diff --git a/joss.06836/10.21105.joss.06836.crossref.xml b/joss.06836/10.21105.joss.06836.crossref.xml new file mode 100644 index 000000000..c3633845b --- /dev/null +++ b/joss.06836/10.21105.joss.06836.crossref.xml @@ -0,0 +1,294 @@ + + + + 20241213134827-a299c849a3b06497dccccc080f9390e2a2513072 + 20241213134827 + + JOSS Admin + admin@theoj.org + + The Open Journal + + + + + Journal of Open Source Software + JOSS + 2475-9066 + + 10.21105/joss + https://joss.theoj.org + + + + + 12 + 2024 + + + 9 + + 104 + + + + DuneCopasi: A multi-compartment reaction-diffusion simulator for systems biology + + + + Santiago + Ospina De Los Ríos + + Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University, Germany + Heidelberg Graduate School of Mathematical and Computational Methods for the Sciences (HGS MathComp), Heidelberg University, Germany + + https://orcid.org/0000-0003-0814-9670 + + + Peter + Bastian + + Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University, Germany + + + + Liam + Keegan + + Scientific Software Center (SSC), Heidelberg University, Germany + + https://orcid.org/0000-0002-0654-4979 + + + Sven + Sahle + + BioQuant, Centre for Organismal Studies (COS), Heidelberg University, Germany + + https://orcid.org/0000-0002-5458-7404 + + + Dylan + Vermoortele + + Cardiovascular Imaging and Dynamics, KU Leuven, Belgium + + https://orcid.org/0000-0001-8769-783X + + + Lilija + Wehling + + BioQuant, Centre for Organismal Studies (COS), Heidelberg University, Germany + Institute of Pathology, University Hospital Heidelberg, Germany + + https://orcid.org/0000-0002-8697-5348 + + + + 12 + 13 + 2024 + + + 6836 + + + 10.21105/joss.06836 + + + http://creativecommons.org/licenses/by/4.0/ + http://creativecommons.org/licenses/by/4.0/ + http://creativecommons.org/licenses/by/4.0/ + + + + Software archive + 10.5281/zenodo.10855069 + + + GitHub review issue + https://github.com/openjournals/joss-reviews/issues/6836 + + + + 10.21105/joss.06836 + https://joss.theoj.org/papers/10.21105/joss.06836 + + + https://joss.theoj.org/papers/10.21105/joss.06836.pdf + + + + + + A generic grid interface for parallel and adaptive scientific computing. Part i: Abstract framework + Bastian + Computing + 82 + 10.1007/s00607-008-0003-x + 2008 + Bastian, P., Blatt, M., Dedner, A., Engwer, C., Klöfkorn, R., Ohlberger, M., & Sander, O. (2008). A generic grid interface for parallel and adaptive scientific computing. Part i: Abstract framework. Computing, 82, 103–119. https://doi.org/10.1007/s00607-008-0003-x + + + Generic implementation of finite element methods in the Distributed and Unified Numerics Environment (DUNE) + Bastian + Kybernetika + 2 + 46 + 2010 + Bastian, P., Heimann, F., & Marnach, S. (2010). Generic implementation of finite element methods in the Distributed and Unified Numerics Environment (DUNE). Kybernetika, 46(2), 294–315. dml.cz/dmlcz/140745 + + + The dune framework: Basic concepts and recent developments + Bastian + Computers & Mathematics with Applications + 81 + 10.1016/j.camwa.2020.06.007 + 0898-1221 + 2021 + Bastian, P., Blatt, M., Dedner, A., Dreier, N.-A., Engwer, C., Fritze, R., Gräser, C., Grüninger, C., Kempf, D., Klöfkorn, R., Ohlberger, M., & Sander, O. (2021). The dune framework: Basic concepts and recent developments. Computers & Mathematics with Applications, 81, 75–112. https://doi.org/10.1016/j.camwa.2020.06.007 + + + Reaction–diffusion systems for spatio-temporal intracellular protein networks: A beginner’s guide with two examples + Eliaš + Computational and Structural Biotechnology Journal + 16 + 10 + 10.1016/j.csbj.2014.05.007 + 2001-0370 + 2014 + Eliaš, J., & Clairambault, J. (2014). Reaction–diffusion