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10.21105/joss + https://joss.theoj.org + + + + + 05 + 2024 + + + 9 + + 97 + + + + STReNGTHS, a Python package to model and simulate +complex reaction-diffusion systems + + + + Thibault + Fillion + + + Francesco + Piazza + + + + 05 + 25 + 2024 + + + 6495 + + + 10.21105/joss.06495 + + + 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.11300235 + + + GitHub review issue + https://github.com/openjournals/joss-reviews/issues/6495 + + + + 10.21105/joss.06495 + https://joss.theoj.org/papers/10.21105/joss.06495 + + + https://joss.theoj.org/papers/10.21105/joss.06495.pdf + + + + + + Exact stochastic simulation of coupled +chemical reactions + Gillespie + The Journal of Physical +Chemistry + 25 + 81 + 10.1021/j100540a008 + 0022-3654 + 1977 + Gillespie, D. T. (1977). Exact +stochastic simulation of coupled chemical reactions. The Journal of +Physical Chemistry, 81(25), 2340–2361. +https://doi.org/10.1021/j100540a008 + + + Simulating mesoscopic reaction-diffusion +systems using the Gillespie algorithm + Bernstein + Physical review. E, Statistical, nonlinear, +and soft matter physics + 71 + 10.1103/PhysRevE.71.041103 + 2005 + Bernstein, D. (2005). Simulating +mesoscopic reaction-diffusion systems using the Gillespie algorithm. +Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, 71, +041103. +https://doi.org/10.1103/PhysRevE.71.041103 + + + Approximate Accelerated Stochastic Simulation +of Chemically Reacting Systems + Gillespie + Journal of Chemical Physics + 115 + 10.1063/1.1378322 + 2001 + Gillespie, D. (2001). 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literal 0 HcmV?d00001 From 96607cab4addd43d70a6069ddd011788613eba27 Mon Sep 17 00:00:00 2001 From: The Open Journals editorial robot <89919391+editorialbot@users.noreply.github.com> Date: Sat, 25 May 2024 18:40:33 +0100 Subject: [PATCH 6/6] Creating 10.21105.joss.06495.jats --- .../paper.jats/10.21105.joss.06495.jats | 1078 +++++++++++++++++ 1 file changed, 1078 insertions(+) create mode 100644 joss.06495/paper.jats/10.21105.joss.06495.jats diff --git a/joss.06495/paper.jats/10.21105.joss.06495.jats b/joss.06495/paper.jats/10.21105.joss.06495.jats new file mode 100644 index 0000000000..ab52f13401 --- /dev/null +++ b/joss.06495/paper.jats/10.21105.joss.06495.jats @@ -0,0 +1,1078 @@ + + +

    + + + + +Journal of Open Source Software +JOSS + +2475-9066 + +Open Journals + + + +6495 +10.21105/joss.06495 + +STReNGTHS, a Python package to model and simulate complex +reaction-diffusion systems + + + + +Fillion +Thibault + + + + + + + +Piazza +Francesco + + + + + + +Université d’Orléans, UFR Sciences Techniques, Avenue du +Parc Floral, BP 6749, 45067 Orléans, France + + + + +Centre de Biophysique Moléculaire (CBM), CNRS-UPR 4301, Rue +Charles Sadron, 45071 Orléans, France + + + + +Dipartimento di fisica & Astronomia, Università di +Firenze, Via G. Sansone 1, 50019 Sesto Fiorentino, Italy + + + + +INFN sezione di Firenze, Via G. Sansone 1, 50019 Sesto +Fiorentino, Italy + + + + +Dipartimento di Medicina Sperimentale e Clinica, Università +di Firenze, Viale Giovanni Batista Morgagni 50, 50314 Firenze, +Italy + + + +9 +97 +6495 + +Authors of papers retain copyright and release the +work under a Creative Commons Attribution 4.0 International License (CC +BY 4.0) +2022 +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) + + + + + + + Summary +

