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1.  Differential Geometry Based Multiscale Models 
Bulletin of mathematical biology  2010;72(6):1562-1622.
Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atom-istic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier–Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson–Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson–Nernst–Planck equations that are coupled to generalized Navier–Stokes equations for fluid dynamics, Newton's equation for molecular dynamics, and potential and surface driving geometric flows for the micro-macro interface. For excessively large aqueous macromolecular complexes in chemistry and biology, we further develop differential geometry based multiscale fluid-electro-elastic models to replace the expensive molecular dynamics description with an alternative elasticity formulation.
doi:10.1007/s11538-010-9511-x
PMCID: PMC2914853  PMID: 20169418
Variational principle; Multiscale; Geometric flows; Solvation analysis; Electrostatic analysis; Implicit solvent models; Molecular dynamics; Elasticity; Navier–Stokes equation; Poisson–Boltzmann equation; Nernst–Planck equation
2.  Determination of Villous Rigidity in the Distal Ileum of the Possum (Trichosurus vulpecula) 
PLoS ONE  2014;9(6):e100140.
We investigated the passive mechanical properties of villi in ex vivo preparations of sections of the wall of the distal ileum from the brushtail possum (Trichosurus vulpecula) by using a flow cell to impose physiological and supra-physiological levels of shear stress on the tips of villi. We directly determined the stress applied from the magnitude of the local velocities in the stress inducing flow and additionally mapped the patterns of flow around isolated villi by tracking the trajectories of introduced 3 µm microbeads with bright field micro particle image velocimetry (mPIV). Ileal villi were relatively rigid along their entire length (mean 550 µm), and exhibited no noticeable bending even at flow rates that exceeded calculated normal physiological shear stress (>0.5 mPa). However, movement of villus tips indicated that the whole rigid structure of a villus could pivot about the base, likely from laxity at the point of union of the villous shaft with the underlying mucosa. Flow moved upward toward the tip on the upper portions of isolated villi on the surface facing the flow and downward toward the base on the downstream surface. The fluid in sites at distances greater than 150 µm below the villous tips was virtually stagnant indicating that significant convective mixing in the lower intervillous spaces was unlikely. Together the findings indicate that mixing and absorption is likely to be confined to the tips of villi under conditions where the villi and intestinal wall are immobile and is unlikely to be greatly augmented by passive bending of the shafts of villi.
doi:10.1371/journal.pone.0100140
PMCID: PMC4067314  PMID: 24956476
3.  Advances in modelling of biomimetic fluid flow at different scales 
Nanoscale Research Letters  2011;6(1):344.
The biomimetic flow at different scales has been discussed at length. The need of looking into the biological surfaces and morphologies and both geometrical and physical similarities to imitate the technological products and processes has been emphasized. The complex fluid flow and heat transfer problems, the fluid-interface and the physics involved at multiscale and macro-, meso-, micro- and nano-scales have been discussed. The flow and heat transfer simulation is done by various CFD solvers including Navier-Stokes and energy equations, lattice Boltzmann method and molecular dynamics method. Combined continuum-molecular dynamics method is also reviewed.
doi:10.1186/1556-276X-6-344
PMCID: PMC3211433  PMID: 21711847
4.  Computational Coupled Method for Multiscale and Phase Analysis 
Journal of Engineering Materials and Technology  2013;135(2):0210131-02101311.
On micro scale the constitutions of porous media are effected by other constitutions, so their behaviors are very complex and it is hard to derive theoretical formulations as well as to simulate on macro scale. For decades, in order to escape this complication, the phenomenological approaches in a field of multiscale methods have been extensively researched by many material scientists and engineers. Their theoretical approaches are based on the hierarchical multiscale methods using a priori knowledge on a smaller scale; however it has a drawback that an information loss can be occurred. Recently, according to a development of the core technologies of computer, the ways of multiscale are extended to a direct multiscale approach called the concurrent multiscale method. This approach is not necessary to deal with complex mathematical formulations, but it is noted as an important factor: development of computational coupling algorithms between constitutions in a porous medium. In this work, we attempt to develop coupling algorithms in different numerical methods finite element method (FEM), smoothed particle hydrodynamics (SPH) and discrete element method (DEM). Using this coupling algorithm, fluid flow, movement of solid particle, and contact forces between solid domains are computed via proposed discrete element which is based on SPH, FEM, and DEM. In addition, a mixed FEM on continuum level and discrete element model with SPH particles on discontinuum level is introduced, and proposed coupling algorithm is verified through numerical simulation.
doi:10.1115/1.4023776
PMCID: PMC3707204  PMID: 23918471
coupled method; porous media; finite element method; discrete element method; smoothed particle hydrodynamics; multiscale model
5.  Characterisation of Mixing in the Proximal Duodenum of the Rat during Longitudinal Contractions and Comparison with a Fluid Mechanical Model Based on Spatiotemporal Motility Data 
PLoS ONE  2014;9(4):e95000.
