Browsing by Author "Heys, Jeffrey J."

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Analysis of convective and diffusive transport in the brain interstitium
(2019-03) Ray, Lori; Iliff, Jeffrey J.; Heys, Jeffrey J.
Background Despite advances in in vivo imaging and experimental techniques, the nature of transport mechanisms in the brain remain elusive. Mathematical modelling verified using available experimental data offers a powerful tool for investigating hypotheses regarding extracellular transport of molecules in brain tissue. Here we describe a tool developed to aid in investigation of interstitial transport mechanisms, especially the potential for convection (or bulk flow) and its relevance to interstitial solute transport, for which there is conflicting evidence. Methods In this work, we compare a large body of published experimental data for transport in the brain to simulations of purely diffusive transport and simulations of combined convective and diffusive transport in the brain interstitium, incorporating current theories of perivascular influx and efflux. Results The simulations show (1) convective flow in the interstitium potentially of a similar magnitude to diffusive transport for molecules of interest and (2) exchange between the interstitium and perivascular space, whereby fluid and solutes may enter or exit the interstitium, are consistent with the experimental data. Simulations provide an upper limit for superficial convective velocity magnitude (approximately v = 50 μm min−1), a useful finding for researchers developing techniques to measure interstitial bulk flow. Conclusions For the large molecules of interest in neuropathology, bulk flow may be an important mechanism of interstitial transport. Further work is warranted to investigate the potential for bulk flow.
Biofilm deformation in response to fluid flow in capillaries
(2011-04) Vo, Garret D.; Heys, Jeffrey J.
Biofilms are complex mixtures of microorganisms and extracellular matrix that exist on many wetted surfaces. Recently, magnetic resonance microscopy has been used to measure fluid velocities near biofilms that are attached to the walls of capillary channels. These velocity measurements showed unexpectedly high secondary velocities (i.e., high velocity magnitudes perpendicular to the direction of bulk flow and perpendicular to the surface that the biofilm is attached), and the presence of high secondary velocities near a biofilm could increase the delivery of substrates to the biofilm. A mathematical model, based on the immersed boundary method, is used here to examine the physical interaction between a biofilm and a moving fluid in a capillary and to analyze possible factors that may contribute to the elevated secondary velocities observed experimentally. The simulation predicts the formation of a recirculation downstream of a biofilm, and this recirculation deforms and lifts the biofilm upward from the surface to which the biofilm is attached. Changing the mechanical properties (i.e., stiffness) of the biofilm impacts both the lifting of the biofilm and the magnitude of the secondary velocities. The maximum lifting of the biofilm occurs when the biofilm properties are similar to previous experimental measurements, which indicates that the mechanical properties of the biofilm may be tuned for the generation of maximum secondary velocity magnitude and transport of substrates to the biofilm.
Combining existing numerical models with data assimilation using weighted least-squares finite element methods
(2017-01) Rajaraman, Prathish K.; Manteuffel, T. A.; Belohlavek, M.; Heys, Jeffrey J.
A new approach has been developed for combining and enhancing the results from an existing computational fluid dynamics model with experimental data using the weighted least-squares finite element method (WLSFEM). Development of the approach was motivated by the existence of both limited experimental blood velocity in the left ventricle and inexact numerical models of the same flow. Limitations of the experimental data include measurement noise and having data only along a two-dimensional plane. Most numerical modeling approaches do not provide the flexibility to assimilate noisy experimental data. We previously developed an approach that could assimilate experimental data into the process of numerically solving the Navier-Stokes equations, but the approach was limited because it required the use of specific finite element methods for solving all model equations and did not support alternative numerical approximation methods. The new approach presented here allows virtually any numerical method to be used for approximately solving the Navier-Stokes equations, and then the WLSFEM is used to combine the experimental data with the numerical solution of the model equations in a final step. The approach dynamically adjusts the influence of the experimental data on the numerical solution so that more accurate data are more closely matched by the final solution and less accurate data are not closely matched. The new approach is demonstrated on different test problems and provides significantly reduced computational costs compared with many previous methods for data assimilation.
Competitive resource allocation to metabolic pathways contributes to overflow metabolisms and emergent properties in cross-feeding microbial consortia
(2018-04) Carlson, Ross P.; Beck, Ashley E.; Phalak, Poonam; Fields, Matthew W.; Gedeon, Tomas; Hanley, Luke; Harcombe, W. R.; Henson, Michael A.; Heys, Jeffrey J.