systems for spatio-temporal intracellular protein networks: A beginner’s guide with two examples. Computational and Structural Biotechnology Journal, 10(16), 12–22. https://doi.org/10.1016/j.csbj.2014.05.007 + + + The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models + Hucka + Bioinformatics + 4 + 19 + 10.1093/bioinformatics/btg015 + 1367-4803 + 2003 + Hucka, M., Finney, A., Sauro, H. M., Bolouri, H., Doyle, J. C., Kitano, H., Arkin, A. P., Bornstein, B. J., Bray, D., Cornish-Bowden, A., Cuellar, A. A., Dronov, S., Gilles, E. D., Ginkel, M., Gor, V., Goryanin, I. I., Hedley, W. J., Hodgman, T. C., Hofmeyr, J.-H., … SBML Forum:, the rest of the. (2003). The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models. Bioinformatics, 19(4), 524–531. https://doi.org/10.1093/bioinformatics/btg015 + + + A general computational framework for modeling cellular structure and function + Schaff + Biophys. J. + 3 + 73 + 10.1016/s0006-3495(97)78146-3 + 1997 + Schaff, J., Fink, C. C., Slepchenko, B., Carson, J. H., & Loew, L. M. (1997). A general computational framework for modeling cellular structure and function. Biophys. J., 73(3), 1135–1146. https://doi.org/10.1016/s0006-3495(97)78146-3 + + + Morpheus: a user-friendly modeling environment for multiscale and multicellular systems biology + Starruß + Bioinformatics + 9 + 30 + 10.1093/bioinformatics/btt772 + 1367-4803 + 2014 + Starruß, J., Back, W. de, Brusch, L., & Deutsch, A. (2014). Morpheus: a user-friendly modeling environment for multiscale and multicellular systems biology. Bioinformatics, 30(9), 1331–1332. https://doi.org/10.1093/bioinformatics/btt772 + + + The deal.II library, version 9.5 + Arndt + Journal of Numerical Mathematics + 3 + 31 + 10.1515/jnma-2023-0089 + 2023 + Arndt, D., Bangerth, W., Bergbauer, M., Feder, M., Fehling, M., Heinz, J., Heister, T., Heltai, L., Kronbichler, M., Maier, M., Munch, P., Pelteret, J.-P., Turcksin, B., Wells, D., & Zampini, S. (2023). The deal.II library, version 9.5. Journal of Numerical Mathematics, 31(3), 231–246. https://doi.org/10.1515/jnma-2023-0089 + + + New development in FreeFem++ + Hecht + J. Numer. Math. + 3-4 + 20 + 10.1515/jnum-2012-0013 + 1570-2820 + 2012 + Hecht, F. (2012). New development in FreeFem++. J. Numer. Math., 20(3-4), 251–265. https://doi.org/10.1515/jnum-2012-0013 + + + Nektar++: An open-source spectral/hp element framework + Cantwell + Computer Physics Communications + 192 + 10.1016/j.cpc.2015.02.008 + 0010-4655 + 2015 + Cantwell, C. D., Moxey, D., Comerford, A., Bolis, A., Rocco, G., Mengaldo, G., De Grazia, D., Yakovlev, S., Lombard, J.-E., Ekelschot, D., Jordi, B., Xu, H., Mohamied, Y., Eskilsson, C., Nelson, B., Vos, P., Biotto, C., Kirby, R. M., & Sherwin, S. J. (2015). Nektar++: An open-source spectral/hp element framework. Computer Physics Communications, 192, 205–219. https://doi.org/10.1016/j.cpc.2015.02.008 + + + Spatial-model-editor/spatial-model-editor: 1.5.0 + Keegan + 10.5281/zenodo.10246531 + 2023 + Keegan, L., Andriushchenko, P., Schreiner, H., Caramizaru, H., & Patel, H. (2023). Spatial-model-editor/spatial-model-editor: 1.5.0 (Version 1.5.0). Zenodo. https://doi.org/10.5281/zenodo.10246531 + + + Spatial modeling reveals nuclear phosphorylation and subcellular shuttling of YAP upon drug-induced liver injury + Wehling + Elife + 11 + 10.7554/eLife.78540 + 2022 + Wehling, L., Keegan, L., Fernández-Palanca, P., Hassan, R., Ghallab, A., Schmitt, J., Tang, Y., Le Marois, M., Roessler, S., Schirmacher, P., & others. (2022). Spatial modeling reveals nuclear phosphorylation and subcellular shuttling of YAP upon drug-induced liver injury. Elife, 