The understanding of mixing and mass transfers of nutrients and drugs in the small intestine is of prime importance in creating formulations that manipulate absorption and digestibility. We characterised mixing using a dye tracer methodology during spontaneous longitudinal contractions, i.e. pendular activity, in 10 cm segments of living proximal duodenum of the rat maintained ex-vivo. The residence time distribution (RTD) of the tracer was equivalent to that generated by a small number (8) of continuous stirred tank reactors in series. Fluid mechanical modelling, that was based on real sequences of longitudinal contractions, predicted that dispersion should occur mainly in the periphery of the lumen. Comparison with the experimental RTD showed that centriluminal dispersion was accurately simulated whilst peripheral dispersion was underestimated. The results therefore highlighted the potential importance of micro-phenomena such as microfolding of the intestinal mucosa in peripheral mixing. We conclude that macro-scale modeling of intestinal flow is useful in simulating centriluminal mixing, whereas multi-scales strategies must be developed to accurately model mixing and mass transfers at the periphery of the lumen.
doi:10.1371/journal.pone.0095000
PMCID: PMC3991651  PMID: 24747714
6.  Quantitation of countercurrent exchange during passive absorption from the dog small intestine: evidence for marked species differences in the efficiency of exchange. 
Journal of Clinical Investigation  1977;59(2):308-318.
The present investigation was designed to quantitatively assess the possible influence of countercurrent exchange on passive absorption from the small intestine of the dog. Villus blood flow was measured with a modification of the microsphere method. Simultaneously, the absorption from the gut lumen of five diffusible gases (H2, He, CH4, 133Xe, and CO) was determined. Villus blood flow averaged 0.247 +/- 0.03 (SEM) ml/min per g. The observed absorption of H2, He, CH4, and 133Xe was only 16.2 +/- 1.8, 12.8 +/- 2.3, 12.0 +/- 1.8, and 15.8 +/- 1.4 %, respectively, of what this villus blood flow could carry away if it reached perfect equilibrium with the luminal gases. This low absorption rate could result from diffusion limitation to absorption or countercurrent exchange. The diffusive permeability of the barrier seperating the luminal gases and villus blood flow was assessed by measuring the absorption rate of CO. Because absorbed CO binds tightly to hemoglobin, it cannot exchange, and when present in low concentrations its uptake is entirely diffusion limited. Knowledge of the diffusion rate through tissue of the unbound gases relative to that of CO made it possible to calculate the degree to which each of the unbound gases should equilibrate with villus tip blood. The percentage equilibration between lumen and blood at the villus tip for H2, He, CH4, and 133Xe was 99.7, 99.9, 75.6, and 36.0% , respectively. Each of these values greatly exceeded the percentage equilibration of blood leaving the villus (calculated from the observed absorption rate and villus blood flow) and indicated an exchange of 83.8, 87.2, 84.1, and 56.1% of initially absorbed H2, He, CH4, and 133Xe. This result is in accord with theoretical calculations which suggest that countercurrent exchange should be exceedingly efficient in the dog. The striking effect of countercurrent exchange on passive absorption in the dog differs from our previous studies in the rabbit where no exchange was demonstrated. This marked species difference may result from anatomical differences in villus architecture. The dog has long, densely packed villi while the rabbit has broad, widely spaced villi. In the dog, only the villus tips may equilibrate with the lumen, hence a countercurrent gradient may be established in the villus. The entire villus of the rabbit may equilibrate with the lumen and no gradient for countercurrent exchange can therefore be established.
Images
PMCID: PMC333361  PMID: 833278
7.  Parameterizing the Morse Potential for Coarse-Grained Modeling of Blood Plasma 
Journal of computational physics  2014;257(Pt A):726-736.
Multiscale simulations of fluids such as blood represent a major computational challenge of coupling the disparate spatiotemporal scales between molecular and macroscopic transport phenomena characterizing such complex fluids. In this paper, a coarse-grained (CG) particle model is developed for simulating blood flow by modifying the Morse potential, traditionally used in Molecular Dynamics for modeling vibrating structures. The modified Morse potential is parameterized with effective mass scales for reproducing blood viscous flow properties, including density, pressure, viscosity, compressibility and characteristic flow dynamics of human blood plasma fluid. The parameterization follows a standard inverse-problem approach in which the optimal micro parameters are systematically searched, by gradually decoupling loosely correlated parameter spaces, to match the macro physical quantities of viscous blood flow. The predictions of this particle based multiscale model compare favorably to classic viscous flow solutions such as Counter-Poiseuille and Couette flows. It demonstrates that such coarse grained particle model can be applied to replicate the dynamics of viscous blood flow, with the advantage of bridging the gap between macroscopic flow scales and the cellular scales characterizing blood flow that continuum based models fail to handle adequately.
doi:10.1016/j.jcp.2013.09.040
PMCID: PMC4045626  PMID: 24910470
Morse potential; inverse problems; coarse-grained; blood plasma fluid
8.  MicroRNA mir-16 is anti-proliferative in enterocytes and exhibits diurnal rhythmicity in intestinal crypts 
Experimental cell research  2010;316(20):3512-3521.
Background and aims
The intestine exhibits profound diurnal rhythms in function and morphology, in part due to changes in enterocyte proliferation. The regulatory mechanisms behind these rhythms remain largely unknown. We hypothesized that microRNAs are involved in mediating these rhythms, and studied the role of microRNAs specifically in modulating intestinal proliferation.
