Geometric Algorithms and Data Structures for Simulating Diffusion Limited Reactions

Radiation therapy is one of the most effective means for treating cancers. An important calculation in radiation therapy is the estimation of dose distribution in the treated patient, which is key to determining the treatment outcome and potential side effects of the therapy. Biological dose — the level of biological damage (e.g., cell killing ratio, DNA damage, etc.) inflicted by the radiation is the best measure of treatment quality, but it is very difficult to calculate. Therefore, most clinics today use physical dose - the energy deposited by incident radiation per unit body mass - for planning radiation therapy, which can be calculated accurately using kinetic Monte Carlo simulations. Studies have found that physical dose correlates with biological dose, but exhibits a very complex relationship that is not yet well understood. Generally speaking, the calculation of biological dose involves four steps: (1) the calculation of physical dose distribution, (2) the generation of radiochemicals based on the physical dose distribution, (3) the simulation of interactions between radiochemicals and bio-matter in the body, and (4) the estimation of biological damage based on the distribution of radiochemicals. This dissertation focuses on the development of a more efficient and effective simulation algorithm to speed up step (3). The main contribution of this research is the development of an efficient and effective kinetic Monte Carlo (KMC) algorithm for simulating diffusion-limited chemical reactions in the context of radiation therapy. The central problem studied is - given n particles distributed among a small number of particle species, all allowed to diffuse and chemically react according to a small number of chemical reaction equations - predict the radiochemical yield over time. The algorithm presented makes use of a sparse grid structure, with one grid per species per radiochemical reactant used to group particles in a way that makes the nearest neighbor search efficient, where particles are stored only once, yet are represented in grids of all appropriate reaction radii. A kinetic data structure is used as the time stepping mechanism, which provides spatially local updates to the simulation at a frequency which captures all events - retaining accuracy. A serial and three parallel versions of the algorithm have been developed. The parallel versions implement the kinetic data structure using both a standard priority queue and a treap data structure in order to investigate the algorithms scalability. The treap provides a way for each thread of execution to do more work in a particular region of space. A comparison with a spatial discretization variant of the algorithm is also provided

Simulated single molecule microscopy with SMeagol

SMeagol is a software tool to simulate highly realistic microscopy data based on spatial systems biology models, in order to facilitate development, validation, and optimization of advanced analysis methods for live cell single molecule microscopy data. Availability and Implementation: SMeagol runs on Matlab R2014 and later, and uses compiled binaries in C for reaction-diffusion simulations. Documentation, source code, and binaries for recent versions of Mac OS, Windows, and Ubuntu Linux can be downloaded from http://smeagol.sourceforge.net.Comment: v2: 14 pages including supplementary text. Pre-copyedited, author-produced version of an application note published in Bioinformatics following peer review. The version of record, and additional supplementary material is available online at: https://academic.oup.com/bioinformatics/article-lookup/doi/10.1093/bioinformatics/btw10

Hierarchical fractional-step approximations and parallel kinetic Monte Carlo algorithms

We present a mathematical framework for constructing and analyzing parallel algorithms for lattice Kinetic Monte Carlo (KMC) simulations. The resulting algorithms have the capacity to simulate a wide range of spatio-temporal scales in spatially distributed, non-equilibrium physiochemical processes with complex chemistry and transport micro-mechanisms. The algorithms can be tailored to specific hierarchical parallel architectures such as multi-core processors or clusters of Graphical Processing Units (GPUs). The proposed parallel algorithms are controlled-error approximations of kinetic Monte Carlo algorithms, departing from the predominant paradigm of creating parallel KMC algorithms with exactly the same master equation as the serial one. Our methodology relies on a spatial decomposition of the Markov operator underlying the KMC algorithm into a hierarchy of operators corresponding to the processors' structure in the parallel architecture. Based on this operator decomposition, we formulate Fractional Step Approximation schemes by employing the Trotter Theorem and its random variants; these schemes, (a) determine the communication schedule} between processors, and (b) are run independently on each processor through a serial KMC simulation, called a kernel, on each fractional step time-window. Furthermore, the proposed mathematical framework allows us to rigorously justify the numerical and statistical consistency of the proposed algorithms, showing the convergence of our approximating schemes to the original serial KMC. The approach also provides a systematic evaluation of different processor communicating schedules.Comment: 34 pages, 9 figure

Stochastic kinetics of viral capsid assembly based on detailed protein structures

We present a generic computational framework for the simulation of viral capsid assembly which is quantitative and specific. Starting from PDB files containing atomic coordinates, the algorithm builds a coarse grained description of protein oligomers based on graph rigidity. These reduced protein descriptions are used in an extended Gillespie algorithm to investigate the stochastic kinetics of the assembly process. The association rates are obtained from a diffusive Smoluchowski equation for rapid coagulation, modified to account for water shielding and protein structure. The dissociation rates are derived by interpreting the splitting of oligomers as a process of graph partitioning akin to the escape from a multidimensional well. This modular framework is quantitative yet computationally tractable, with a small number of physically motivated parameters. The methodology is illustrated using two different viruses which are shown to follow quantitatively different assembly pathways. We also show how in this model the quasi-stationary kinetics of assembly can be described as a Markovian cascading process in which only a few intermediates and a small proportion of pathways are present. The observed pathways and intermediates can be related a posteriori to structural and energetic properties of the capsid oligomers

3D mesh processing using GAMer 2 to enable reaction-diffusion simulations in realistic cellular geometries

Recent advances in electron microscopy have enabled the imaging of single cells in 3D at nanometer length scale resolutions. An uncharted frontier for in silico biology is the ability to simulate cellular processes using these observed geometries. Enabling such simulations requires watertight meshing of electron micrograph images into 3D volume meshes, which can then form the basis of computer simulations of such processes using numerical techniques such as the Finite Element Method. In this paper, we describe the use of our recently rewritten mesh processing software, GAMer 2, to bridge the gap between poorly conditioned meshes generated from segmented micrographs and boundary marked tetrahedral meshes which are compatible with simulation. We demonstrate the application of a workflow using GAMer 2 to a series of electron micrographs of neuronal dendrite morphology explored at three different length scales and show that the resulting meshes are suitable for finite element simulations. This work is an important step towards making physical simulations of biological processes in realistic geometries routine. Innovations in algorithms to reconstruct and simulate cellular length scale phenomena based on emerging structural data will enable realistic physical models and advance discovery at the interface of geometry and cellular processes. We posit that a new frontier at the intersection of computational technologies and single cell biology is now open.Comment: 39 pages, 14 figures. High resolution figures and supplemental movies available upon reques

Numerical study of the coupling between reaction and mass transfer for liquid-liquid slug flow in square microchannels

While the benefits of miniaturisation on processes have been widely demonstrated, its impact on microfluidics and local mechanisms such as mass transfer is still little understood. The aim of this work is to simulate coupling between reaction and mass transfer in microchannels for liquid-liquid slug flow. First, the extrapolation to confined flow of the classical model used to calculate interfacial mass fluxes in reactive infinite media was studied. This model consists in estimating transferred fluxes between two phases as a function of the enhancement factor E. Its expression depends on the model used to represent interfacial mass transfer. In infinite media, Lewis and Whitman’s stagnant film theory is generally preferred for its simplicity and its reliability. In the case of confined slug flow, the limitation of such a model to predict interfacial fluxes is highlighted. Secondly, the case of liquid-liquid competitive consecutive reactions in microchannels is considered. This work emphasizes the unfavourable impact of the length between droplets on selectivity. This is a direct consequence of mass transport mechanisms in microchannels