    STReNGTHS is an open-source Python package that provides a simple + and intuitive interface for designing models of discrete 3D + heterogeneous reaction-diffusion systems and simulating their + trajectories. Different algorithms are available, both stochastic + (exact or approximate solutions of the associated master equation) and + deterministic (numerical solutions of the corresponding rate + equations). The acronym stands for “Simulation and modeling Tool for + REaction-diffusion Networks in Graphs and Tridimensional Heterogeneous + Systems” (STReNGTHS). The simulation algorithms are interfaced through + a general abstract interface, which makes it easy to extend STReNGTHS + with new algorithms and other features. It is implemented in Python + (standard library, Numpy + (C. + R. Harris et al., 2020) and Matplotlib + (Hunter, + 2007), as well as pytest + (Krekel + et al., 2004) for unit testing) and C++ (standard C++11 or + later), and can be easily installed from the Python Package Index + (PyPI, + https://pypi.org) + with (i.e.)

    + pip install strengths +
    + + Statement of need +

    Biology at the cell scale relies on complex networks of biochemical + reactions, usually operating across multiple membrane-associated as + well as membrane-less compartments (i.e. plasma membrane, cytoplasm, + cellular organelles, stress granules, etc) and driven far from + equilibrium by highly regulated species, such as nucleotides + (ATP/GTP), amino acids and different ions. In order to understand the + properties of such reaction-diffusion networks, and especially their + role in macroscopic emergent phenomena, convenient, + reliable and efficient modeling and simulation tools supporting + heterogeneous systems are necessary. Moreover, the choice of the + simulation algorithm to be used may depend on the system: + deterministic approaches such as ODE integration (rate equations) are + effective, but inappropriate for systems that are sensitive to + fluctuations, such as systems that operate with species present at low + copy numbers (e.g. certain enzymes, many mRNA species) and/or in tiny + reaction volumes (i.e. within mitochondria), for which stochastic + methods should be preferred. This is why one needs to have multiple, + flexible approaches available. STReNGTHS provides an interface to + simulate reaction-diffusion systems and manipulate their trajectories, + as well as full control and access to the simulation algorithms + themselves.

    +

    A reaction-diffusion system is represented by the + RDSystem class. This defines a reaction-diffusion + network, which is a set of coupled chemical transformations + represented by the RDNetwork class, augmented with a + physical space where chemical species may diffuse. The system space is + discrete and consists of a 3D mesh of individual volume elements, + which we refer to as cells. It can be either a + regular grid of cubic cells with uniform volumes, or an arbitrary + network of cells with different volumes, which can be obtained by + coarse-graining a cell grid.

    +

    In order to account for systems with different compartments, + STReNGTHS implements the system of reaction-diffusion environments, + which allows the user to define different types of cells (referred to + as environments) with specific reactive and diffusive properties. Many + properties, such as the initial density of species, diffusion + coefficients, or reaction occurrence, can be defined + environment-wise.

    +

    Importantly, species can be chemostatted, + i.e. kept at a fixed, prescribed concentration during the simulation, + globally or only in specific environments or cells. Chemostatted + species allow one to model non-equilibrium conditions existing in + living cells that are associated with chemical potential baths, such + as in the case of the tightly regulated cytoplasmic levels of ATP or + ADP.

    + +

    Definition of a simple reaction-diffusion system + implementing an association reaction over 3 cells using the + JSON/dictionary format. The rates used were: + + + k+=1 + M + + 1s + + 1, + + + k=1 + s + + 1. +

    + +
    +

    In STReNGTHS, reaction-diffusion systems can be defined either + using Python dictionaries or through JSON input files, following a + specific intuitive syntax, as shown in figure + [jsonsyntax]. + Simulations are handled by objects called simulation + engines, which offer a general abstract interface for + simulation algorithms. The simulate function wraps + the engine call to run the whole simulation at once. The resulting + system trajectory, which is the sequence of system states successively + sampled during the simulation and the corresponding sampling times, is + stored in a RDTrajectory object.