Methods
Diurnal rhythmicity of microRNAs in rat jejunum was analyzed by microarrays and validated by qPCR. Temporal expression of diurnally rhythmic mir-16 was further quantified in intestinal crypts, villi, and smooth muscle using laser capture microdissection and qPCR. Morphological changes in rat jejunum were assessed by histology and proliferation by immunostaining for bromodeoxyuridine. In IEC-6 cells stably overexpressing mir-16, proliferation was assessed by cell counting and MTS assay, cell cycle progression and apoptosis by flow cytometry, and cell cycle gene expression by qPCR and immunoblotting.
Results
mir-16 peaked 6 hours after light onset (HALO 6) with diurnal changes restricted to crypts. Crypt depth and villus height peaked at HALO 13-14 in antiphase to mir-16. Overexpression of mir-16 in IEC-6 cells suppressed specific G1/S regulators (Cyclins D1-3, Cyclin E1 and Cyclin-dependent kinase 6) and produced G1 arrest. Protein expression of these genes exhibited diurnal rhythmicity in rat jejunum, peaking between HALO 11-17 in antiphase to mir-16.
Conclusions
This is the first report of circadian rhythmicity of specific microRNAs in rat jejunum. Our data provide a link between anti-proliferative mir-16 and the intestinal proliferation rhythm and point to mir-16 as an important regulator of proliferation in jejunal crypts. This function may be essential to match proliferation and absorptive capacity with nutrient availability.
doi:10.1016/j.yexcr.2010.07.007
PMCID: PMC2976799  PMID: 20633552
microRNA; diurnal; proliferation; enterocyte
9.  Modeling the flow of dense suspensions of deformable particles in three dimensions 
We describe here a rigorous and accurate model for the simulation of three-dimensional deformable particles (DPs). The method is very versatile, easily simulating various types of deformable particles such as vesicles, capsules, and biological cells. Each DP is resolved explicitly and advects within the surrounding Newtonian fluid. The DPs have a preferred rest shape (e.g., spherical for vesicles, or biconcave for red blood cells). The model uses a classic hybrid system: an Eulerian approach is used for the Navier-Stokes solver (the lattice Boltzmann method) and a Lagrangian approach for the evolution of the DP mesh. Coupling is accomplished through the lattice Boltzmann velocity field, which transmits force to the membranes of the DPs. The novelty of this method resides in its ability (by design) to simulate a large number of DPs within the bounds of current computational limitations: our simple and efficient approach is to (i) use the lattice Boltzmann method because of its acknowledged efficiency at low Reynolds number and its ease of parallelization, and (ii) model the DP dynamics using a coarse mesh (approximately 500 nodes) and a spring model constraining (if necessary) local area, total area, cell volume, local curvature, and local primary stresses. We show that this approach is comparable to the more common—yet numerically expensive—approach of membrane potential function, through a series of quantitative comparisons. To demonstrate the capabilities of the model, we simulate the flow of 200 densely packed red blood cells—a computationally challenging task. The model is very efficient, requiring of the order of minutes for a single DP in a 50 μm×40 μm×40 μm simulation domain and only hours for 200 DPs in 80 μm×30 μm×30 μm. Moreover, the model is highly scalable and efficient compared to other models of blood cells in flow, making it an ideal and unique tool for studying blood flow in microvessels or vesicle or capsule flow (or a mixture of different particles). In addition to directly predicting fluid dynamics in complex suspension in any geometry, the model allows determination of accurate, empirical rules which may improve existing macroscopic, continuum models.
PMCID: PMC2752716  PMID: 17677389
10.  Spatial and temporal operation of the Scotia Sea ecosystem: a review of large-scale links in a krill centred food web 
The Scotia Sea ecosystem is a major component of the circumpolar Southern Ocean system, where productivity and predator demand for prey are high. The eastward-flowing Antarctic Circumpolar Current (ACC) and waters from the Weddell–Scotia Confluence dominate the physics of the Scotia Sea, leading to a strong advective flow, intense eddy activity and mixing. There is also strong seasonality, manifest by the changing irradiance and sea ice cover, which leads to shorter summers in the south. Summer phytoplankton blooms, which at times can cover an area of more than 0.5 million km2, probably result from the mixing of micronutrients into surface waters through the flow of the ACC over the Scotia Arc. This production is consumed by a range of species including Antarctic krill, which are the major prey item of large seabird and marine mammal populations. The flow of the ACC is steered north by the Scotia Arc, pushing polar water to lower latitudes, carrying with it krill during spring and summer, which subsidize food webs around South Georgia and the northern Scotia Arc. There is also marked interannual variability in winter sea ice distribution and sea surface temperatures that is linked to southern hemisphere-scale climate processes such as the El Niño–Southern Oscillation. This variation affects regional primary and secondary production and influences biogeochemical cycles. It also affects krill population dynamics and dispersal, which in turn impacts higher trophic level predator foraging, breeding performance and population dynamics. The ecosystem has also been highly perturbed as a result of harvesting over the last two centuries and significant ecological changes have also occurred in response to rapid regional warming during the second half of the twentieth century. This combination of historical perturbation and rapid regional change highlights that the Scotia Sea ecosystem is likely to show significant change over the next two to three decades, which may result in major ecological shifts.
doi:10.1098/rstb.2006.1957
PMCID: PMC1764830  PMID: 17405210
Scotia Sea; ecosystem; advection; Antarctic krill; heterogeneity; interannual variability
11.  Multiscale Finite Element Modeling of the Lamina Cribrosa Microarchitecture in the Eye 
Conference Proceedings  2009;2009:4277-4280.
