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Chowdhury R, Wan J, Gardier R, Rafael-Patino J, Thiran JP, Gibou F, Mukherjee A. Molecular Imaging with Aquaporin-Based Reporter Genes: Quantitative Considerations from Monte Carlo Diffusion Simulations. ACS Synth Biol 2023; 12:3041-3049. [PMID: 37793076 DOI: 10.1021/acssynbio.3c00372] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/06/2023]
Abstract
Aquaporins provide a unique approach for imaging genetic activity in deep tissues by increasing the rate of cellular water diffusion, which generates a magnetic resonance contrast. However, distinguishing aquaporin signals from the tissue background is challenging because water diffusion is influenced by structural factors, such as cell size and packing density. Here, we developed a Monte Carlo model to analyze how cell radius and intracellular volume fraction quantitatively affect aquaporin signals. We demonstrated that a differential imaging approach based on subtracting signals at two diffusion times can improve specificity by unambiguously isolating aquaporin signals from the tissue background. We further used Monte Carlo simulations to analyze the connection between diffusivity and the percentage of cells engineered to express aquaporin and established a mapping that accurately determined the volume fraction of aquaporin-expressing cells in mixed populations. The quantitative framework developed in this study will enable a broad range of applications in biomedical synthetic biology, requiring the use of aquaporins to noninvasively monitor the location and function of genetically engineered devices in live animals.
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Affiliation(s)
| | | | - Remy Gardier
- Signal Processing Laboratory (LTS5), Ecole Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland
| | - Jonathan Rafael-Patino
- Signal Processing Laboratory (LTS5), Ecole Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland
- Radiology Department, Centre Hospitalier Universitaire Vaudois (CHUV) and University of Lausanne (UNIL), 1005 Lausanne, Switzerland
| | - Jean-Philippe Thiran
- Signal Processing Laboratory (LTS5), Ecole Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland
- Radiology Department, Centre Hospitalier Universitaire Vaudois (CHUV) and University of Lausanne (UNIL), 1005 Lausanne, Switzerland
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Chowdhury R, Wan J, Gardier R, Rafael-Patino J, Thiran JP, Gibou F, Mukherjee A. Molecular imaging with aquaporin-based reporter genes: quantitative considerations from Monte Carlo diffusion simulations. bioRxiv 2023:2023.06.09.544324. [PMID: 37333205 PMCID: PMC10274877 DOI: 10.1101/2023.06.09.544324] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/20/2023]
Abstract
Aquaporins provide a new class of genetic tools for imaging molecular activity in deep tissues by increasing the rate of cellular water diffusion, which generates magnetic resonance contrast. However, distinguishing aquaporin contrast from the tissue background is challenging because water diffusion is also influenced by structural factors such as cell size and packing density. Here, we developed and experimentally validated a Monte Carlo model to analyze how cell radius and intracellular volume fraction quantitatively affect aquaporin signals. We demonstrated that a differential imaging approach based on time-dependent changes in diffusivity can improve specificity by unambiguously isolating aquaporin-driven contrast from the tissue background. Finally, we used Monte Carlo simulations to analyze the connection between diffusivity and the percentage of cells engineered to express aquaporin, and established a simple mapping that accurately determined the volume fraction of aquaporin-expressing cells in mixed populations. This study creates a framework for broad applications of aquaporins, particularly in biomedicine and in vivo synthetic biology, where quantitative methods to measure the location and performance of genetic devices in whole vertebrates are necessary.
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Affiliation(s)
- Rochishnu Chowdhury
- Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA
| | - Jinyang Wan
- Department of Chemistry, University of California, Santa Barbara, CA 93106, USA
| | - Remy Gardier
- Signal Processing Laboratory (LTS5), Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
| | - Jonathan Rafael-Patino
- Signal Processing Laboratory (LTS5), Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
- Radiology Department, Centre Hospitalier Universitaire Vaudois (CHUV) and University of Lausanne (UNIL), Lausanne, Switzerland
| | - Jean-Philippe Thiran
- Signal Processing Laboratory (LTS5), Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
- Radiology Department, Centre Hospitalier Universitaire Vaudois (CHUV) and University of Lausanne (UNIL), Lausanne, Switzerland
| | - Frederic Gibou
- Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA
- Department of Computer Science, University of California, Santa Barbara, CA 93106, USA
| | - Arnab Mukherjee
- Department of Chemistry, University of California, Santa Barbara, CA 93106, USA
- Department of Chemical Engineering, University of California, Santa Barbara, CA 93106, USA
- Biomolecular Science and Engineering, University of California, Santa Barbara, CA 93106, USA
- Biological Engineering, University of California, Santa Barbara, CA 93106, USA
- Neuroscience Research Institute, University of California, Santa Barbara, CA 93106, USA
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Johnson I, Ratsch C, Gibou F, Margetis D. Slope selection in unstable multilayer growth in 1+1 dimensions: Step flow models with downward funneling. Phys Rev E 2019; 100:052802. [PMID: 31870009 DOI: 10.1103/physreve.100.052802] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2019] [Indexed: 06/10/2023]
Abstract
We study analytically and numerically aspects of the dynamics of slope selection for one-dimensional models describing the motion of line defects, steps, in homoepitaxial crystal growth. The kinetic processes include diffusion of adsorbed atoms (adatoms) on terraces, attachment and detachment of atoms at steps with large yet finite, positive Ehrlich-Schwoebel step-edge barriers, material deposition on the surface from above, and the mechanism of downward funneling (DF) via a phenomenological parameter. In this context, we account for the influence of boundary conditions at extremal steps on the dynamics of slope selection. Furthermore, we consider the effect of repulsive, nearest-neighbor force-dipole step-step interactions. For geometries with straight steps, we carry out numerical simulations of step flow, which demonstrate that slope selection eventually occurs. We apply perturbation theory to characterize time-periodic solutions of step flow for slope-selected profiles. By this method, we show how a simplified step flow theory with constant probabilities for the motion of deposited atoms can serve as an effective model of slope selection in the presence of DF. Our analytical findings compare favorably to step simulations.