    +

    For now, STReNGTHS implements simulation engines for the original + Gillespie algorithm + (D. + T. Gillespie, 1977), the + + τ-leap + approximation to the Gillespie algorithm + (D. + Gillespie, 2001), and the Euler Method, operating on both grid + and graph spaces, with diffusion handled according to the method + described in Ref. + (Bernstein, + 2005) (with a slight adaptation for graph spaces).

    +
    + + STReNGTHS and similar tools +

    There already exist various computational tools to model and + simulate complex reaction-diffusion systems. Some of them are + general-purpose tools, while others have been designed to handle more + specific systems. Existing simulation packages include:

    + + +

    STEPS + (Wils + & De Schutter, 2009). This is a reaction-diffusion + program interfaced with Python, which uses the Gillespie + algorithm. It handles simulations in geometries composed of + tetrahedral voxels with faces that can represent biological + membranes + (Wils + & De Schutter, 2009).

    +
    + +

    ReaDDy + (Hoffmann + et al., 2019). This is a reaction-diffusion tool with a + Python interface that uses a particle-based approach. An + especially interesting feature is that it can deal with complex + molecule geometries and reaction patterns, such as polymer + dynamics + (Hoffmann + et al., 2019). A Python interface is also available + (Hoffmann + et al., 2019).

    +
    + +

    MesoRD + (Hattne + et al., 2005). This is a tool that employs a stochastic + approach based on the Next Subvolume Method + (Elf + & Ehrenberg, 2004 December). The simulation parameters + are defined through XML script files, using the System Biology + Markup Language (SBML) format + (Hattne + et al., 2005). The software relies on Constructive Solid + Geometry (CSG) to define the different reaction-diffusion + compartments + (Hattne + et al., 2005). It comes with graphical (Windows) and + command-line (Unix) user interfaces + (Hattne + et al., 2005).

    +
    + +

    BioNetGen + (L. + A. Harris et al., 2016). This is a modeling and simulation + tool that provides a rich scripting language with a rule-based + approach + (L. + A. Harris et al., 2016). Such an approach enables one to + consider systems that may be difficult to apprehend with methods + requiring to define explicitly the full reaction network (such as + polymerization) + (L. + A. Harris et al., 2016). BioNetGen supports both + deterministic and stochastic methods + (L. + A. Harris et al., 2016).

    +
    +
    +

    Compared to the aforementioned tools, STReNGTHS is more rudimentary + and only handles reaction networks with explicitly defined species and + reactions, as opposed to pattern-based approaches or rule-based + approaches used by tools such as BioNetGen + (L. + A. Harris et al., 2016). Still, it allows one to build in a + very intuitive and user-friendly way simulations able to describe a + vast range of complex systems.

    +

    So far, as opposed to Readdy, STReNGTHS only implements + non-particle-based methods, similar to those proposed by the other + software. However, rather than proposing only one all-purpose fitting + method, STReNGTHS’s approach is to provide a collection of various + simulation methods, leaving the choice at the user’s discretion. + Moreover, simulation features can be easily extended using the + simulation engine interface. In fact, STReNGTHS has been designed to + be extended easily.

    +

    One of STReNGTHS’ key features is the use of + reaction-diffusion environments, which make it easy + to design extremely rich system landscapes, i.e. featuring plenty of + different compartments of arbitrary shape that encode physical and + chemical segregation.

    +

    The use of a JSON/dictionary syntax for the definition of + reaction-diffusion systems brings readability and simplicity to the + workflow.