11, e78540. https://doi.org/10.7554/eLife.78540 + + + Parafields: A generator for distributed, stationary gaussian processes + Kempf + Journal of Open Source Software + 92 + 8 + 10.21105/joss.05735 + 2023 + Kempf, D., Klein, O., Kutri, R., Scheichl, R., & Bastian, P. (2023). Parafields: A generator for distributed, stationary gaussian processes. Journal of Open Source Software, 8(92), 5735. https://doi.org/10.21105/joss.05735 + + + A flexible framework for multi physics and multi domain PDE simulations + Müthing + 10.18419/opus-3620 + 2015 + Müthing, S. (2015). A flexible framework for multi physics and multi domain PDE simulations [PhD thesis, Universität Stuttgart]. https://doi.org/10.18419/opus-3620 + + + Arrhythmia risk stratification of patients after myocardial infarction using personalized heart models + Arevalo + Nature communications + 1 + 7 + 10.1038/ncomms11437 + 2016 + Arevalo, H. J., Vadakkumpadan, F., Guallar, E., Jebb, A., Malamas, P., Wu, K. C., & Trayanova, N. A. (2016). Arrhythmia risk stratification of patients after myocardial infarction using personalized heart models. Nature Communications, 7(1), 11437. https://doi.org/10.1038/ncomms11437 + + + COPASI—a COmplex PAthway SImulator + Hoops + Bioinformatics + 24 + 22 + 10.1093/bioinformatics/btl485 + 1367-4803 + 2006 + Hoops, S., Sahle, S., Gauges, R., Lee, C., Pahle, J., Simus, N., Singhal, M., Xu, L., Mendes, P., & Kummer, U. (2006). COPASI—a COmplex PAthway SImulator. Bioinformatics, 22(24), 3067–3074. https://doi.org/10.1093/bioinformatics/btl485 + + + + + + diff --git a/joss.06836/10.21105.joss.06836.pdf b/joss.06836/10.21105.joss.06836.pdf new file mode 100644 index 000000000..7a51531c6 Binary files /dev/null and b/joss.06836/10.21105.joss.06836.pdf differ diff --git a/joss.06836/paper.jats/10.21105.joss.06836.jats b/joss.06836/paper.jats/10.21105.joss.06836.jats new file mode 100644 index 000000000..cef2c3da3 --- /dev/null +++ b/joss.06836/paper.jats/10.21105.joss.06836.jats @@ -0,0 +1,858 @@ + + +
+ + + + +Journal of Open Source Software +JOSS + +2475-9066 + +Open Journals + + + +6836 +10.21105/joss.06836 + +DuneCopasi: A multi-compartment reaction-diffusion +simulator for systems biology + + + +https://orcid.org/0000-0003-0814-9670 + +Ospina De Los Ríos +Santiago + + + + + + +Bastian +Peter + + + + +https://orcid.org/0000-0002-0654-4979 + +Keegan +Liam + + + + +https://orcid.org/0000-0002-5458-7404 + +Sahle +Sven + + + + +https://orcid.org/0000-0001-8769-783X + +Vermoortele +Dylan + + + + +https://orcid.org/0000-0002-8697-5348 + +Wehling +Lilija + + + + + + +Interdisciplinary Center for Scientific Computing (IWR), +Heidelberg University, Germany + + + + +Heidelberg Graduate School of Mathematical and +Computational Methods for the Sciences (HGS MathComp), Heidelberg +University, Germany + + + + +Scientific Software Center (SSC), Heidelberg University, +Germany + + + + +BioQuant, Centre for Organismal Studies (COS), Heidelberg +University, Germany + + + + +Institute of Pathology, University Hospital Heidelberg, +Germany + + + + +Cardiovascular Imaging and Dynamics, KU Leuven, +Belgium + + + +9 +104 +6836 + +Authors of papers retain copyright and release the +work under a Creative Commons Attribution 4.0 International License (CC +BY 4.0) +2024 +The article authors + +Authors of papers retain copyright and release the work under +a Creative Commons Attribution 4.0 International License (CC BY +4.0) + + + +Diffusion +Reaction Networks +Multiple Compartments +Continuous Galerkin Method +Partial Differential Equations +Finite Element Method +Systems Biology +C++ +WebAssembly +Docker +DUNE + + + + + + Summary +

