We are planning to augment NEURON to implement biochemical reaction-diffusion (RD) as well as facilitated cytoplasmic transport in NEURON. This would involve complementing the present integration of the one-dimensional cable equation with a meshed integration of diffusing reactants in multiple 3D (cytosolic, intranuclear, intravacuolar) and 2D (intramembranous) compartments. For this first iteration of the tool we will not address extracellular diffusion.

We plan to work with the VCELL simulator group (http://www.vcell.org). VCell utilizes some of the same integrators as NEURON (e.g. CVODE) and will provide immediate access to a set of VCML models as well as models specified in the SBML modeling metalanguage. A key difference between VCML and SBML is that VCML supports arbitrary geometries, while SBML has utilized stylized geometries and is only now being extended to full geometries.

Because tool development proceeds most efficiently in the context of real problems and user input, we are very interested in hearing how you might use such a tool in your own research. Do you have modeling projects that involve reaction-diffusion, which you were unable to pursue with NEURON? Or are you aware of important neurobiological problems that are ready to be pursued once such a tool is in place? In either case, we would like to hear from you, and we welcome the opportunity to see how your research questions might help guide the development of NEURON_RD.

Your contribution is invited, if only to vote as in "great idea" or "not needed." To help stimulate discussion, here are some questions that have arisen in our own deliberations:

o How important is it to handle arbitrary geometries?

o How much effort should be put into modeling spines?

o How important is simulation of gene expression? Of microtubule transport?

o Are there other features that may be particularly relevant to neural cells, that may not have been addressed in general cellular modeling?

## Introduction and request for suggestions

**Moderators:** hines, wwlytton, ramcdougal

### Re: Introduction and request for suggestions

Dear Bill,

I am very interested in this venture. Arjen van Ooyen and myself have been developing models of neurite outgrowth and branching based on construction of the microtubule cytoskeleton, mediated by the diffusion and active transport of tubulin and other substances. We have written our own code to do this (e.g. in Java), but it would be very nice to be easily able to do it in NEURON. One aspect of this that may go beyond your remit is that the "product" of the model is a changing (growing) cell morphology, involving elongation of neurites and formation of new branches.

So I am interested in whatever you achieve, and am willing to be involved in any way possible.

Best wishes,

Bruce Graham (University of Stirling, Scotland)

I am very interested in this venture. Arjen van Ooyen and myself have been developing models of neurite outgrowth and branching based on construction of the microtubule cytoskeleton, mediated by the diffusion and active transport of tubulin and other substances. We have written our own code to do this (e.g. in Java), but it would be very nice to be easily able to do it in NEURON. One aspect of this that may go beyond your remit is that the "product" of the model is a changing (growing) cell morphology, involving elongation of neurites and formation of new branches.

So I am interested in whatever you achieve, and am willing to be involved in any way possible.

Best wishes,

Bruce Graham (University of Stirling, Scotland)

### Re: Introduction and request for suggestions

Spines change their shapes in a rather fast mode. Therefore, I would suggest that Neuron-rd could treat the geometry parameters as temporal varabiles and could be the function of other parameters.

### Re: Introduction and request for suggestions

It would be very interesting, yet there may be a computation problem with not elementary network. More computing power would be very useful on desktops. What about using General Purpose Graphical Processing Unit? I think about nVidia GPGPU using CUDA...

### Re: Introduction and request for suggestions

Hi,

Somewhat related to this is the following short utility for converting SBML to native NEURON code (NMODLfiles):

http://www.neuroml.org/neuron_tools.php

It needs some further development but could be useful for getting more advanced signalling pathway in SBML format directly into NEURON.

It will be extended to help define the interaction between SBML and NeuroML version 2.0. Note though that reaction & diffusion in 3D will probably be outside the scope of NeuroML v2.0; we'll wait until there is greater simulator support before attempting to make a simulator independent method of representing such complex 3D structures, and we'll keep an interested eye on developments here.

Padraig

Somewhat related to this is the following short utility for converting SBML to native NEURON code (NMODLfiles):

http://www.neuroml.org/neuron_tools.php

It needs some further development but could be useful for getting more advanced signalling pathway in SBML format directly into NEURON.

It will be extended to help define the interaction between SBML and NeuroML version 2.0. Note though that reaction & diffusion in 3D will probably be outside the scope of NeuroML v2.0; we'll wait until there is greater simulator support before attempting to make a simulator independent method of representing such complex 3D structures, and we'll keep an interested eye on developments here.

Padraig

### Re: Introduction and request for suggestions

It is probably too late to answer to this post. Anyway, as far as I have learned about the reaction-diffusion implementation in NEURON 7.3, I am not sure how it can be used in the modeling of dendritic spines since it models ion diffusion along the cable independent of membrane potential. I am also not sure about the accuracy of the electric potential calculation inside a spine without considering "diffusion potential" or vice versa.

Is membrane potential calculated with the traditional cable equations or it uses Nernst-Plank equation?

I think Mori and Peskins recent advances about the modeling of electrodiffusion in excitable cables are the best way to solve these problems, if you accept the existence of such problems.

Their detailed model:

Mori2009 [A Numerical Method for Cellular Electrophysiology based on the Electrodiffusion Equations with Internal Boundary Conditions at Membranes]

or their simplified models:

Mori2009 [From Three-Dimensional Electrophysiology to the Cable Model - an Asymptotic Study]

I think we need a simplified version of their model. One of the features that I like about their work is that they have found a way to dissociate the capacitive current to its ionic components. With their model also it is possible to simulate "ephaptic coupling" accurately.

Is membrane potential calculated with the traditional cable equations or it uses Nernst-Plank equation?

I think Mori and Peskins recent advances about the modeling of electrodiffusion in excitable cables are the best way to solve these problems, if you accept the existence of such problems.

Their detailed model:

Mori2009 [A Numerical Method for Cellular Electrophysiology based on the Electrodiffusion Equations with Internal Boundary Conditions at Membranes]

or their simplified models:

Mori2009 [From Three-Dimensional Electrophysiology to the Cable Model - an Asymptotic Study]

I think we need a simplified version of their model. One of the features that I like about their work is that they have found a way to dissociate the capacitive current to its ionic components. With their model also it is possible to simulate "ephaptic coupling" accurately.