Kondrat, S., O. Zimmermann, W. Wiechert, and E. von Lieres,
Eur. Phys. J. E 39:11, 2016
In many soft and biological physics applications, there are multiple distinct time and length scales.
For example, enzymes are large, move slowly, and are few, while metabolites are small, fast, and abundant.
The authors addressed this with a new hybrid simulation method, which is stochastic-deterministic and discrete-continuous.
They demonstrate it by modelling enzyme-catalysed reactions with discrete enzymes and continuous metabolites (see figure).
They validated their method by comparing simulation results from their new method against those from Smoldyn.
Meinecke, L. and M. Eriksson,
Simulations with off-lattice Brownian dynamics (e.g. Smoldyn) are computationally expensive in
crowded environments. This paper investigates the extent to which on-lattice simulations can
simulate reactions and diffusion in the presence of crowders. The authors show that diffusion is
slowed down in the off-lattice model since randomly distributed obstacles effectively exclude more volume than those
ordered on an artificial grid. Crowded reaction rates can be both increased and decreased by the grid structure. Grid
artifacts increase with increasing crowder density. The authors conclude that the computationally more efficient on-lattice
simulations are accurate only for low crowder densities.
This paper presents a multiscale approach to modeling diffusion and reactions rates in a crowded environment.
The method combines jumping according to local first exit times and jumping on a coarser Cartesian grid. Excluded volume
is modeled by a diffusion equation with space-dependent diffusion coefficients. Simulations showed that crowding molecule
shape and size play a crucial role in the effects on diffusive motion. They also showed that molecular crowding can
enhance or inhibit chemical reactions depending on local obstacle density fluctuations.
Andrews, S.S., S.N.V. Arjunan, G. Balbo, A.T. Bittig, J. Feret, K. Kaizu, and F. Liu,
In D. Gilbert, M. Heiner, K. Takahashi, and A.M. Uhrmacher, eds.
Multiscale Spatial Computational Systems Biology 170-187, 2015
The authors investigated the effect of macromolecular crowding on reaction rates using 5 different simulators,
both to develop a better understanding of the topic and to compare the simulators. The eGFRD algorithm was presumably
very accurate but ran very slowly, Smoldyn and NL-space worked well although Smoldyn appeared to
produce more accurate results, Spatiocyte was very fast but results had lattice artifacts, and KaSim worked, which was
remarkable because it is typically a non-spatial method. The Smoldyn results (figure) agreed with qualitative expectations
but showed that the theory that the authors investigated was incorrect.
Bates, J., I. Teh, P. Kohl, J.E. Schneider, and V. Grau,
Lecture Notes In Computer Science 9126:120-128, 2015
Diffusion MRI (magnetic resonance imaging) is a non-invasive experimental method for visualizing diffusion in tissues,
in this case in rat heart tissue. Here, the authors modeled this method using Smoldyn and found close correspondance
between model and experimental results. Next, they used the simulations to test the method sensitivity. They found
that the diffusivity has the greatest effect and the cross-sectional area and aspect ratio of cells are important, but
the cell length and volume fraction of cells had no marked effect.
Subburaj, Y., K. Cosentino, M. Axmann, E. Pedrueza-Villalmanzo, E. Hermann, S. Bleicken, J. Spatz, and A.J. García-Sáez,
Nature Comm. 6:8042, 2015
Bax is a key regulator of apoptosis, mediating cytochrome c release to the cytosol via oligomerization in the
outer mitochondrial membrane. These authors investigated the molecular mechanism of Bax assembly and regulation by
other Bcl-2 members. They found that Bax binds to the membrane in a monomeric state and then rapidly self-assembles.
They also show that other proteins, cBid and Bcl-xL, help drive Bax activity. Based on these experimental results, they
developed a theoretical model, using Smoldyn, which presents a new mechanism for the molecular pathway of Bax assembly
to form the apoptotic pore.
