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NASA NTRS2017

Developing Model Benchtop Systems for Microbial Experimental Evolution

Understanding how microbes impact an ecosystem has improved through advances of molecular and genetic tools, but creating complex systems that emulate natural biology goes beyond current technology. In fact, many chemical, biological, and metabolic pathways of even model organisms are still poorly characterized. Even then, standard laboratory techniques for testing microbial impact on environmental change can have many drawbacks; they are time-consuming, labor intensive, and are at risk of contamination. By having an automated process, many of these problems can be reduced or even eliminated. We are developing a benchtop system that can run for long periods of time without the need for human intervention, involve multiple environmental stressors at once, perform real-time adjustments of stressor exposure based on current state of the population, and minimize contamination risks. Our prototype device allows operators to generate an analogue of real world micro-scale ecosystems that can be used to model the effects of disruptive environmental change on microbial ecosystems. It comprises of electronics, mechatronics, and fluidics based systems to control, measure, and evaluate the before and after state of microbial cultures from exposure to environmental stressors. Currently, it uses four parallel growth chambers to perform tests on liquid cultures. To measure the population state, optical sensors (LED/photodiode) are used. Its primary selection pressure is UV-C radiation, a well-studied stressor known for its cell- and DNA-damaging effects and as a mutagen. Future work will involve improving the current growth chambers, as well as implementing additional sensors and environmental stressors into the system. Full integration of multiple culture testing will allow inter-culture comparisons. Besides the temperature and OD sensors, other types of sensors can be integrated such as conductivity, biomass, pH, and dissolved gasses such as CO and O. Additional environmental stressor systems like temperature (extreme heat or cold), metal toxicity, and other forms of radiation will increase the scale and testing range.

Developing↗

DOE OSTI2022

Data for: Patel et al. Carbon flux estimates are sensitive to data source: A comparison of field and lab temperature sensitivity data

This dataset contains data and code used for the paper "Carbon flux estimates are sensitive to data source: A comparison of field and lab temperature sensitivity data" [DOI COMING SOON]A large literature exists on mechanisms driving soil production of the greenhouse gases CO2 and CH4. Measurements of these gases’ fluxes are often performed using closed-chamber incubations in the laboratory or in situ, i.e., in the field. Although it is common knowledge that measurements obtained through field studies vs. laboratory incubations can diverge because of the vastly different conditions of these environments, few studies have systematically examined these patterns. It is crucial to understand the magnitude and reasons for any differences, as these data are used to parametrize and benchmark ecosystem- to global-scale models, which are then susceptible to the biases of the source data. Here, we specifically examine how greenhouse gas measurements may be influenced by whether the measurement/incubation was conducted in the field vs. laboratory, focusing on CO2 and CH4 measurements. We use Q10 of greenhouse gas flux (temperature sensitivity) for our analyses, because of the ubiquity of this metric in biological and Earth system sciences and its importance to many modeling frameworks. We predicted that laboratory measurements would be less variable, but also less representative of true field conditions. However, there was greater variability in the Q10 values calculated from lab-based measurements of CO2 fluxes, because lab experiments explore extremes rarely seen in situ, and reflect the physical and chemical disturbances occurring during sampling, transport, and incubation. Overall, respiration Q10 values were significantly greater in laboratory incubations (mean = 4.19) than field measurements (mean = 3.05), with strong influences of incubation temperature and climate region/biome. However, this was in part because field measurements typically represent total respiration (Rs), whereas lab incubations typically represent heterotrophic respiration (Rh), making direct comparisons difficult to interpret. Focusing only on Rh-derived Q10, these values showed almost identical distributions across laboratory (n = 1110) and field (n = 581) experiments, providing strong support for using the former as an experimental proxy for the latter, although we caution that geographic biases in the extant data make this conclusion tentative. Due to a smaller sample size of CH4 Q10 data, we were unable to perform a comparable robust analysis, but we expect similar interactions with soil temperature, moisture, and environmental/climatic variables. Our results here suggest the need for more concerted efforts to document and standardize these data, including sample and site metadata. This dataset contains a compressed (.zip) archive of the data and R scripts used for this manuscript. The dataset includes files in .csv format, which can be accessed and processed using MS Excel or R. This archive can also be accessed on GitHub at https://github.com/kaizadp/field_lab_q10 (DOI: 10.5281/zenodo.7106554).