    +
    + + Examples +

    For the first example, let us consider a simple model of signal + transduction, where some extracellular chemical signal is sensed by a + cell, which triggers the production of a second messenger, as well as + the scavenging of the signal species. The network is designed as + follows: The extracellular ligand + + L + can bind to a plasma membrane receptor + + R + to form a complex + + C. + This species catalyzes the conversion of the inactive second messenger + + + X + to its active form, + + Y. + The complex + + C + is directly converted back into + + R, + which accounts for the internalization of the complex, the degradation + of the ligand and the full recycling of the receptor. No degradation + of the receptors (either through the proteasomes or lysosomes) is + assumed for simplicity, although it would be straightforward to add + additional reactions to implement such reaction channels (see Fig. + [example1] a,c). The + model features 3 reaction-diffusion environments, “ext”, “cyt” and + “mmb”, accounting, respectively, for the extracellular space, the + cytoplasm and the interface between these two compartments containing + the plasma membrane. We use two different system spaces. The first one + is a + + 26×26 + cell grid consisting of 1 + + μm + + 3 + cubic cells, while the second one is a coarse-grained version of the + first that contains only 85 nodes/cells (for 676 cells in the grid) + (Fig. [example1] b). The + trajectory of the system state is simulated, both for the fully + detailed grid and for its coarse-grained version, using the + + + τ-leap + algorithm + (D. + Gillespie, 2001) and the Euler method, for a total duration of + 1 hour using a time step of 1 ms. The global trajectory of + + + Y + as well as its distribution at + + t=0,100,1500 + s are plotted in Fig. + [example1] (f, g).

    + +

    Example of simulation with STReNGTHS implementing a + simple model of signal transduction by a single cell. (a) Schematic + representation of the system. (b) Layout of the two different system + spaces used, the + + 26×26 + cell grid (left) and its coarse-grained graph version (right). (c) + Set of coupled stoichiometric equations that compose the reaction + network. (d) Diffusion coefficients of individual species in the + different environments. (e) Initial densities of each species in the + different environments. (f) Time course of the transduced signal: + Global trajectory of + + Y + obtained from the simulation using the + + + τ-leap + algorithm + (D. + Gillespie, 2001) and the Euler method using both system + spaces (see b). (g) Distribution of the + + + Y + species at different times from the + + τ-leap + simulations. The rates used were: + + L+RC: + + + k1=0.5 + nM + + 1s + + 1. + + + CL+R: + + + k1=0.5×103 + s + + 1. + + + CR: + + + k2=102 + s + + 1. + + + C+XC+Y: + + + k3=1  + + μM + + 1s + + 1. + + + C+YC+X: + + + k3=104 + + + μM + + 1s + + 1. + + + YX,k4=102 + s + + 1. + The diffusion coefficients for the different species were: + + + DL=100 + + + μm + + 2s + + 1 + (order of magnitude for the diffusion coefficient of a protein + around 30 kDa in water + (Milo + & Phillips, 2015)), + + DR=DC=0.1 + + + μm + + 2s + + 1 + (order of magnitude for the diffusion coefficient of a transmembrane + protein in a compartmented plasma + membrane(Fujiwara + et al., 2016)), + + DX=DY=10 + + + μm + + 2s + + 1 + (order of magnitude for the diffusion coefficient of a protein + around 30 kDa in the cytosol + (Milo + & Phillips, 2015)). +

    + +
    +

    For the second example, we consider a pattern-forming + reaction-diffusion network based on the one used in the documentation + of the package + (Fillion + & Piazza, 2024), similar to the Gray-Scott model and + related reaction-diffusion schemes + (McGough + & Riley, 2004) + (Ruijgrok + & Ruijgrok, 1997), that features two competitive + auto-catalytic species + + A + and + + B + mutually converting into each other (Fig. + [example2] (a)). We first + simulate the evolution of the system in 1 dimension using the + + + τ-leap + algorithm + (D. + Gillespie, 2001). The corresponding spatiotemporal evolution of + + + A + concentration over time is reported in Fig. + [example2] (c) as a 2D + heat map. It can be observed how the system, starting from a + homogeneous state, progressively builds up spatial reaction-diffusion + patterns. We also simulate a square + + 100×100 + cell system and plot the final distribution of + + + A, + so that the shape of the pattern can be appreciated directly (Fig. + [example2] (d)).