Xiaji Liu, Erik S. Welf, and Jason M. Haugh,
J. R. Soc. Interface 12:20141412, 2015
These researchers experimentally investigated T lymphocyte motility, which is similar to ameboid motility.
They found that cells typically turn by first creating a bifurcation of the lamellipodium at the cell's
leading edge and then following one of the new projections. They proposed a model of the major interactions
in this process. Simulation with Smoldyn (shown in the figure) agreed with their experimental results. The figure
shows the cell rear in beige and bifurcated actin regions in green.
Robert G. Endres,
PLoS ONE 10:e0121681, 2015
Many cell systems, including cell cycle ones and some signaling ones, are bistable. This has been studied most often
using deterministic and/or non-spatial models. This paper used Smoldyn models to investigate the more physiologically relevent case, which
is for stochastic chemical reactions in the confined 3-dimensional volume of a cell, considering both bacteria and
eukaryotic cells. The author finds that bistability is fragile in these conditions, often requiring finely tuned parameters,
small volumes, and fast diffusion coefficients. Switching can occur upon cell growth.
Hugo G. Schmidt, Sven Sewitz, Steven S. Andrews, and Karen Lipkow,
PLoS ONE 9:e108575, 2014
Transcription factors and other DNA binding proteins find their DNA binding sites faster than simple 3D diffusion allows.
These authors explored this acceleration with Smoldyn models. As in prior work, they found that non-specific DNA binding
followed by 1D sliding reduces finding times. They also found that intersegmental transfer, in which a transcription factor
that is non-specifically bound to DNA simultaneously binds a separate DNA loop and then releases the first binding site,
is also effective. Finally, they found that DNA binding proteins are enriched in dimers and tetramers, perhaps because this
favors intersegmental transfer.
Daniel E. Strongin, Mark Groudine, Joan C. Ritland Politz,
Nucleus 5:474-481, 2014
The genome is spatially organized within the eukaryotic nucleus. One aspect of this is that gene loci on different chromosomes
can preferentially colocalize. Using mouse strains that have different gene arragements on their chromosomes,
these authors investigated the driving force behind the colocalization of the IgH and Myc loci. They found
that it arose when both loci were on chromosomes that had nucleolar organizer regions (NORs). These are sites of ribosomal
DNA repeat sequences, which nucleate nucleoli. Together with simulations, these results implied that chromosome tethering
to nucleoli can help colocalize genes. The figure shows one chromosome in yellow, another in blue, and nucleoli in red,
in a strain where colocalization occurs.
H. Arthur Woods,
J. Experiment. Biol. 217:35-45, 2014
In this paper, the author proposes that stochastic variation during organismal development causes physiological
diversity within a single individual. He calls this mosaic physiology. This article reviews known mechanisms by which
stochastic effects arise in, and are controlled by, biological systems. It then goes on to show how then can give rise
to mosaic physiology. This provides a set of diversified phenotypes within single organisms, which may help the organism
to cope with novel environmental challenges. The figure shows stochastic effects in receptor-ligand binding, a simple
example of biological stochasticity.
Jacek T. Mika, Paul E. Schavemaker, Victor Krasnikov, Bert Poolman,
Mol. Microbiol. 94:857-870, 2014
Proteins diffuse many times slower inside cells than they do in aqueous solutions due to macromolecular
crowding, non-specific binding, and hydrodynamic effects. This has been investigated most thoroughly in E.
coli, a Gram-negative bacterium. The authors investigated diffusion in L. lactis, a Gram-positive bacterium
here. They found similar diffusion coefficients and similar cell-to-cell variation in unstressed cells, but a smaller
increase upon osmotic challenge (as expected due to a higher turgor pressure). They measured intracellular diffusion with FRAP
methods, which they validated with Smoldyn simulations (figure).