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Exploring Multiscale Earth System and Human-Earth System Dynamics in the Puget Sound Region

With its mountain-to-coast hydroclimate, strong influence of Pacific Ocean weather systems and climate patterns, and unique land use history with strong rural-to-urban gradients, the Puget Sound region is a natural laboratory for studying a number of complex processes in, and interactions among, different Earth and human systems. A 1-year scoping study was initiated by the Earth and Environmental Systems Modeling program of the Department of Energy’s Office of Science Biological and Environmental Research. It was intended to elucidate and highlight the rich opportunities Puget Sound offers to advance our understanding of and ability to simulate Earth system changes and human-Earth system interactions. A literature review, multi-day community workshop, and external input were used to develop this scoping study report. The report first summarizes scientific understanding and knowledge gaps associated with major regional systems, including atmosphere and climate, the land surface, coastal and marine processes, and human systems, as well as how these systems are changing over time. It then highlights some of the most notable extreme events in the region, including heat waves, atmospheric rivers, droughts, and wildfires. Finally, key research opportunities for Earth and environmental systems modeling in, above, and around Puget Sound are highlighted.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1985

Numerical Estimation of the Curvature of Biological Surfaces

Many biological systems may profitably be studied as surface phenomena. A model consisting of isotropic growth of a curved surface from a flat sheet is assumed. With such a model, the Gaussian curvature of the final surface determines whether growth rate of the surface is subharmonic or superharmonic. These properties correspond to notions of convexity and concavity, and thus to local excess growth and local deficiency of growth. In biological models where the major factors controlling surface growth are intrinsic to the surface, researchers thus gained from geometrical study information on the differential growth undergone by the surface. These ideas were applied to an analysis of the folding of the cerebral cortex, a geometrically rather complex surface growth. A numerical surface curvature technique based on an approximation to the Dupin indicatrix of the surface was developed. A metric for comparing curvature estimates is introduced, and considerable numerical testing indicated the reliability of this technique.

Todd, P. H.↗

NASA NTRS2003

Biologically Inspired Micro-Flight Research

Natural fliers demonstrate a diverse array of flight capabilities, many of which are poorly understood. NASA has established a research project to explore and exploit flight technologies inspired by biological systems. One part of this project focuses on dynamic modeling and control of micro aerial vehicles that incorporate flexible wing structures inspired by natural fliers such as insects, hummingbirds and bats. With a vast number of potential civil and military applications, micro aerial vehicles represent an emerging sector of the aerospace market. This paper describes an ongoing research activity in which mechanization and control concepts for biologically inspired micro aerial vehicles are being explored. Research activities focusing on a flexible fixed- wing micro aerial vehicle design and a flapping-based micro aerial vehicle concept are presented.

Raney, David L.↗

NASA NTRS1988

USSR Space Life Sciences Digest, issue 19

This is the 19th issue of NASA's USSR Space Life Sciences Digest. It contains abstracts of 47 papers published in Russian language periodicals or presented at conferences and of 5 new Soviet monographs. Selected abstracts are illustrated with figures and tables from the original. Reports on two conferences, one on adaptation to high altitudes, and one on space and ecology are presented. A book review of a recent work on high altitude physiology is also included. The abstracts in this issue have been identified as relevant to 33 areas of space biology and medicine. These areas are: adaptation, biological rhythms, biospherics, body fluids, botany, cardiovascular and respiratory systems, cytology, developmental biology, endocrinology, enzymology, biology, group dynamics, habitability and environmental effects, hematology, human performance, immunology, life support systems, man-machine systems, mathematical modeling, metabolism, microbiology, musculoskeletal system, neurophysiology, nutrition, operational medicine, perception, personnel selection, psychology, radiobiology, and space biology and medicine.

Hooke, Lydia Razran↗

DOE OSTI2022

Proteome-scale Deployment of Protein Structure Prediction Workflows on the Summit Supercomputer

Deep learning has contributed to major advances in the prediction of protein structure from sequence, a fundamental problem in structural bioinformatics. With predictions now approaching the accuracy of crystallographic experiments, and with accelerators like GPUs and TPUs making inference using large models rapid, genome-level structure prediction becomes an obvious aim. Leadership-class computing resources can be used to perform genome-scale protein structure prediction using state-of-the-art deep learning models, providing a wealth of new data for systems biology applications. Here we describe our efforts to efficiently deploy the AlphaFold v.2 program, for full-proteome structure prediction, at scale on the Oak Ridge Leadership Computing Facility's resources, including the Summit supercomputer. We performed inference to produce the predicted structures for 40,526 protein sequences, corresponding to four prokaryotic proteomes and one plant proteome, using under 4,400 total Summit node hours, equivalent to using the majority of the supercomputer for a little over one hour. We also designed an optimized structure refinement that reduced the time for the relaxation stage of the AlphaFold pipeline by over 10X for longer sequences. We demonstrate the types of analyses that can be performed on proteome-scale collections of sequences, including a search for novel quaternary structures and implications for functional annotation.

Gao, Mu↗

NASA NTRS1992

Life sciences and space research XXIV(1) - Gravitational biology; Proceedings of Symposia 10 and 13 of the Topical Meeting of the Interdisciplinary Scientific Commission F (Meetings F1 and F2) of the COSPAR 28th Plenary Meeting, The Hague, Netherlands, June 25-July 6, 1990

Topics presented include an introduction to theories and models of biological response to gravity, gravity effects on biological systems, the function of calcium in plant graviperception, developmental biology on unmanned spacecraft, and the effect of microgravity on the development of plant protoplasts flown on Biocosmos 9. Also presented are the mechanism by which an asymmetric distribution of plant growth hormone is attained, the perception of gravity by plants, an animal research facility for Space Station Freedom, the long-term effects of microgravity and possible countermeasures, and an experimental system for determining the influence of microgravity on B lymphocyte activation and cell fusion.

