9 research outputs found
On the Statistics of Reaction-Diffusion Simulations for Molecular Communication
A molecule traveling in a realistic propagation environment can experience
stochastic interactions with other molecules and the environment boundary. The
statistical behavior of some isolated phenomena, such as dilute unbounded
molecular diffusion, are well understood. However, the coupling of multiple
interactions can impede closed-form analysis, such that simulations are
required to determine the statistics. This paper compares the statistics of
molecular reaction-diffusion simulation models from the perspective of
molecular communication systems. Microscopic methods track the location and
state of every molecule, whereas mesoscopic methods partition the environment
into virtual containers that hold molecules. The properties of each model are
described and compared with a hybrid of both models. Simulation results also
assess the accuracy of Poisson and Gaussian approximations of the underlying
Binomial statistics.Comment: 6 pages, 1 table, 10 figures. Submitted to the 2nd ACM International
Conference on Nanoscale Computing and Communication (ACM NANOCOM 2015) on May
16, 201
Multi-Scale Stochastic Simulation for Diffusive Molecular Communication
Recently, hybrid models have emerged that combine microscopic and mesoscopic
regimes in a single stochastic reaction-diffusion simulation. Microscopic
simulations track every individual molecule and are generally more accurate.
Mesoscopic simulations partition the environment into subvolumes, track when
molecules move between adjacent subvolumes, and are generally more
computationally efficient. In this paper, we present the foundation of a
multi-scale stochastic simulator from the perspective of molecular
communication, for both mesoscopic and hybrid models, where we emphasize
simulation accuracy at the receiver and efficiency in regions that are far from
the communication link. Our multi-scale models use subvolumes of different
sizes, between which we derive the diffusion event transition rate. Simulation
results compare the accuracy and efficiency of traditional approaches with that
of a regular hybrid method and with those of our proposed multi-scale methods.Comment: 7 pages, 2 tables, 6 figures. Will be presented at the 2015 IEEE
International Conference on Communications (ICC) in June 201
Fractional diffusion emulates a human mobility network during a simulated disease outbreak
From footpaths to flight routes, human mobility networks facilitate the
spread of communicable diseases. Control and elimination efforts depend on
characterizing these networks in terms of connections and flux rates of
individuals between contact nodes. In some cases, transport can be
parameterized with gravity-type models or approximated by a diffusive random
walk. As a alternative, we have isolated intranational commercial air traffic
as a case study for the utility of non-diffusive, heavy-tailed transport
models. We implemented new stochastic simulations of a prototypical
influenza-like infection, focusing on the dense, highly-connected United States
air travel network. We show that mobility on this network can be described
mainly by a power law, in agreement with previous studies. Remarkably, we find
that the global evolution of an outbreak on this network is accurately
reproduced by a two-parameter space-fractional diffusion equation, such that
those parameters are determined by the air travel network.Comment: 26 pages, 4 figure
A Novel A Priori Simulation Algorithm for Absorbing Receivers in Diffusion-Based Molecular Communication Systems
A novel a priori Monte Carlo (APMC) algorithm is proposed to accurately
simulate the molecules absorbed at spherical receiver(s) with low computational
complexity in diffusion-based molecular communication (MC) systems. It is
demonstrated that the APMC algorithm achieves high simulation efficiency since
by using this algorithm, the fraction of molecules absorbed for a relatively
large time step length precisely matches the analytical result. Therefore, the
APMC algorithm overcomes the shortcoming of the existing refined Monte Carlo
(RMC) algorithm which enables accurate simulation for a relatively small time
step length only. Moreover, for the RMC algorithm, an expression is proposed to
quickly predict the simulation accuracy as a function of the time step length
and system parameters, which facilitates the choice of simulation time step for
a given system. Furthermore, a rejection threshold is proposed for both the RMC
and APMC algorithms to significantly save computational complexity while
causing an extremely small loss in accuracy.Comment: 11 pages, 14 figures, submitted to IEEE Transactions on
NanoBioscience. arXiv admin note: text overlap with arXiv:1803.0463
Symmetry breaking in a bulk-surface reaction-diffusion model for signaling networks
Signaling molecules play an important role for many cellular functions. We
investigate here a general system of two membrane reaction-diffusion equations
coupled to a diffusion equation inside the cell by a Robin-type boundary
condition and a flux term in the membrane equations. A specific model of this
form was recently proposed by the authors for the GTPase cycle in cells. We
investigate here a putative role of diffusive instabilities in cell
polarization. By a linearized stability analysis we identify two different
mechanisms. The first resembles a classical Turing instability for the membrane
subsystem and requires (unrealistically) large differences in the lateral
diffusion of activator and substrate. The second possibility on the other hand
is induced by the difference in cytosolic and lateral diffusion and appears
much more realistic. We complement our theoretical analysis by numerical
simulations that confirm the new stability mechanism and allow to investigate
the evolution beyond the regime where the linearization applies.Comment: 21 pages, 6 figure
Algorithm for Mesoscopic Advection-Diffusion
In this paper, an algorithm is presented to calculate the transition rates
between adjacent mesoscopic subvolumes in the presence of flow and diffusion.
These rates can be integrated in stochastic simulations of reaction-diffusion
systems that follow a mesoscopic approach, i.e., that partition the environment
into homogeneous subvolumes and apply the spatial stochastic simulation
algorithm (spatial SSA). The rates are derived by integrating Fick's second law
over a single subvolume in one dimension (1D), and are also shown to apply in
three dimensions (3D). The proposed algorithm corrects the derived rates to
ensure that they are physically meaningful and it is implemented in the AcCoRD
simulator (Actor-based Communication via Reaction-Diffusion). Simulations using
the proposed method are compared with a naive mesoscopic approach, microscopic
simulations that track every molecule, and analytical results that are exact in
1D and an approximation in 3D. By choosing subvolumes that are sufficiently
small, such that the Peclet number associated with a subvolume is sufficiently
less than 2, the accuracy of the proposed method is comparable with the
microscopic method, thus enabling the simulation of
advection-reaction-diffusion systems with the spatial SSA.Comment: 12 pages, 9 figures. Submitted to IEEE Transactions on NanoBioscienc
Coupled mesoscopic and microscopic simulation of stochastic reaction–diffusion processes in mixed dimensions
We present a new simulation algorithm that allows for dynamic switching between a mesoscopic and a microscopic modeling framework for stochastic reaction-diffusion kinetics. The more expensive and more accurate microscopic model is used only for those species and in those regions in space where there is reason to believe that a microscopic model is needed to capture the dynamics correctly. The microscopic algorithm is extended to simulation on curved surfaces in order to model reaction and diffusion on membranes. The accuracy of the method on and near a spherical membrane is analyzed and evaluated in a numerical experiment. Two biologically motivated examples are simulated in which the need for microscopic simulation of parts of the system arises for different reasons. First, we apply the method to a model of the phosphorylation reactions in a MAPK signaling cascade where microscale methods are necessary to resolve fast rebinding events. Then a model is considered for transport of a species over a membrane coupled to reactions in the bulk. The new algorithm attains an accuracy similar to a full microscopic simulation by handling critical interactions on the microscale, but at a significantly reduced cost by using the mesoscale framework for most parts of the biological model
Numerical Methods for the Chemical Master Equation
The dynamics of biochemical networks can be described by a Markov jump process on a high-dimensional state space, with the corresponding probability distribution being the solution of the Chemical Master Equation (CME). In this thesis, adaptive wavelet methods for the time-dependent and stationary CME, as well as for the approximation of committor probabilities are devised. The methods are illustrated on multi-dimensional models with metastable solutions and large state spaces