DuneCopasi is a C++ library designed to simulate how chemical + reactions and diffusion processes occur in space, which is crucial for + understanding many biological systems. It allows users to model these + processes in both simple and complex environments, using grids that + represent one, two, or three dimensions. Optimised for modern + computers, DuneCopasi can be used as a standalone command-line + application, accessed through tools like Docker or a web-based + terminal, as a C++ library, or integrated into a graphical interface. + One such interface is the Spatial Model + Editor (SME) + (Keegan + et al., 2023), which helps users create and manipulate + biological reaction models. The project was initiated to provide the + numerical foundation for a spatial modelling tool for biochemical + reaction networks, complementing the COmplex + PAthway SImulator (COPASI) software + (Hoops + et al., 2006). This development resulted from a collaboration + between the COPASI team and the Distributed and + Unified Numerics Environment + (DUNE) team + (Bastian + et al., 2021).

+ + + Background +

In the context of cell biology, computational modelling has become + an essential technique for understanding and discovering biological + processes. By comparing model simulations with experimental data, + researchers can set up models, validate them, and test hypotheses + about these processes. Traditionally, most biological systems studied + this way have been spatially homogeneous. That is, the data are + typically time-resolved concentrations or quantities of biochemical + species, modelled using Ordinary + Differential Equations (ODEs).

+

However, recent advances in live-cell imaging technology have made + more detailed spatio-temporal data available, leading to a growing + need for models that capture not only the time dynamics but also the + spatial distribution of these biochemical species. This has prompted a + shift toward spatially resolved models.

+ + + Model Problem +

A natural extension of spatially homogeneous ODE models is to + incorporate spatio-temporal dynamics by formulating the problem as a + system of Partial Differential + Equations (PDEs) across multiple compartments. In such + models, each compartment’s PDE represents the reaction-diffusion + processes of biochemical species in a specific physical domain (e.g., + the cytosol), while boundary conditions between compartments (e.g., + membrane fluxes) govern the interactions between them.

+

Specifically, our program solves the mass balance equation for the + species + + uik + in the + + k-th + compartment + + Ωk + for every + + k∈K + and + + i∈Nk. + Each mass balance equation is given by

+

+ + [c]∂t(ϕikuik)=∇⋅𝐣ik+ℛik(𝐮)in Ωk⊂ℝd,uik=uik(0)on ΓkD⊆∂Ωk,𝐣ik⋅𝐧k=∑l∈Tk𝒯ikl(𝐮)on ∂Ωk\ΓkD,with[c]𝐣ik:=∑j∈Nk𝖣ijk∇ujk.

+

Here, + + 𝐮k:=(u1k,…,udim(Nk)k) + represents the vector of species concentrations in compartment + + + k, + while the full vector of species concentrations across all + compartments is denoted as + + 𝐮:=(𝐮1,…,𝐮dim(K)). + The unit outer normal vector on the boundary + + + ∂Ωk + is represented by + + 𝐧k, + and the set of neighbouring compartments to + + + k + is given by + + Tk:={l∈K:∂Ωk∩Ω¯l≠⌀}, + indicating the compartments that share a boundary with + + + Ωk.

+

The reaction operator + + ℛik(𝐮) + governs the local reaction dynamics within + + + Ωk, + while the storage terms + + ϕik + account for species accumulation in the compartment. Cross-diffusion + terms + + 𝖣ijk + describe how species diffuse between different species within the same + compartment. The non-linear transmission conditions + + + 𝒯ikl(𝐮) + represent the outflow of species + + uik + from compartment + + Ωk, + where the outflow can either move to a neighbouring compartment + + + l + (if + + l≠k) + or exit the system. Likewise, Dirichlet boundary conditions + + + uik(0) + are imposed on the subset + + ΓkD + of the boundary + + ∂Ωk, + specifying the fixed concentrations of species on that portion of the + boundary.