Matthew L. Robb and Vahid Shahrezaei,
PLOS One 9:e103636, 2014
Bacteriophage lambda is a classic system for studying cellular decision making. Upon infection, lambda can adopt the
lytic state in which it reproduces rapidly in the bacterium causing cell death and the release of virus, or it can adopt
the lysogenic state in which it incorporates itself into the cell genome; later, it may stochastically return to the lytic
state. This decision is made through a genetic switch, shown in the figure. These authors extended prior work by
investigating the role of the cell volume and bacterial growth rate on the decision. They also investigated spatial
effects, which arise primarily from the slow diffusion of mRNA across a bacterium (about 10 minutes), finding that
spatial effects were minimal.
Eder Zavala and Tatiana T. Marquez-Lago,
PLoS Comp. Biol. 10:e1003725, 2014
Yeast cells retain their nuclear membranes during cell division, in a processs called closed mitosis. Membrane-bound proteins
segregate aysmmetrically in the process, with some getting localized in the mother cell and others in the bud (dots in
the figure). These authors explored mechanisms by which yeast cells might prevent protein diffusion across the division plane,
and hence maintain the localization. They found that a combination of protein rings and sphingolipid domains is
necessary during early anaphase, but that sphingolipid domains alone are adequate during late anaphase (figure), due to the
elongated nuclear neck.
Max Hoffmann and Ulrich S. Schwarz,
Soft Matter 10:2388, 2014
One way in which E. coli bacteria find their mid-planes, so that cell division yields two equal size daughter
cells, is with spatiotemporal oscillations of the Min proteins. These proteins oscillate from pole to pole, with
minimal occupancy of the mid-plane. The simplicity and remarkable dynamics of this system has made it popular for
spatial stochastic simulations. These authors investigated Min system operation in artificial micropatterned environments
and in mutant filamentous cells, such as the one shown in the figure. This work highlights the robustness and variability
of Min system oscillations, puts limits on the effect of putative division sites, and provides a computational framework
for future studies.
Steven A. Frank,
Biology Direct 8:31, 2013
This paper discusses relations among Michaelis-Menten kinetics, the Hill equation, and biological information processing.
A central question that the paper probes regards why Michaelis-Menten kinetics leads to linear input-output relations
for low signal levels, but the Hill equation exhibits logarithmic sensitivity at these levels. This paper has numerous
misconceptions and non-standard terminology but nevertheless presents some intriguing points. A particularly interesting
result is that dose-response curve for the Michaelis-Menten reaction, which normally exhibits Hill equation behavior with Hill
coefficient of 1, becomes ultrasensitive when reactions are substantially diffusion influenced, as shown in the figure.
Meghan McCabe Pryor, Shalini T. Low-Nam, Ádám M. Halász, Diane S. Lidke, Bridget S. Wilson, and Jeremy S. Edwards,
Biophys. J. 105:1533-1543, 2013
ErbB1 (epidermal growth factor receptor) is an important receptor for growth and development, and its overexpression can
cause cancer. These authors built on their prior erbB1 single molecule tracking experiments to build a spatial stochastic model for erbB1
diffusion, dimerization, kinase activation, and phosphorylation. The figure shows erbB1 dimerization. The model yields new
insight into the activation states of individual erbB1 monomers. For the most part, the authors used their own reimplementation of Smoldyn's
algorithms, although they also used the Smoldyn for part of the research as well.
Günther Gerisch, Mary Ecke, Ralph Neujahr, Jana Prassler, Andreas Stengl, Max Hoffmann, Ulrich S. Schwarz and Eberhard Neumann,
J. Cell Science 127:4507-4517, 2013
Electric pulses induce Dictyostelium discoideum cells to fuse. The authors combined electron microscopy,
fluorescence microscopy, and simulation to study the fusion pores and actin localization that arise in the membrane
during cell fusion. They found that the plasma membranes of the contiguous cells become tangles of highly bent and
interdigitated membranes. By imaging GFP diffusion from one cell to its neighbor, and then modeling this diffusion with
Smoldyn simulations as shown in the figure, they found that membranes persist in a fusogenic state for up to 24 seconds
before pores of about 3 nm are formed.