In this paper, we describe a new method for constructing macro-scale models of the posterior pole of the eye to investigate the role of intraocular pressure in the development and progression of glaucoma. We also describe a method and present results from micro-scale finite element models of the lamina cribrosa microarchitecture that are derived from parent macro-scale continuum models using a novel multiscale substructuring approach. The laminar micro-scale models capture the biomechanical behavior of the laminar trabeculae in a way that cannot be estimated using macro-scale techniques, and predict much higher stresses and strains than those calculated within macro-scale models of the coincident region in the same eye.
doi:10.1109/IEMBS.2009.5332755
PMCID: PMC3268703  PMID: 19963817
12.  Race and Space in the 1990s: Changes in the Geographic Scale of Racial Residential Segregation, 1990-2000 
Social science research  2009;38(1):55-70.
We use newly developed methods of measuring spatial segregation across a range of spatial scales to assess changes in racial residential segregation patterns in the 100 largest U.S. metropolitan areas from 1990 to 2000. Our results point to three notable trends in segregation from 1990 to 2000: 1) Hispanic-white and Asian-white segregation levels increased at both micro- and macro-scales; 2) black-white segregation declined at a micro-scale, but was unchanged at a macro-scale; and 3) for all three racial groups and for almost all metropolitan areas, macro-scale segregation accounted for more of the total metropolitan area segregation in 2000 than in 1990. Our examination of the variation in these trends among the metropolitan areas suggests that Hispanic-white and Asian-white segregation changes have been driven largely by increases in macro-scale segregation resulting from the rapid growth of the Hispanic and Asian populations in central cities. The changes in black-white segregation, in contrast, appear to be driven by the continuation of a 30-year trend in declining micro-segregation, coupled with persistent and largely stable patterns of macro-segregation.
PMCID: PMC4057018  PMID: 19569292
13.  Focal reduction of villous blood flow in early indomethacin enteropathy: a dynamic vascular study in the rat 
Gut  1998;42(3):366-373.
Background—Oral indomethacin causes villous shortening, microvascular damage, and distortion, which might induce mucosal ischaemia and necrosis. 
Aims—In order to determine the early events in indomethacin induced jejunal injury we examined the temporal relations between morphological damage and changes in villous blood flow following indomethacin. 
Methods—In anaesthetised rats, mid jejunal villi were exteriorised in a chamber and observed by fluorescence microscopy. Blood flow in surface capillaries was calculated from velocities and diameters. Indomethacin was applied by both luminal and intravenous routes for 90 minutes, after which the animal was perfusion fixed and the villi were processed for histological examination. Control animals received intravenous or luminal bicarbonate (1.25%). 
Results—Blood flow slowed in individual villi at 20 minutes, and progressed to complete stasis (in another group) by 45 minutes. Histological examination at 20 minutes revealed microvascular distortion, but no villous shortening: crypt depth:villous height ratios were 0.356 (0.02) in test and 0.386 (0.01) in surrounding villi (p>0.5). At stasis, the villi under study showed epithelial clumping and were shortened: crypt depth:villous height ratios were 0.92 (0.2) in test and 0.42 (0.06) in surrounding villi (p<0.02). Vehicle alone had no effect on either blood flow or histology. 
Conclusions—Focal slowing of villous blood flow and microvascular distortion precede villus shortening and epithelial disruption, and indicate that damage to surface microvasculature is an early event in indomethacin induced mucosal injury in this model. 


Keywords: indomethacin; jejunum; villi; microcirculation; endothelium; microthrombi
PMCID: PMC1727016  PMID: 9577343
14.  A mesoscopic bridging scale method for fluids and coupling dissipative particle dynamics with continuum finite element method 
A multiscale procedure to couple a mesoscale discrete particle model and a macroscale continuum model of incompressible fluid flow is proposed in this study. We call this procedure the mesoscopic bridging scale (MBS) method since it is developed on the basis of the bridging scale method for coupling molecular dynamics and finite element models [G.J. Wagner, W.K. Liu, Coupling of atomistic and continuum simulations using a bridging scale decomposition, J. Comput. Phys. 190 (2003) 249–274]. We derive the governing equations of the MBS method and show that the differential equations of motion of the mesoscale discrete particle model and finite element (FE) model are only coupled through the force terms. Based on this coupling, we express the finite element equations which rely on the Navier–Stokes and continuity equations, in a way that the internal nodal FE forces are evaluated using viscous stresses from the mesoscale model. The dissipative particle dynamics (DPD) method for the discrete particle mesoscale model is employed. The entire fluid domain is divided into a local domain and a global domain. Fluid flow in the local domain is modeled with both DPD and FE method, while fluid flow in the global domain is modeled by the FE method only.