+

The parameters governing these equations are fully configurable at + run-time, either through the command line or via a configuration file. + By allowing full control over these parameters, users can adapt the + software to simulate a wide variety of biochemical processes, from + simple reactions in homogeneous environments to complex, + multi-compartmental systems with intricate boundary conditions and + interactions.

+ + + Capabilities +

Many features of DuneCopasi have been designed and developed with + the specific case of systems biology in mind. Thus, a substantial + effort has been made to have a library that is interoperable with + systems biology data assets and requirements needed by their + practitioners. Among others, include:

+ + +

a single executable configurable at run-time,

+ + +

a run-time mathematical expression parser that understands the + Systems Biology Markup Language SBML + (Hucka + et al., 2003) specification,

+ + +

the input of custom grid data and image files in the TIFF + format for initial spatial concentrations and other + parameters,

+ + +

a powerful, yet simple, boundary/transmission condition + specification for each compartment to account for generic + trans-membrane fluxes,

+ + +

a (non-linear) cross-diffusion specification that allows any + species to cross-diffuse into other mass balance equations,

+ + +

a specification to compare results with user-defined objective + functions,

+ + +

an in-place function interpolator that reduces the + computational cost of evaluating common expensive reaction + operations, and

+ + +

an embedded random field generator + (Kempf + et al., 2023) to represent statistical spatial variations + on the domain.

+ + +

Furthermore, DuneCopasi is a stand-alone multi-compartment + reaction-diffusion solver that may easily be used for many other + fields of research and engineering fitting our model problem + (e.g. [fig:cardiac_ep]).

+ +

DuneCopasi is a highly flexible simulator that is + run-time configurable using dedicated configuration files. + DuneCopasi can autonomysly interpret mathematical equations, + assemble the computational problems and solve these equations based + on the configuration file. Here we illustrate the integration of + DuneCopasi within a computational electrophysiology pipeline + allowing to solve the electrophysiological mono-domain equations + with Mitchell-Schaefer cell model using a medical imaging derived + from biventricular geometry. +

+ + + + + Statement of Need +

Finite element frameworks like DUNE + (Bastian + et al., 2008), Deal.II + (Arndt + et al., 2023), Necktar++ + (Cantwell + et al., 2015), or FreeFem++ + (Hecht, + 2012) are too generic by design and don’t address the specific + requirements of the computational modelling practices in systems + biology out of the box. In particular, most finite element frameworks + don’t consider the multi-compartment systems in their design, + resulting, if at all possible, in inefficient simulations or obscure + tricks to force this feature. Here, we extended DUNE-PDELab + (Bastian + et al., 2010; + Müthing, + 2015) with efficient data structures especially tailored for + this task.

+

In the space of systems biology, two well-known software packages + also provide similar features to DuneCopasi, namely Morpheus + (Starruß + et al., 2014) and VCell + (Schaff + et al., 1997). Morpheus is a computational tool for + multi-cellular systems which follows a cellular automata design to set + rules of interactions between individual cells. It focuses on + modelling approaches like cellular Potts models combined with + gradients modelled by PDEs, rather than multi-compartment PDE models. + Furthermore, due to its design, it falls short for moderate and big + PDE computations since explicit solvers are severely limited by the + required time steps. On the other hand, VCell provides a fully + implicit finite volume solver on structured grids that can very well + manage the multi-compartment case in addition to membrane unknowns. In + comparison, our solution aims to resolve the geometry and the + transmission conditions directly in the weak formulation of the + problem while also being designed to provide implicit and monolithic + solvers as well as tailored preconditioners for the underlying linear + solvers.

+ + + Research and Use Cases +

The principal purpose of our project has been to bridge the gap + between systems biology and scientific computing by providing + researchers with an accessible and reproducible spatial simulator. An + illustration of this is the study depicted in + [fig:wehling_2022] + (Wehling + et al., 2022), where simulations with the SME + (Keegan + et al., 2023) aided in assessing and better understanding the + mechanisms of the YAP and TAZ proteins that regulate cell + proliferation in liver cells. Further examples that fit our model + problem in this context have been presented by others + (Eliaš + & Clairambault, 2014). Additionally, DuneCopasi stands as a + versatile tool capable of accommodating diverse computational needs + beyond its initial focus on systems biology. For example, the general + purpose nature allows for seamless integration into electrophysiology + simulations, without requiring any modifications. The emerging concept + of identifying patients based on personalised cardiac + electrophysiology simulations + (Arevalo + et al., 2016) underscores the demand for easy-to-use and + efficient simulators. + [fig:cardiac_ep] + demonstrates how DuneCopasi emerges as a flexible solver poised to + meet these evolving needs.