Resource scarcity is a common stress in nature and has a major impact on microbial physiology. This review highlights microbial acclimations to resource scarcity, focusing on resource investment strategies for chemoheterotrophs from the molecular level to the pathway level. Competitive resource allocation strategies often lead to a phenotype known as overflow metabolism; the resulting overflow byproducts can stabilize cooperative interactions in microbial communities and can lead to cross-feeding consortia. These consortia can exhibit emergent properties such as enhanced resource usage and biomass productivity. The literature distilled here draws parallels between in silico and laboratory studies and ties them together with ecological theories to better understand microbial stress responses and mutualistic consortia functioning.
Effect of model selection on prediction of periodic behavior in gene regulatory networks
(2012-08) Gedeon, Tomas; Cummins, G.; Heys, Jeffrey J.
One of the current challenges for cell biology is understanding of the system level cellular behavior from the knowledge of a network of the individual subcellular agents. We address a question of how the model selection affects the predicted dynamic behavior of a gene network. In particular, for a fixed network structure, we compare protein-only models with models in which each transcriptional activation is represented both by mRNA and protein concentrations. We compare linear behavior near equilibria for both cyclic feedback systems and a general system. We show that, in general, explicit inclusion of the mRNA in the model weakens the stability of equilibria. We also study numerically dynamics of a particular gene network and show significant differences in global dynamics between the two types of models.
Effects of Spatial Localization on Microbial Consortia Growth
(2017-01) Venters, Michael; Carlson, Ross P.; Gedeon, Tomas; Heys, Jeffrey J.
Microbial consortia are commonly observed in natural and synthetic systems, and these consortia frequently result in higher biomass production relative to monocultures. The focus here is on the impact of initial spatial localization and substrate diffusivity on the growth of a model microbial consortium consisting of a producer strain that consumes glucose and produces acetate and a scavenger strain that consumes the acetate. The mathematical model is based on an individual cell model where growth is described by Monod kinetics, and substrate transport is described by a continuum-based, non-equilibrium reaction-diffusion model where convective transport is negligible (e.g., in a biofilm). The first set of results focus on a single producer cell at the center of the domain and surrounded by an initial population of scavenger cells. The impact of the initial population density and substrate diffusivity is examined. A transition is observed from the highest initial density resulting in the greatest cell growth to cell growth being independent of initial density. A high initial density minimizes diffusive transport time and is typically expected to result in the highest growth, but this expected behavior is not predicted in environments with lower diffusivity or larger length scales. When the producer cells are placed on the bottom of the domain with the scavenger cells above in a layered biofilm arrangement, a similar critical transition is observed. For the highest diffusivity values examined, a thin, dense initial scavenger layer is optimal for cell growth. However, for smaller diffusivity values, a thicker, less dense initial scavenger layer provides maximal growth. The overall conclusion is that high density clustering of members of a food chain is optimal under most common transport conditions, but under some slow transport conditions, high density clustering may not be optimal for microbial growth.
Environment Constrains Fitness Advantages of Division of Labor in Microbial Consortia Engineered for Metabolite Push or Pull Interactions
(American Society for Microbiology, 2022-08) Beck, Ashely E.; Pintar, Kathryn; Schepens, Diana; Schrammeck, Ashely; Johnson, Timothy; Bleem, Alissa; Du, Martina; Harcombe, William R.; Bernstein, Hans C.; Heys, Jeffrey J.; Gedeon, Tomas; Carlson, Ross P.
Fitness benefits from division of labor are well documented in microbial consortia, but the dependency of the benefits on environmental context is poorly understood. Two synthetic Escherichia coli consortia were built to test the relationships between exchanged organic acid, local environment, and opportunity costs of different metabolic strategies. Opportunity costs quantify benefits not realized due to selecting one phenotype over another. The consortia catabolized glucose and exchanged either acetic or lactic acid to create producer-consumer food webs. The organic acids had different inhibitory properties and different opportunity costs associated with their positions in central metabolism. The exchanged metabolites modulated different consortial dynamics. The acetic acid-exchanging (AAE) consortium had a “push” interaction motif where acetic acid was secreted faster by the producer than the consumer imported it, while the lactic acid-exchanging (LAE) consortium had a “pull” interaction motif where the consumer imported lactic acid at a comparable rate to its production. The LAE consortium outperformed wild-type (WT) batch cultures under the environmental context of weakly buffered conditions, achieving a 55% increase in biomass titer, a 51% increase in biomass per proton yield, an 86% increase in substrate conversion, and the complete elimination of by-product accumulation all relative to the WT. However, the LAE consortium had the trade-off of a 42% lower specific growth rate. The AAE consortium did not outperform the WT in any considered performance metric. Performance advantages of the LAE consortium were sensitive to environment; increasing the medium buffering capacity negated the performance advantages compared to WT.