The MBS method is suitable for modeling complex (colloidal) fluid flows, where continuum methods are sufficiently accurate only in the large fluid domain, while small, local regions of particular interest require detailed modeling by mesoscopic discrete particles. Solved examples – simple Poiseuille and driven cavity flows illustrate the applicability of the proposed MBS method.
doi:10.1016/j.cma.2007.09.011
PMCID: PMC3693461  PMID: 23814322
Multiscale modeling of fluid flow; Mesoscopic bridging scale method; Dissipative particle dynamics method; Finite element method; Coupling Navier; Stokes and dissipative particle dynamics equations
15.  Chondrocyte Deformations as a Function of Tibiofemoral Joint Loading Predicted by a Generalized High-Throughput Pipeline of Multi-Scale Simulations 
PLoS ONE  2012;7(5):e37538.
Cells of the musculoskeletal system are known to respond to mechanical loading and chondrocytes within the cartilage are not an exception. However, understanding how joint level loads relate to cell level deformations, e.g. in the cartilage, is not a straightforward task. In this study, a multi-scale analysis pipeline was implemented to post-process the results of a macro-scale finite element (FE) tibiofemoral joint model to provide joint mechanics based displacement boundary conditions to micro-scale cellular FE models of the cartilage, for the purpose of characterizing chondrocyte deformations in relation to tibiofemoral joint loading. It was possible to identify the load distribution within the knee among its tissue structures and ultimately within the cartilage among its extracellular matrix, pericellular environment and resident chondrocytes. Various cellular deformation metrics (aspect ratio change, volumetric strain, cellular effective strain and maximum shear strain) were calculated. To illustrate further utility of this multi-scale modeling pipeline, two micro-scale cartilage constructs were considered: an idealized single cell at the centroid of a 100×100×100 μm block commonly used in past research studies, and an anatomically based (11 cell model of the same volume) representation of the middle zone of tibiofemoral cartilage. In both cases, chondrocytes experienced amplified deformations compared to those at the macro-scale, predicted by simulating one body weight compressive loading on the tibiofemoral joint. In the 11 cell case, all cells experienced less deformation than the single cell case, and also exhibited a larger variance in deformation compared to other cells residing in the same block. The coupling method proved to be highly scalable due to micro-scale model independence that allowed for exploitation of distributed memory computing architecture. The method’s generalized nature also allows for substitution of any macro-scale and/or micro-scale model providing application for other multi-scale continuum mechanics problems.
doi:10.1371/journal.pone.0037538
PMCID: PMC3359292  PMID: 22649535
16.  Electrochemical Ionization and Analyte Charging in the Array of Micromachined UltraSonic Electrospray (AMUSE) Ion Source 
Electrochemistry and ion transport in a planar array of mechanically-driven, droplet-based ion sources are investigated using an approximate time scale analysis and in-depth computational simulations. The ion source is modeled as a controlled-current electrolytic cell, in which the piezoelectric transducer electrode, which mechanically drives the charged droplet generation using ultrasonic atomization, also acts as the oxidizing/corroding anode (positive mode). The interplay between advective and diffusive ion transport of electrochemically generated ions is analyzed as a function of the transducer duty cycle and electrode location. A time scale analysis of the relative importance of advective vs. diffusive ion transport provides valuable insight into optimality, from the ionization prospective, of alternative design and operation modes of the ion source operation. A computational model based on the solution of time-averaged, quasi-steady advection-diffusion equations for electroactive species transport is used to substantiate the conclusions of the time scale analysis. The results show that electrochemical ion generation at the piezoelectric transducer electrodes located at the back-side of the ion source reservoir results in poor ionization efficiency due to insufficient time for the charged analyte to diffuse away from the electrode surface to the ejection location, especially at near 100% duty cycle operation. Reducing the duty cycle of droplet/analyte ejection increases the analyte residence time and, in turn, improves ionization efficiency, but at an expense of the reduced device throughput. For applications where this is undesirable, i.e., multiplexed and disposable device configurations, an alternative electrode location is incorporated. By moving the charging electrode to the nozzle surface, the diffusion length scale is greatly reduced, drastically improving ionization efficiency. The ionization efficiency of all operating conditions considered is expressed as a function of the dimensionless Peclet number, which defines the relative effect of advection as compared to diffusion. This analysis is general enough to elucidate an important role of electrochemistry in ionization efficiency of any arrayed ion sources, be they mechanically-driven or electrosprays, and is vital for determining optimal design and operation conditions.
