them are doing exactly what I had in mind, though that review articles mentions some models in the same vein of thinking...

 

[Andy Resnick]

Of course that's all true but people still publish these models. I'm explicitly looking for citations to papers that consider this as a stochastic boundary value problem. Almost everything I've seen treats only the unbounded case.

I'm not sure I can give you exactly what you are looking for, but a PubMed search turned up 67 articles under "diffusion intracellular stochastic", and a couple of possible hits are:

Fluitt A, Pienaar E, Viljoen H.
Ribosome kinetics and aa-tRNA competition determine rate and fidelity of peptide synthesis.
Comput Biol Chem. 2007 Oct;31(5-6):335-46. Epub 2007 Aug 15.
PMID: 17897886 [PubMed - indexed for MEDLINE]

Rino J, Carvalho T, Braga J, Desterro JM, Lührmann R, Carmo-Fonseca M.
A stochastic view of spliceosome assembly and recycling in the nucleus.
PLoS Comput Biol. 2007 Oct;3(10):2019-31. Epub 2007 Sep 5.
PMID: 17967051 [PubMed - indexed for MEDLINE]

Guisoni N, de Oliveira MJ.
Calcium dynamics on a stochastic reaction-diffusion lattice model.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Dec;74(6 Pt 1):061905. Epub 2006 Dec 18.
PMID: 17280094 [PubMed - indexed for MEDLINE]

Wylie DC, Hori Y, Dinner AR, Chakraborty AK.
A hybrid deterministic-stochastic algorithm for modeling cell signaling dynamics in spatially inhomogeneous environments and under the influence of external fields.
J Phys Chem B. 2006 Jun 29;110(25):12749-65.
PMID: 16800611 [PubMed - indexed for MEDLINE]

 

[Cincinnatus]

Thanks for the references. I don't think any of those articles consider boundary effects either. I couldn't find much that considers the effect of the boundary on diffusion in cellular microdomains either. I'm not sure why this seems to have been somewhat ignored. The effects of the boundary may be negligible... but at least that doesn't seem obvious...

 

[seggahme]

stochastic motion of molecule in closed area leads to constant distribution. so?

 

[Cincinnatus]

stochastic motion of molecule in closed area leads to constant distribution. so?

Well large macromolecules move by anisotropic diffusion. So I'm not sure that's true for this case... I think it is highly dependent on what kind of boundary we are talking about. There are also other quantities of interest aside from just the equilibrium distribution of molecules. MFPTs to get from place to place, etc.