T.T. Marquez-Lago, A. Leier, and K. Burrage,
IET Syst. Biol. 6:134-142, 2012
The study compares both fractional Brownian motion and continuous time random walks and highlights how
well they can represent different types of spatial crowding and physical obstacles. Although diffusion around
immovable obstacles could be reasonably characterised by a single Hurst exponent, the authors found that diffusion in
a crowded environment seemed to exhibit multifractional properties in the form of a different short- and
long-time behaviors. The figure shows a 2-dimensional crowded environment, developed with the Smoldyn utility
Barbara Boettcher, Tatiana T. Marquez-Lago, Mathias Bayer, Eric L. Weiss, and Yves Barral,
J. Cell Biol. 197:921-937, 2012
The authors investigated the establishment and maintenance of asymmetric cell division in budding yeast. Here,
unlike in mammalian cells, the nuclear envelope is maintained during cell division, and divides at about the same
time as the cell membrane. Using photobleaching and Smoldyn simulations, they found that diffusion barriers
compartmentalize the nuclear membranes, whereas protein diffusion was well explained by the dumbbell shape of the
anaphase nucleus. The figure shows a dividing cell with the nucleoplasmic GFP in green and mCherry-Tub1 spindles
Khan, S., T.S. Reese, N. Rajpoot, and A. Shabbir, J. Comput. Neurosci.
The authors investigated the sequestration of calcium calmodulin dependent kinase (CaMKII) in neural
dendritic spines, which is a key cellular mechanism for the formation and storage of memories. The
figure shows confocal microscopy data of GFP-CamKII localization shortly the GFP was photo-activated at
the asterisk; bright green regions, such as at the spine tip, indicate CamKII sequestration, while red
regions indicate low CamKII concentrations. Smoldyn simulations showed that a major cause of sequestion
is the high number of cytoskeletal binding sites at spine tips, rather than high binding affinities.
Leier, A. and T.T. Marquez-Lago, J. Chem. Phys. 135:134109, 2011
The two primary methods for simulating chemical reactions and diffusion are continuous-space single particle
methods, like Smoldyn uses, and lattice-based reaction-diffusion master equation (RDME) methods. The
latter are typically more efficient but can suffer from several artifacts. In this work, the authors presented
an accurate RDME method for simulating reactive boundary conditions, which they validated using Smoldyn.
The figure shows simulation results from their methods in black, analytical results in red, and Smoldyn
results in gray.
Jilkine, A., S.B. Angenent, L.F. Wu, and S.J. Altschuler, PLoS Comput. Biol.
Many cell types, including budding yeast, mammalian neutrophils, and amoeba, can spontaeously polarize in
the absence of spatial cues. The authors propose that this polarization arises from positive feedback; it
robustly maintains an off state at low concentrations of signaling molecules, and then switches to highly
localized signaling clusters at higher concentrations. The figures show that in their model, increasing
signaling molecule concentrations (right panel vs. left panel) leads to clusters of molecules that are in
their active states (red).
Singh, P., A.J. Hockenberry, V. Tiruvadi, and D.F. Meaney, PLoS Comput. Biol.
Neural NMDA receptors mediate many physiological functions, including the molecular basis for learning and
memory. These receptors exist in various subtypes, which enables them to discriminate between different types
of signals. Using Smoldyn models, the authors found that different receptors have different
dynamic ranges, that specific subtypes dominate in long-term depression and long-term potentiation situations,
and that the content of a specific subtype enhances response magnitude and fidelity during long-term potentiation.
The yellow and red portions of the figure show pre- and post-synaptic regions, while dots represent receptors.
Khan, S., Y. Zou, A. Amjad, A. Gardezi, C.L. Smith, C. Winters, T.S. Reese, J. Comput.