doi:10.1016/j.jelechem.2010.05.004
PMCID: PMC2896042  PMID: 20607111
Ion transport; Scaling analysis; Electrochemical ion generation; Analyte charging; Mass spectrometry
17.  Gastric flow and mixing studied using computer simulation. 
The fed human stomach displays regular peristaltic contraction waves that originate in the proximal antrum and propagate to the pylorus. High-resolution concurrent manometry and magnetic resonance imaging (MRI) studies of the stomach suggest a primary function of antral contraction wave (ACW) activity unrelated to gastric emptying. Detailed evaluation is difficult, however, in vivo. Here we analyse the role of ACW activity on intragastric fluid motions, pressure, and mixing with computer simulation. A two-dimensional computer model of the stomach was developed with the 'lattice-Boltzmann' numerical method from the laws of physics, and stomach geometry modelled from MRI. Time changes in gastric volume were specified to match global physiological rates of nutrient liquid emptying. The simulations predicted two basic fluid motions: retrograde 'jets' through ACWs, and circulatory flow between ACWs, both of which contribute to mixing. A well-defined 'zone of mixing', confined to the antrum, was created by the ACWs, with mixing motions enhanced by multiple and narrower ACWs. The simulations also predicted contraction-induced peristaltic pressure waves in the distal antrum consistent with manometric measurements, but with a much lower pressure amplitude than manometric data, indicating that manometric pressure amplitudes reflect direct contact of the catheter with the gastric wall. We conclude that the ACWs are central to gastric mixing, and may also play an indirect role in gastric emptying through local alterations in common cavity pressure.
doi:10.1098/rspb.2004.2886
PMCID: PMC1691895  PMID: 15615685
18.  Delineation of the Dimensions and Permeability Characteristics of the Two Major Diffusion Barriers to Passive Mucosal Uptake in the Rabbit Intestine 
Journal of Clinical Investigation  1974;54(3):718-732.
The rate of passive absorption into the intestinal mucosal cell is determined by at least two major diffusion barriers: an unstirred water layer and the cell membrane. This study defines the morphology and permeability characteristics of these two limiting structures. The unstirred water layer was resolved into two compartments: one behaves like a layer of water overlying the upper villi while the other probably consists of solution between villi. The superficial layer is physiologically most important during uptake of highly permeant compounds and varies in thickness from 115 to 334 μm as the rate of mixing of the bulk mucosal solution is varied. From data derived from a probe molecule whose uptake was limited by the unstirred layer, the effective surface area of this diffusion barrier also was determined to vary with stirring rate and equaled only 2.4 cm2·100 mg-1 in the unstirred condition but increased to 11.3 cm2·100 mg-1 with vigorous mixing. This latter value, however, was still only 1/170 of the anatomical area of the microvillus membrane. With these values, uptake rates for a number of passively absorbed probe molecules were corrected for unstirred layer resistance, and these data were used to calculate the incremental free energy changes associated with uptake of the -CH2- (-258 cal·mol-1), -OH (+564), and taurine (+1,463) groups. These studies, then, have defined the thickness and area of the unstirred layer in the intestine and have shown that this barrier is rate-limiting for the mucosal uptake of compounds such as fatty acids and cholesterol; in addition, the lipid membrane of the microvillus surface has been shown to be a relatively polar structure.
Images
PMCID: PMC301606  PMID: 4851286
19.  Lubiprostone targets prostanoid signaling and promotes ion transporter trafficking, mucus exocytosis and contractility 
Digestive diseases and sciences  2012;57(11):2826-2845.
Background and Aim
Lubiprostone is a chloride channel activator in clinical use for the treatment of chronic constipation, but the mechanisms of action of the drug are poorly understood. The aim of this study was to determine whether lubiprostone exerts secretory effects in the intestine by membrane trafficking of ion transporters and associated machinery.
Methods
Immunolabeling and quantitative fluorescence intensity were used to examine lubiprostone-induced trafficking of the cystic fibrosis transmembrane conductance regulator (CFTR), sodium/potassium-coupled chloride co-transporter 1 (NKCC1), electrogenic sodium/bicarbonate co-transporter 1 (NBCe1), down-regulated in adenoma (DRA), putative anion transporter 1 (PAT1), sodium/proton exchanger 3 (NHE3), Ca2+ activated chloride channel 2 (ClC-2) serotonin and its transporter SERT, E prostanoid receptors EP4 and EP1, sodium/potassium ATPase (Na-K-ATPase) and protein kinase A (PKA). The effects of lubiprostone on mucus exocytosis in rat intestine and human rectosigmoid explants were also examined.
Results
Lubiprostone induced contraction of villi and proximal colonic plicae and membrane trafficking of transporters that was more pronounced in villus/surface cells compared to the crypt. Membrane trafficking was determined by: (1) increased membrane labeling for CFTR, PAT1, NKCC1, and NBCe1 and decreased membrane labeling for NHE3, DRA and ClC-2; (2) increased serotonin, SERT, EP4, EP1 and PKA labeling in enterochromaffin cells; (3) increased SERT, EP4, EP1, PKA and Na-K-ATPase in enterocytes; (4) and increased mucus exocytosis in goblet cells.