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Affiliation(s)
- Ian Johnson
- Department of Mathematics, University of Maryland, College Park, Maryland 20742, USA
| | - Christian Ratsch
- Institute for Pure and Applied Mathematics and Department of Mathematics, University of California, Los Angeles, California 90095, USA
| | - Frederic Gibou
- Department of Mechanical Engineering, Department of Computer Science, and Department of Mathematics, University of California, Santa Barbara, California 93106, USA
| | - Dionisios Margetis
- Institute for Physical Science and Technology, Department of Mathematics, and Center for Scientific Computation and Mathematical Modeling, University of Maryland, College Park, Maryland 20742, USA
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Schneider JP, Margetis D, Gibou F, Ratsch C. An examination of scaling behavior in unstable epitaxial mound growth via kinetic Monte Carlo simulations. J Phys Condens Matter 2019; 31:365301. [PMID: 31071698 DOI: 10.1088/1361-648x/ab20b3] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We investigate the scaling behavior for roughening and coarsening of mounds during unstable epitaxial growth. By using kinetic Monte Carlo (KMC) simulations of two lattice-gas models of crystal surfaces, we find scaling exponents that characterize roughening and coarsening at long times. Our simulation data show that these exponents have a complicated dependence on key model parameters that describe a step edge barrier and downward transport mechanisms. This behavior has not been fully described in previous works. In particular, we find that these scaling exponents vary continuously with parameters controlling the surface current. The kinetic processes of the KMC models that we employ include surface diffusion, edge diffusion, step-edge barriers, and also account for transient kinetics during deposition via downward funneling and transient mobility. Our extensive simulations make evident the salient interplay between step-edge barrier strength and transient kinetic processes.
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Affiliation(s)
- Joshua P Schneider
- Department of Mathematics, University of California, Los Angeles, CA 90095, United States of America. Department of Science, Technology and Mathematics, Gallaudet University, Washington, DC 20002, United States of America
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Przybylowski M, Ghosh P, Gibou F. An Efficient Object Tracking Method on Quad-/Oc-Trees. PLoS One 2016; 11:e0150889. [PMID: 26986970 PMCID: PMC4795650 DOI: 10.1371/journal.pone.0150889] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2015] [Accepted: 02/19/2016] [Indexed: 11/18/2022] Open
Abstract
We introduce a fast error-free tracking method applicable to sequences of two and three dimensional images. The core idea is to use Quadtree (resp. Octree) data structures for representing the spatial discretization of an image in two (resp. three) spatial dimensions. This representation enables one to merge into large computational cells the regions that can be faithfully described with such a coarse representation, thus significantly reducing the total number of degrees of freedom that are processed, without compromising accuracy. This encoding is particularly effective in the case of algorithms based on moving fronts, since the adaptive refinement provides a natural means to focus the processing resources on information near the moving front. In this paper, we use an existing contour based tracker and reformulate it to the case of Quad-/Oc-tree data structures. Relevant mathematical assumptions and derivations are presented for this purpose. We then demonstrate that, on standard bio-medical image sequences, a speed up of 5X is easily achieved in 2D and about 10X in 3D.