An experimentally validated immersed boundary model of fluid-biofilm interaction
(2010-06) Vo, Garret D.; Brindle, Eric R.; Heys, Jeffrey J.
Biofilms are colonies of microorganisms that live on wetted surfaces in a matrix consisting of polysaccharides, proteins, and nucleic acids. According to the National Institute of Health (NIH), biofilms play a role in over 80 percent of microbial infections in the body and these infections are remarkably difficult to treat with antimicrobial compounds. The objective here is to understand and predict the physical interaction between a biofilm and the surrounding fluid flow.We have developed a biofilm-fluid interaction model, based on the Immersed Boundary Method, to simulate the interaction between the biofilm and a moving fluid. The model predictions of biofilm deformation quantitatively agree with experimental measurements for a range a biofilms using a simple immersed elastic solid to model the biofilm matrix. An immersed viscoelastic solid model is also developed and compared with experimental measurements. The results show that the viscoelastic behavior inherent to the immersed boundary method (even when using a simple immersed elastic solid) is sufficient for some biofilms, but a slightly viscoelastic solid gives more general agreement with experimental measurements.
A Model of Filiform Hair Distribution on the Cricket Cercus
(2012-10) Heys, Jeffrey J.; Rajaraman, Prathish K.; Gedeon, Tomas; Miller, J. P.
Crickets and other orthopteran insects sense air currents with a pair of abdominal appendages resembling antennae, called cerci. Each cercus in the common house cricket Acheta domesticus is covered with between 500 to 750 filiform mechanosensory hairs. The distribution of the hairs on the cerci, as well as the global patterns of their movement axes, are very stereotypical across different animals in this species, and the development of this system has been studied extensively. Although hypotheses regarding the mechanisms underlying pattern development of the hair array have been proposed in previous studies, no quantitative modeling studies have been published that test these hypotheses. We demonstrate that several aspects of the global pattern of mechanosensory hairs can be predicted with considerable accuracy using a simple model based on two independent morphogen systems. One system constrains inter-hair spacing, and the second system determines the directional movement axes of the hairs.
Python Source Code for Individual Based Biofilm Model [dataset]
(Montana State University ScholarWorks, 2016-05) Heys, Jeffrey J.; Venters, Michael
Python source code for simulating growth of individual microbes in a biofilm with diffusible substrates.
Quantifying the effects of the division of labor in metabolic pathways
(Elsevier, 2014-11) Harvey, Emily; Heys, Jeffrey J.; Gedeon, Tomas
Division of labor is commonly observed in nature. There are several theories that suggest diversiﬁcation in a microbial community may enhance stability and robustness, decrease concentration of inhibitory intermediates, and increase efﬁciency. Theoretical studies to date have focused on proving when the stable co-existence of multiple strains occurs, but have not investigated the productivity or biomass production of these systems when compared to a single ‘super microbe’ which has the same metabolic capacity. In this work we prove that if there is no change in the growth kinetics or yield of the metabolic pathways when the metabolism is specialised into two separate microbes, the biomass (and productivity) of a binary consortia system is always less than that of the equivalent monoculture. Using a speciﬁc example of Escherichia coli growing on a glucose substrate, we ﬁnd that increasing the growth rates or substrate aﬃnities of the pathways is not suﬃcient to explain the experimentally observed productivity increase in a community. An increase in pathway eﬃciency (yield) in specialised organisms provides the best explanation of the observed increase in productivity.
Quantitative analysis of macroscopic solute transport in the murine brain
(Springer Nature, 2021-12) Ray, Lori A.; Pike, Martin; Simon, Matthew; Iliff, Jeffrey J.; Heys, Jeffrey J.