Conclusion
These data suggest that lubiprostone can target serotonergic, EP4/PKA and EP1 signaling in surface/villus regions; stimulate membrane trafficking of CFTR/NBCe1/NKCC1 in villus epithelia and PAT1/NBCe1/NKCC1 in colonic surface epithelia; suppress NHE3/DRA trafficking and fluid absorption; enhance mucus-mobilization and mucosal contractility.
doi:10.1007/s10620-012-2352-8
PMCID: PMC3482986  PMID: 22923315
ion transporters; membrane trafficking; receptor signaling; cystic fibrosis conductance regulator
20.  Assessment of stretched vortex subgrid-scale models for LES of incompressible inhomogeneous turbulent flow 
Summary
The physical space version of the stretched vortex subgrid scale model [Phys. Fluids 12, 1810 (2000)] is tested in large eddy simulations (LES) of the turbulent lid driven cubic cavity flow. LES is carried out using a higher order finite-difference method [J. Comput. Phys. 229, 8802 (2010)]. The effects of different vortex orientation models and subgrid turbulence spectrums are assessed through comparisons of the LES predictions against direct numerical simulations (DNS) [Phys. Fluids 12, 1363 (2000)]. Three Reynolds numbers 12000, 18000, and 22000 are studied. Good agreement with the DNS data for the mean and fluctuating quantities is observed.
doi:10.1002/fld.3793
PMCID: PMC3810418  PMID: 24187423
Large Eddy Simulation; WENO; High-Order Finite Difference; Driven Cavity; Incompressible flows; Stretched Vortex Subgrid-scale Model
21.  Upward nitrate transport by phytoplankton in oceanic waters: balancing nutrient budgets in oligotrophic seas 
PeerJ  2014;2:e302.
In oceanic subtropical gyres, primary producers are numerically dominated by small (1–5 µm diameter) pro- and eukaryotic cells that primarily utilize recycled nutrients produced by rapid grazing turnover in a highly efficient microbial loop. Continuous losses of nitrogen (N) to depth by sinking, either as single cells, aggregates or fecal pellets, are balanced by both nitrate inputs at the base of the euphotic zone and N2-fixation. This input of new N to balance export losses (the biological pump) is a fundamental aspect of N cycling and central to understanding carbon fluxes in the ocean. In the Pacific Ocean, detailed N budgets at the time-series station HOT require upward transport of nitrate from the nutricline (80–100 m) into the surface layer (∼0–40 m) to balance productivity and export needs. However, concentration gradients are negligible and cannot support the fluxes. Physical processes can inject nitrate into the base of the euphotic zone, but the mechanisms for transporting this nitrate into the surface layer across many 10s of m in highly stratified systems are unknown. In these seas, vertical migration by the very largest (102–103 µm diameter) phytoplankton is common as a survival strategy to obtain N from sub-euphotic zone depths. This vertical migration is driven by buoyancy changes rather than by flagellated movement and can provide upward N transport as nitrate (mM concentrations) in the cells. However, the contribution of vertical migration to nitrate transport has been difficult to quantify over the required basin scales. In this study, we use towed optical systems and isotopic tracers to show that migrating diatom (Rhizosolenia) mats are widespread in the N. Pacific Ocean from 140°W to 175°E and together with other migrating phytoplankton (Ethmodiscus, Halosphaera, Pyrocystis, and solitary Rhizosolenia) can mediate time-averaged transport of N (235 µmol N m-2 d-1) equivalent to eddy nitrate injections (242 µmol NO3− m-2 d-1). This upward biotic transport can close N budgets in the upper 250 m of the central Pacific Ocean and together with diazotrophy creates a surface zone where biological nutrient inputs rather than physical processes dominate the new N flux. In addition to these numerically rare large migrators, there is evidence in the literature of ascending behavior in small phytoplankton that could contribute to upward flux as well. Although passive downward movement has dominated models of phytoplankton flux, there is now sufficient evidence to require a rethinking of this paradigm. Quantifying these fluxes is a challenge for the future and requires a reexamination of individual phytoplankton sinking rates as well as methods for capturing and enumerating ascending phytoplankton in the sea.
doi:10.7717/peerj.302
PMCID: PMC3961152  PMID: 24688877
Vertical migration; Diatoms; Marine; Nitrogen; Dinoflagellates; Rhizosolenia; Nitrate; Biological pump; Gyres; Mixed layer
22.  IL-10 production differentially influences the magnitude, quality, and protective capacity of Th1 responses depending on the vaccine platform 
The Journal of Experimental Medicine  2010;207(7):1421-1433.
The quality of a Th1 response can be a prospective correlate of vaccine-mediated protection against certain intracellular pathogens. Using two distinct vaccine platforms, we evaluate the influence of interleukin (IL) 10 production on the magnitude, quality, and protective capacity of CD4+ T cell responses in the mouse model of Leishmania major infection. Multiparameter flow cytometry was used to delineate the CD4+ T cell production of interferon (IFN) γ, IL-2, tumor necrosis factor (TNF), and IL-10 (or combinations thereof) after vaccination. Immunization with a high dose of adenovirus (ADV) expressing leishmanial proteins (MML-ADV) elicited a limited proportion of multifunctional IFN-γ+IL-2+TNF+ Th1 cells, a high frequency of IL-10–producing CD4+ T cells, and did not protect against subsequent challenge. Surprisingly, in the absence of IL-10, there was no change in the magnitude, quality, or protective capacity of the Th1 response elicited by high-dose MML-ADV. In contrast, after immunization with MML protein and CpG (MML + CpG), IL-10 limited the production of IL-12 by DCs in vivo, thereby decreasing the generation of multifunctional Th1 cells. Consequently, three immunizations with MML + CpG were required for full protection. However, inhibiting IL-10 at the time of immunization enhanced the magnitude and quality of the Th1 response sufficiently to mediate protection after only a single immunization. Overall, we delineate distinct mechanisms by which vaccines elicit protective Th1 responses and underscore the importance of multifunctional CD4+ T cells.