Neurosci. 31:581-594, 2011
This work investigated the sequestration of calcium dependent kinase II (CamKII) in neural dendritic spines
following synaptic stimulation. It looked at the effects of spine geometry on CamKII diffusion, binding of
CamKII to the post-synaptic density, to the cytoskeleton, and to other CamKII proteins. Simulation results
compared favorably with microscopy experiments. This work showed that self-aggregation of CamKII could provide
a switch that amplifies CamKII sequestration and regulates its activity.
Dushek, O., P.A. van der Merwe, and V. Shahrezaei, Biophys. J. 100:1189-1197, 2011
The authors showed that multiple phosphorylation sites on a single protein
can produce switch-like responses when reactions between proteins are limited by diffusion.
This is the case for many reactions that occur on the plasma membrane. The figure shows that
ultrasensitivity increases with as the number of protein phosphorylation sites increase.
Oliveira, R.F., A. Terrin, G. Di Benedetto, R.C. Cannon, W. Koh, M. Kim, M. Zaccolo, and K.T. Blackwell,
PLoS ONE 5:e11725, 2010
This work investigates mechanisms that increase the local concentration of cyclic AMP (cAMP), which is essential for
normal neural functioning, including for synaptic plasticity. To do so, the authors developed a new spatial simulator
called NeuroRD, which is a compartment-based simulator. It combines the spatial Gillespie method with tau-leaping and
a new diffusion algorithm. The authors validated NeuroRD by comparing results against mass action theory and against
Smoldyn simulations. These comparisons are shown in the figure.
Andrews, S.S., N.J. Addy, R. Brent, and A.P. Arkin, PLoS Comp. Biol. 6:e1000705, 2010
The authors investigated mating pheromone signaling between yeast cells. A central "receiver" cell is covered
with receptors that bind mating pheromone, which is secreted by surrounding "sender" cells (in the figure, unbound
receptors are blue, bound receptors are red, and pheromone is green). This work showed that the central cell can better
locate strong pheromone emitting cells when the central cell secretes a pheromone-degrading protease because
the protease cloud sharpens the local pheromone gradient.
DePristo, M.A., L. Chang, R.D. Vale, S.M. Khan, and K. Lipkow, Prog. Biophys. Mol. Biol. 100:25-32, 2009
The authors used simulations to analyze and quantify experimental Fluorescence Recovery After Photobleaching
(FRAP) data for proteins in the E. coli chemotaxis system. They quantified protein diffusion
coefficients of 2 μm2/s and assessed turnover rates between
cytoplasmic proteins and membrane-associated protein clusters. The figure shows simulated CheY-YFP fluorescence in
a protein cluster as it is photobleached and then recovers from protein exchange. In general, simulations
can be useful tools for the quantitative analysis of fluorescent microscopy experiments.
Lipkow, K. and D.J. Odde, Cell. Mol. Bioeng. 1:84-92, 2008
Using simulations, the authors showed that several of the E. coli chemotaxis proteins (CheY and CheZ)
likely have stable protein concentration gradients across the length of cells. This arises from protein activation
that is localized to one cell pole and activation-dependent protein complexation that affects protein
diffusion coefficients. These mechanisms, and similar ones, occur for many other proteins as well, so stable
protein concentration gradients within cells are likely to be widespread.
Grati, M., M.E. Schneider, K. Lipkow, E.E. Strehler, R.J. Wenthold, and B. Kachar,
J. Neuroscience 26:6386-6395, 2006
This work combined experimental and modeling approaches to investigate membrane protein turnover in stereocilia
(fine hairs in the inner ear that convert mechanical motion to electrical signals) to better understand
stereocilia recovery from trauma, such as loud noises. The authors focused on the spatial distribution, mobility,
and trafficking of the PMCA2 protein, which is both abundant and essential to stereocilia function. They found
that PMCA2 exhibits rapid turnover, which supports other evidence that stereocilia undergo rapid continuous renewal.
The figure shows PMCA2 (green dots) distribution on an unrolled stereocilia membrane over time.