    +

    Next, we apply this model to two systems with higher complexity, + where the synthesis rates of + + A + and + + B + vary depending on the region (Fig. + [example2] (b), (e), + (g)). The first one (Fig. + [example2] (e)) + represents pattern formation at the surface of a sphere, while the + second one (Fig. + [example2] (g)) + illustrates a similar phenomenon of pattern formation in a domain that + takes the shape of an animal. Panels (f) and (h) in Fig. + [example2] demonstrate + the evolution of both systems (levels of the + + + A + species) in time, highlighting the progressive evolution of the + spatial patterns that form as a result of the subtle combination of + the underlying auto-catalytic process with the inhomogeneous reaction + landscape. Figure + [example2] (i) + additionally illustrates how, due to the stochastic nature of the + process, different patterns may arise from the same homogeneous + initial state.

    + +

    Example of simulations of different pattern-forming + reaction-diffusion systems at increasing levels of environmental + complexity. All simulations are performed with the + + + τ-leap + algorithm + (D. + Gillespie, 2001). (a) Description of the chemical reactions + and associated rates. This reaction-diffusion network is similar to + the Gray-Scott model + (McGough + & Riley, 2004) and the one studied by Ruijgrok and + Ruijgrok + (Ruijgrok + & Ruijgrok, 1997). Other examples using a similar + reaction-diffusion network can be found in the documentation of the + package + (Fillion + & Piazza, 2024). (c) Evolution of a 1D system in time and + space. (d) Pseudo-stationary state of a 2D system. (e) + Reaction-diffusion environments for the two inhomogeneous systems. + (b) Layout of a 3D system where the patterns are forming at the + surface of a sphere. (f) States of the 3D system described at + different time points along a stochastic trajectory (concentration + of the + + A + species). (g) Layout of a 2D system mimicking the shape of an + animal. (h) States of the system (distribution of the + + + A + species) at different time points from one simulation. (i) Patterns + formed at + + t=3500.0 + h resulting from 3 different stochastic simulations. The rates used + were: + + A: + + + k1=104 + molecules + + ×μm + + 3×h + + 1 + in + + a + and + + c + and + + 1.05×104 + molecules + + ×μm + + 3×h + + 1 + in + + b. + + + A: + + + k1=103 + h + + 1. + + + B: + + + k2=104 + molecules + + ×μm + + 3×h + + 1 + in + + a + and + + b + and + + 1.05×104 + molecules + + ×μm + + 3×h + + 1 + in + + c. + + + B: + + + k2=0.001 + h + + 1. + + + A+2B3B: + + + k3=1 + molecules + + 2×μm + + 6×h + + 1. + + + B+2A3A: + + + k4=1 + molecules + + 2×μm + + 6×h + + 1. + The diffusion coefficients for the different species were: + + + DA=DB=80 + + + μm + + 2h + + 1. + Reaction and diffusion rate constants are all 0 in compartment + “ext”.

    + +
    +
    + + Source code and documentation +

    STReNGTHS’s source code and documentation are distributed under the + terms of the MIT license and can be found on the dedicated GitHub + repository:

    +

    https://github.com/ThibaultFillion/strengths

    +

    The documentation includes tutorials and an API reference. The + tutorials demonstrate how to define reaction-diffusion systems by + taking advantage of STReNGTHS’s different features (environments, + chemostats, boundary conditions, etc.) as well as how to carry out + simulations and post-process the trajectories. The API reference + documents the exposed functions and classes.

    +
    + + Conclusions and perspectives +

    STReNGTHS is a new integrated and flexible platform for modeling + and simulation of inhomogeneous reaction-diffusion systems, which aims + to provide an extensible collection of stochastic and deterministic + simulation engines. It has been designed to be easily integrated with + new tools and we do hope it will continue to grow. Perspectives for + future developments include:

    + + +

    developing CPU-GPU massively parallel implementations of the + existing simulation methods,

    +
    + +

    implementing methods with dynamically adaptive time steps,

    +
    + +

    implementing methods combining stochastic and deterministic + approaches for faster simulations, and

    +
    + +

    developing a GUI that would facilitate the design of the + reaction-diffusion system layouts.

    +
    +
    +
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