Background. Understanding molecular transport in the brain is critical to care and prevention of neurological disease and injury. A key question is whether transport occurs primarily by diffusion, or also by convection or dispersion. Dynamic contrast-enhanced (DCE-MRI) experiments have long reported solute transport in the brain that appears to be faster than diffusion alone, but this transport rate has not been quantified to a physically relevant value that can be compared to known diffusive rates of tracers. Methods. In this work, DCE-MRI experimental data is analyzed using subject-specific finite-element models to quantify transport in different anatomical regions across the whole mouse brain. The set of regional effective diffusivities (Deff), a transport parameter combining all mechanisms of transport, that best represent the experimental data are determined and compared to apparent diffusivity (Dapp), the known rate of diffusion through brain tissue, to draw conclusions about dominant transport mechanisms in each region. Results. In the perivascular regions of major arteries, Deff for gadoteridol (550 Da) was over 10,000 times greater than Dapp. In the brain tissue, constituting interstitial space and the perivascular space of smaller blood vessels, Deff was 10–25 times greater than Dapp. Conclusions. The analysis concludes that convection is present throughout the brain. Convection is dominant in the perivascular space of major surface and branching arteries (Pe > 1000) and significant to large molecules (> 1 kDa) in the combined interstitial space and perivascular space of smaller vessels (not resolved by DCE-MRI). Importantly, this work supports perivascular convection along penetrating blood vessels.
Quantitative characterization of the filiform mechanosensory hair array on the cricket cercus
(2011-11) Miller, J. P.; Krueger, S.; Heys, Jeffrey J.; Gedeon, Tomas
Background: Crickets and other orthopteran insects sense air currents with a pair of abdominal appendages resembling antennae, called cerci. Each cercus in the common house cricket Acheta domesticus is approximately 1 cm long, and is covered with 500 to 750 filiform mechanosensory hairs. The distribution of the hairs on the cerci, as well as the global patterns of their movement vectors, have been characterized semi-quantitatively in studies over the last 40 years, and have been shown to be very stereotypical across different animals in this species. Although the cercal sensory system has been the focus of many studies in the areas of neuroethology, development, biomechanics, sensory function and neural coding, there has not yet been a quantitative study of the functional morphology of the receptor array of this important model system. Methodology/Principal Findings: We present a quantitative characterization of the structural characteristics and functional morphology of the cercal filiform hair array. We demonstrate that the excitatory direction along each hair's movement plane can be identified by features of its socket that are visible at the light-microscopic level, and that the length of the hair associated with each socket can also be estimated accurately from a structural parameter of the socket. We characterize the length and directionality of all hairs on the basal half of a sample of three cerci, and present statistical analyses of the distributions. Conclusions/Significance: The inter-animal variation of several global organizational features is low, consistent with constraints imposed by functional effectiveness and/or developmental processes. Contrary to previous reports, however, we show that the filiform hairs are not re-identifiable in the strict sense.
Spatiotemporal modeling of laser tissue soldering using photothermal nanocomposites
(2017-10) Mushaben, M.; Urie, R.; Flake, T.; Jaffe, M.; Rege, K.; Heys, Jeffrey J.
OBJECTIVE: Laser tissue soldering using photothermal solders is a technology that facilitates rapid sealing using heat-induced changes in the tissue and the solder material. The solder material is made of gold nanorods embedded in a protein matrix patch that can be placed over the tissue rupture site and heated with a laser. Although laser tissue soldering is an attractive approach for surgical repair, potential photothermal damage can limit the success of this approach. Development of predictive mathematical models of photothermal effects including cell death, can lead to more efficient approaches in laser-based tissue repair. METHODS: We describe an experimental and modeling investigation into photothermal solder patches for sealing porcine and mouse cadaver intestine sections using near-infrared laser irradiation. Spatiotemporal changes in temperature were determined at the surface as well as various depths below the patch. A mathematical model, based on the finite element method, predicts the spatiotemporal temperature distribution in the patch and surrounding tissue, as well as concomitant cell death in the tissue is described. RESULTS: For both the porcine and mouse intestine systems, the model predicts temperatures that are quantitatively similar to the experimental measurements with the model predictions of temperature increase often being within a just a few degrees of experimental measurements. CONCLUSION: This mathematical model can be employed to identify optimal conditions for minimizing healthy cell death while still achieving a strong seal of the ruptured tissue using laser soldering.