Andrews, S.S. and A.P. Arkin, Current Biology 16:R523-R527, 2006
This is a primer on how to simulate cell biology systems. It presents the basics of ODE (ordinary differential
equation) modeling, stochastic modeling, spatial modeling, and spatial-stochastic modeling. Of particular
interest, it presents simulations of the same Lotka-Volterra predator-prey system that used each of the different
methods. The results differ dramatically. Deterministic simulations show nearly sinusoidal oscillations,
non-spatial stochastic simulations show oscillations with increasing amplitudes, and particle-tracking
(Smoldyn; figure show here) simulations show a characteristic boom-and-bust pattern.
Lipkow, K., PLoS Comp. Biol. 2:e39, 2006
In the E. coli chemotaxis system, the CheY messenger protein is phosphorylated at a receptor
cluster near one cell pole and is dephosphorylated by the CheZ protein. The author used simulations
to explore the signaling behaviors that arise with different CheZ localizations. She found that the model
that best agreed with experiments included CheZ proteins that oligomerize and localize to the receptor
cluster upon cellular stimulation. The black dots in the figure are CheZ oligomers (also, pink dots are CheY, red
are CheYp, and green are non-oligomeric CheZ). This creates a negative feedback loop which improves
system precision, robustness, and adaptation.
Lipkow, K., S.S. Andrews, and D. Bray, J. Bact. 187:45-53, 2005
The authors developed a spatial stochastic simulation of the central E. coli chemotaxis system. It
includes the core proteins and reactions, a polar-localized receptor cluster, and several flagellar motors
in the cell membrane. Increasing cytoplasmic crowding, due to ribosomes and other macromolecules, resulted
in slower protein diffusion, steepened concentration gradients, and substantial differences in signal
propagation delays to motors at different positions (figure).
Andrews, S.S., BioRxiv
This article presents a new approach to rule-based modeling, which is a method for automatically generating new chemical
species for modified and complexed molecules. This approach is based on wildcards that match to species names,
much as wildcards can match to file names in computer operating systems. It is simple to use and remarkably powerful.
This article demonstrates the approach through examples for: signaling systems, protein complexation, polymerization,
nucleic acid sequence copying and mutation, the "SMILES" chemical notation, and others. It is implemented in Smoldyn
for both the generate-first and on-the-fly expansion.
Andrews, S.S., Bioinformatics 33:710, 2017
This paper describes several additions to the Smoldyn software. Smoldyn now supports rule-based modeling with a
convenient wildcard method, and also with the BioNetGen package with extensions for spatial simulation.
New algorithms for simulating the diffusion of surface-bound molecules and molecules with excluded volume provide
excellent accuracy (figure). In addition, Smoldyn supports single-molecule tracking simulations. Finally, the Smoldyn source
code can be accessed through a C/C++ language library interface.
Seeliger, C. and N. Le Novère, BMC Res. Notes 8:752, 2015
The authors added support for diffusion coefficients of surface-bound molecules to depend on the surface
to which the molecule is bound. For example, in the figure, certain surface-bound molecules diffuse more
slowly within the blue region of the surface than in other portions of the surface. This is useful for
simulating lipid rafts or similar structures. Unfortunately, this addition is not included in the current
Smoldyn release, but only in the authors' modification of Smoldyn 2.22, which is otherwise largely obsolete.
Robinson, M., S.S. Andrews, and R. Erban, Bioinformatics 31:2406-2408, 2015
The authors integrated a lattice-based simulation solver with Smoldyn's existing particle-based simulations.
This is an adjacent-space type of hybrid method, meaning that different regions of space get simulated with
different levels of detail. They used recently devloped methods (by Flegg and Erban) to address the boundary
between two different simulation regions. This accelerates simulations several-fold. It is very easy to use.