doi:10.1084/jem.20092532
PMCID: PMC2901071  PMID: 20530206
23.  Microbial diversity affects self-organization of the soil–microbe system with consequences for function 
Soils are complex ecosystems and the pore-scale physical structure regulates key processes that support terrestrial life. These include maintaining an appropriate mixture of air and water in soil, nutrient cycling and carbon sequestration. There is evidence that this structure is not random, although the organizing mechanism is not known. Using X-ray microtomography and controlled microcosms, we provide evidence that organization of pore-scale structure arises spontaneously out of the interaction between microbial activity, particle aggregation and resource flows in soil. A simple computational model shows that these interactions give rise to self-organization involving both physical particles and microbes that gives soil unique material properties. The consequence of self-organization for the functioning of soil is determined using lattice Boltzmann simulation of fluid flow through the observed structures, and predicts that the resultant micro-structural changes can significantly increase hydraulic conductivity. Manipulation of the diversity of the microbial community reveals a link between the measured change in micro-porosity and the ratio of fungal to bacterial biomass. We suggest that this behaviour may play an important role in the way that soil responds to management and climatic change, but that this capacity for self-organization has limits.
doi:10.1098/rsif.2011.0679
PMCID: PMC3350731  PMID: 22158839
soil structure; self-organization; microbial diversity; modelling; biophysics
24.  Differential geometry based solvation model II: Lagrangian formulation 
Journal of mathematical biology  2011;63(6):1139-1200.
Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation model. The Lagrangian representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the Lagrangian representation does not need to resort to artificially enlarged van der Waals radii as often required by the Eulerian representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the Eulerian and Lagrangian formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory (SPT) of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The minimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and Poisson-Boltzmann equations. Due to the development of singularities and nonsmooth manifolds in the Lagrangian representation, the resulting potential-driven geometric flow equation is embedded into the Eulerian representation for the purpose of computation, thanks to the equivalence of the Laplace-Beltrami operator in the two representations. The coupled partial differential equations (PDEs) are solved with an iterative procedure to reach a steady state, which delivers desired solvent-solute interface and electrostatic potential for problems of interest. These quantities are utilized to evaluate the solvation free energies and protein-protein binding affinities. A number of computational methods and algorithms are described for the interconversion of Lagrangian and Eulerian representations, and for the solution of the coupled PDE system. The proposed approaches have been extensively validated. We also verify that the mean curvature flow indeed gives rise to the minimal molecular surface (MMS) and the proposed variational procedure indeed offers minimal total free energy. Solvation analysis and applications are considered for a set of 17 small compounds and a set of 23 proteins. The salt effect on protein-protein binding affinity is investigated with two protein complexes by using the present model. Numerical results are compared to the experimental measurements and to those obtained by using other theoretical methods in the literature.
doi:10.1007/s00285-011-0402-z
PMCID: PMC3113640  PMID: 21279359
Differential geometry based multiscale model; Poisson-Boltzmann equation; Potential driving geometric flows; Solvation free energy; Implicit solvent model; Laplace-Beltrami operator; Protein-protein interaction
25.  Distribution of immunoglobulin G receptors in the small intestine of the young rat 
The Journal of Cell Biology  1980;85(1):18-32.
Conjugates of horseradish peroxidase (HRP) and immunoglobulin G (IgG) were used to map the distribution of cell surface receptors that can bind IgG at 0 degrees C within the small intestine of 10-12-d-old rats. Luminal receptors are present only within the duodenum and proximal jejunum. In these locations, receptors are limited to absorptive cells that line the upper portion of individual villi. Near villus tips, receptors are relatively evenly distributed over the entire luminal plasmalemma. In the midregion of villi, receptors are unevenly distributed over the luminal surface. Receptors (a) specifically bind rat and rabbit IgG, (b) recognize the Fc portion of the immunoglobulins, and (c) bind at pH 6.0 but not pH 7.4. To determine whether IgG receptors are confined to the luminal portion of the plasmalemma, intact epithelial cells were isolated from the proximal intestine of 10-12-d-old rats and incubated with HRP conjugates at 0 degree C. The specific binding of rat IgG-HRP to cells at pH 6.0 indicates that IgG receptors, which are functionally similar to those found on the luminal surface, are also present over the entire abluminal surface of absorptive cells. These results are consistent with the transport of IgG to the abluminal plasma membrane in the form of IgG-receptor complexes on the surface of vesicles. Exposure of these complexes to the serosal plasma, which is presumably at pH 7.4, would cause release of IgG from the receptors. To assess possible inward movement of vesicles from the abluminal surface after discharge of IgG, intravenously injected HRP was used as a space-filling tracer in the serosal plasma. HRP could be visualized within the coated and tubular vesicles responsible for transport of IgG in the opposite direction. These vesicles may, therefore, provide a pathway whereby receptors shuttle between the luminal and abluminal surfaces of cells.
PMCID: PMC2110598  PMID: 7364873

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