Models of the diffusion of biological macromolecules

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Discussion Overview

The discussion revolves around the modeling of the diffusion of biological macromolecules within cellular microdomains, focusing on the theoretical and computational approaches to describe their motion. Participants explore the complexities of stochastic partial differential equations and the influence of boundary conditions defined by cellular geometry and permeability.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant inquires about computational work on stochastic partial differential equations for macromolecule motion in cellular microdomains, noting that existing literature often neglects boundary effects.
  • Another participant highlights the abundance of diffusion theories and techniques but points out the lack of high-quality physiologically relevant data, complicating the selection of appropriate mathematical models.
  • Several participants express a desire for citations specifically addressing stochastic boundary value problems, indicating that most existing models treat unbounded cases.
  • References to various studies are provided, although participants note that these do not adequately address boundary effects in diffusion.
  • One participant questions the assumption that stochastic motion in closed areas leads to constant distribution, suggesting that anisotropic diffusion may play a significant role and that boundary types could influence outcomes.
  • Concerns are raised about the potential neglect of boundary effects in current models, with some participants suggesting that the significance of these effects is not well understood.

Areas of Agreement / Disagreement

Participants generally agree on the complexity of modeling diffusion in cellular environments and the limitations of current approaches. However, there is no consensus on the significance of boundary effects or the appropriateness of existing models, indicating multiple competing views remain.

Contextual Notes

Limitations include the lack of high-quality data relevant to physiological conditions, the dependence on specific definitions of boundaries, and unresolved mathematical considerations regarding stochastic processes in confined spaces.

Cincinnatus
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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
 
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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.
 
Andy Resnick said:
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.
 
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.
 
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...
 
Cincinnatus said:
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]
 
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...
 
stochastic motion of molecule in closed area leads to constant distribution. so?
 
seggahme said:
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.
 
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