Andrews, S.S., In Bacterial Molecular Networks: Methods and Protocols,
van Helden at al. (eds.) Methods in Molecular Biology 804:519-542, 2012
This paper describes the use of the Smoldyn simulation program. It focuses on the basic concepts, while
leaving syntax details to the Smoldyn User's Manual. This figure was taken from an example
simulation that presents the use of reactions, molecule-surface interactions, compartments, and other
Smoldyn features. This paper presents an especially useful Notes section that gives suggestions on choosing
simulation parameters (e.g. diffusion coefficient and reaction rates) and methods for improving
Dematté, L., IEEE Trans. Comput. Biol. Bioinform. 9:655-667, 2012
This is a more thorough presentation of the work described below by the same author. In brief, he parallelized
the core Smoldyn code to run on Graphics Processing Units (GPUs), thus accelerating it 130-fold.
Gladkov, D.V., S. Alberts, R.M. D'Souza, and S. Andrews, Proceedings of the
19th High Performance Computing Symposia, 2011
The authors accelerated Smoldyn simulations by about 200 fold by parallelizing the core code to run
on Graphics Processing Units (GPUs). This work was performed independently of Dematté's work, listed
below. The figure shows code acceleration for different Smoldyn algorithms. Diffusion has the best performace,
while bimolecular reactions have the worst (but still excellent) performance.
Dematté, L., 2010 Ninth International Workshop on Parallel and
Distributed Methods in Verification/2010 Second International Workshop on High Performance Computing
The author parallelized the core Smoldyn code to run on Graphics Processing Units (GPUs).
This can accelerate simulations by factors of up to 130, thus enabling the efficient simulation
of models that would be impractical to run on conventional computer hardware. The figure explains
efficient memory organization for GPUs.
Andrews, S.S., N.J. Addy, R. Brent, and A.P. Arkin, PLoS Comp. Biol. 6:e1000705, 2010
This paper (which is also listed above) describes the Smoldyn software. It gives an overview of the
software algorithms, features, and performance. It shows that Smoldyn is very accurate, is more than
twice as fast as either MCell or ChemCell, and has a wide range of features. This figure shows the number
of molecules adsorbed to a surface over time for several adsorption coefficients; close accuracy between
simulation data (dots) and theoretical calculations (lines) show Smoldyn's accuracy. The inset shows
that simulation noise matches theoretical calculations.
Andrews, S.S., Phys. Biol. 6:046015, 2009
This paper describes methods for quantitatively simulating the adsorption of molecules to surfaces, the desorption
of molecules from surfaces, and the partial transmission of molecules through surfaces. Central results of the paper
include look-up tables that give a molecule's adsorption or transmission probability based on the surface's adsorption or
transmission coefficient, the molecule's diffusion coefficient, the simulation time step, and the rate of the reverse
desorption or transmission process. Smoldyn uses these algorithms for molecule-surface interactions.
Dobrzynski, M., J.V. Rodríguez, J.A. Kaandorp, and J.G. Blom,
Bioinformatics 23:1969-1977, 2007
The authors compared the three major spatial stochastic simulation methods, which are particle-based methods
(with Smoldyn), spatial Gillespie methods (with GMP), and Green's Function Reaction Dynamics (GFRD; with custom code).
They found that GFRD is most accurate and that the relative accuracy between particle-based and spatial
Gillepsie methods depends on the latter's spatial resolution; with fine resolution, spatial Gillespie methods can
be better than particle-based methods. For systems with many molecules, GFRD is extremely slow, while Smoldyn takes
about twice as long as GMP to yield results with comparable accuracy. The authors noted that particle-based methods
are particularly flexible for creating realistic geometries.
Andrews, S.S. and D. Bray, Phys. Biol. 1:137, 2004
The authors derived several of the central algorithms for particle-based simulation, all designed for
high accuracy and good computational efficiency. Methods are presented for simulating diffusion and
chemical reactions, where the reactions can be 0th, 1st, or 2nd order and they can be irreversible or reversible.
This figure shows one of the paper's central results, which is a look-up table that enables simulated
bimolecular chemical reaction rates (y-axis) to be determined from simulation parameters (x-axis) for
both irreversible (bottom line) and reversible reactions (other lines).