+ +

Mathematical modelling predicts that nuclear + phosphorylation controls spatial localization of Hippo signalling + pathway components YAP and TAZ. Here, we compare two model + topologies - “Model 1” (canonical) and “Model 2” (alternative model) + - concerning the intracellular distribution of YAP and TAZ proteins + (Pr) and their phosphorylated counterparts (pPr). If the + phosphorylation of YAP/TAZ takes place exclusively outside the + nucleus, as shown in “Model 1”, PDE simulation indicates low spatial + accordance with the experimentally measured subcellular localization + of YAP/TAZ. Whereas, “Model 2” describes YAP/TAZ protein + phosphorylation and dephosphorylation in the nucleus. The simulation + of “Model 2” agrees with experimentally measured subcellular + distribution of YAP/TAZ proteins, as reported in + (Wehling + et al., 2022). +

+ + + + + Acknowledgements +

We want to thank all the contributions that aided in the + development and deployment of the package. Special thanks to Ursula + Kummer from the COPASI team for valuable guidance. This work has been + funded and supported by the German Federal Ministry of Education and + Research (BMBF) FKZ 031L0158.

+ + + + + + + + + BastianPeter + BlattMarkus + DednerAndreas + EngwerChristian + KlöfkornRobert + OhlbergerMario + SanderOliver + + A generic grid interface for parallel and adaptive scientific computing. Part i: Abstract framework + Computing + Springer + 2008 + 82 + 10.1007/s00607-008-0003-x + 103 + 119 + + + + + + BastianPeter + HeimannFelix + MarnachSven + + Generic implementation of finite element methods in the Distributed and Unified Numerics Environment (DUNE) + Kybernetika + 2010 + 20171012 + 46 + 2 + dml.cz/dmlcz/140745 + 294 + 315 + + + + + + BastianPeter + BlattMarkus + DednerAndreas + DreierNils-Arne + EngwerChristian + FritzeRené + GräserCarsten + GrüningerChristoph + KempfDominic + KlöfkornRobert + OhlbergerMario + SanderOliver + + The dune framework: Basic concepts and recent developments + Computers & Mathematics with Applications + 2021 + 81 + 0898-1221 + https://www.sciencedirect.com/science/article/pii/S089812212030256X + 10.1016/j.camwa.2020.06.007 + 75 + 112 + + + + + + EliašJán + ClairambaultJean + + Reaction–diffusion systems for spatio-temporal intracellular protein networks: A beginner’s guide with two examples + Computational and Structural Biotechnology Journal + 2014 + 10 + 16 + 2001-0370 + https://www.sciencedirect.com/science/article/pii/S2001037014000087 + 10.1016/j.csbj.2014.05.007 + 12 + 22 + + + + + + HuckaM. + FinneyA. + SauroH. M. + BolouriH. + DoyleJ. C. + KitanoH. + ArkinA. P. + BornsteinB. J. + BrayD. + Cornish-BowdenA. + CuellarA. A. + DronovS. + GillesE. D. + GinkelM. + GorV. + GoryaninI. I. + HedleyW. J. + HodgmanT. C. + HofmeyrJ.-H. + HunterP. J. + JutyN. S. + KasbergerJ. L. + KremlingA. + KummerU. + Le NovèreN. + LoewL. M. + LucioD. + MendesP. + MinchE. + MjolsnessE. D. + NakayamaY. + NelsonM. R. + NielsenP. F. + SakuradaT. + SchaffJ. C. + ShapiroB. E. + ShimizuT. S. + SpenceH. D. + StellingJ. + TakahashiK. + TomitaM. + WagnerJ. + WangJ. + SBML Forum: + + The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models + Bioinformatics + 200303 + 19 + 4 + 1367-4803 + 10.1093/bioinformatics/btg015 + 524 + 531 + + + + + + SchaffJ + FinkC C + SlepchenkoB + CarsonJ H + LoewL M + + A general computational framework for modeling cellular structure and function + Biophys. 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