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Affiliation(s)
- Magda Przybylowski
- Department of Mechanical Engineering, University of California Santa Barbara, Santa Barbara, CA 93106-5070, United States of America
- * E-mail:
| | - Pratim Ghosh
- Department of Electrical and Computer Engineering, University of California Santa Barbara, Santa Barbara, CA 93106-5110, United States of America
| | - Frederic Gibou
- Department of Computer Science, University of California Santa Barbara, Santa Barbara, CA 93106-5110, United States of America
- Department of Mechanical Engineering, University of California Santa Barbara, Santa Barbara, CA 93106-5070, United States of America
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Mirzadeh M, Gibou F, Squires TM. Enhanced charging kinetics of porous electrodes: surface conduction as a short-circuit mechanism. Phys Rev Lett 2014; 113:097701. [PMID: 25216005 DOI: 10.1103/physrevlett.113.097701] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2014] [Indexed: 06/03/2023]
Abstract
We use direct numerical simulations of the Poisson-Nernst-Planck equations to study the charging kinetics of porous electrodes and to evaluate the predictive capabilities of effective circuit models, both linear and nonlinear. The classic transmission line theory of de Levie holds for general electrode morphologies, but only at low applied potentials. Charging dynamics are slowed appreciably at high potentials, yet not as significantly as predicted by the nonlinear transmission line model of Biesheuvel and Bazant. We identify surface conduction as a mechanism which can effectively "short circuit" the high-resistance electrolyte in the bulk of the pores, thus accelerating the charging dynamics and boosting power densities. Notably, the boost in power density holds only for electrode morphologies with continuous conducting surfaces in the charging direction.
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Affiliation(s)
- Mohammad Mirzadeh
- Department of Mechanical Engineering, University of California, Santa Barbara, California 93106, USA
| | - Frederic Gibou
- Department of Mechanical Engineering, University of California, Santa Barbara, California 93106, USA
| | - Todd M Squires
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, USA
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Papac J, Margetis D, Gibou F, Ratsch C. Island-dynamics model for mound formation: effect of a step-edge barrier. Phys Rev E Stat Nonlin Soft Matter Phys 2014; 90:022404. [PMID: 25215739 DOI: 10.1103/physreve.90.022404] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2014] [Indexed: 06/03/2023]
Abstract
We formulate and implement a generalized island-dynamics model of epitaxial growth based on the level-set technique to include the effect of an additional energy barrier for the attachment and detachment of atoms at step edges. For this purpose, we invoke a mixed, Robin-type, boundary condition for the flux of adsorbed atoms (adatoms) at each step edge. In addition, we provide an analytic expression for the requisite equilibrium adatom concentration at the island boundary. The only inputs are atomistic kinetic rates. We present a numerical scheme for solving the adatom diffusion equation with such a mixed boundary condition. Our simulation results demonstrate that mounds form when the step-edge barrier is included, and that these mounds steepen as the step-edge barrier increases.
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Affiliation(s)
- Joe Papac
- Department of Mathematics, University of California, Los Angeles, California 90095, USA
| | - Dionisios Margetis
- Department of Mathematics, and Institute for Physical Science and Technology, and Center for Scientific Computation and Mathematical Modeling, University of Maryland, College Park, Maryland 20742, USA
| | - Frederic Gibou
- Department of Mechanical Engineering and Department of Computer Science and Department of Mathematics, University of California, Santa Barbara, California 93106, USA
| | - Christian Ratsch
- Department of Mathematics and Institute for Pure and Applied Mathematics, University of California, Los Angeles, California 90095, USA
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Gibou F, Levy D, Cardenas C, Liu P, Boyer A. Partial differential equations-based segmentation for radiotherapy treatment planning. Math Biosci Eng 2005; 2:209-226. [PMID: 20369919 DOI: 10.3934/mbe.2005.2.209] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
Abstract
The purpose of this study is to develop automatic algorithms for the segmentation phase of radiotherapy treatment planning. We develop new image processing techniques that are based on solving a partial diferential equation for the evolution of the curve that identifies the segmented organ. The velocity function is based on the piecewise Mumford-Shah functional. Our method incorporates information about the target organ into classical segmentation algorithms. This information, which is given in terms of a three- dimensional wireframe representation of the organ, serves as an initial guess for the segmentation algorithm. We check the performance of the new algorithm on eight data sets of three diferent organs: rectum, bladder, and kidney. The results of the automatic segmentation were compared with a manual seg- mentation of each data set by radiation oncology faculty and residents. The quality of the automatic segmentation was measured with the k-statistics", and with a count of over- and undersegmented frames, and was shown in most cases to be very close to the manual segmentation of the same data. A typical segmentation of an organ with sixty slices takes less than ten seconds on a Pentium IV laptop.
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Affiliation(s)
- Frederic Gibou
- Department of Computer Science and Department of Mechanical Engineering, University of California at Santa Barbara, CA 93106-5070.
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Vvedensky DD, Ratsch C, Gibou F, Vardavas R. Singularities and spatial fluctuations in submonolayer epitaxy. Phys Rev Lett 2003; 90:189601-189602. [PMID: 12786050 DOI: 10.1103/physrevlett.90.189601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2001] [Indexed: 05/24/2023]
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