Young, R. S.↗

NASA NTRS2003

Modeling beta-adrenergic control of cardiac myocyte contractility in silico

The beta-adrenergic signaling pathway regulates cardiac myocyte contractility through a combination of feedforward and feedback mechanisms. We used systems analysis to investigate how the components and topology of this signaling network permit neurohormonal control of excitation-contraction coupling in the rat ventricular myocyte. A kinetic model integrating beta-adrenergic signaling with excitation-contraction coupling was formulated, and each subsystem was validated with independent biochemical and physiological measurements. Model analysis was used to investigate quantitatively the effects of specific molecular perturbations. 3-Fold overexpression of adenylyl cyclase in the model allowed an 85% higher rate of cyclic AMP synthesis than an equivalent overexpression of beta 1-adrenergic receptor, and manipulating the affinity of Gs alpha for adenylyl cyclase was a more potent regulator of cyclic AMP production. The model predicted that less than 40% of adenylyl cyclase molecules may be stimulated under maximal receptor activation, and an experimental protocol is suggested for validating this prediction. The model also predicted that the endogenous heat-stable protein kinase inhibitor may enhance basal cyclic AMP buffering by 68% and increasing the apparent Hill coefficient of protein kinase A activation from 1.0 to 2.0. Finally, phosphorylation of the L-type calcium channel and phospholamban were found sufficient to predict the dominant changes in myocyte contractility, including a 2.6x increase in systolic calcium (inotropy) and a 28% decrease in calcium half-relaxation time (lusitropy). By performing systems analysis, the consequences of molecular perturbations in the beta-adrenergic signaling network may be understood within the context of integrative cellular physiology.

Non-NASA Center↗

NASA NTRS2001

Impact of dilution on microbial community structure and functional potential: comparison of numerical simulations and batch culture experiments

A series of microcosm experiments was performed using serial dilutions of a sewage microbial community to inoculate a set of batch cultures in sterile sewage. After inoculation, the dilution-defined communities were allowed to regrow for several days and a number of community attributes were measured in the regrown assemblages. Based upon a set of numerical simulations, community structure was expected to differ along the dilution gradient; the greatest differences in structure were anticipated between the undiluted-low-dilution communities and the communities regrown from the very dilute (more than 10(-4)) inocula. Furthermore, some differences were expected among the lower-dilution treatments (e.g., between undiluted and 10(-1)) depending upon the evenness of the original community. In general, each of the procedures used to examine the experimental community structures separated the communities into at least two, often three, distinct groups. The groupings were consistent with the simulated dilution of a mixture of organisms with a very uneven distribution. Significant differences in community structure were detected with genetic (amplified fragment length polymorphism and terminal restriction fragment length polymorphism), physiological (community level physiological profiling), and culture-based (colony morphology on R2A agar) measurements. Along with differences in community structure, differences in community size (acridine orange direct counting), composition (ratio of sewage medium counts to R2A counts, monitoring of each colony morphology across the treatments), and metabolic redundancy (i.e., generalist versus specialist) were also observed, suggesting that the differences in structure and diversity of communities maintained in the same environment can be manifested as differences in community organization and function.

Non-NASA Center↗

NASA NTRSDate not supplied

Open Science for Life in Space: Data Sharing and Tools for Knowledge Discovery

The fast-growing array of space biological data, which in the past was simply archived after minimal analysis, holds great potential if it can be reorganized and formatted for Open Science. Organizing the data for such analysis is a challenge because of its diverse nature (molecular, cellular, tissue, whole organism, behavior; tabular, imagery). Open Science is the concept that the more people have access to scientifically curated data, the more knowledge will be gained. This led NASA to start the development of GeneLab in 2015. GeneLab houses spaceflight and space-analog multi-omics datasets from plant, rodent, small animal, and microbial experiments. The success and knowledge gained from GeneLab led to a new alliance of NASA “Open Science Data Repositories” (OSDR), which include the Ames Life Sciences Data Archive (ALSDA) and the NASA Biological Institutional Scientific Collection (NBISC). Both are adopting the GeneLab data system, so data are more findable, accessible, interoperable, and reusable (FAIR). OSDR systems provide users the ability to upload, download, search, share, analyze, and visualize. Open Science also needs strong confidence in the data, which is gained through building science communities. With ~400 current members, GeneLab and ALSDA formed Analysis Working Groups (AWGs) to provide feedback on processing pipelines, metadata curation standards (for ‘omics and phenotypic-physiological-behavioral assays), and to collaborate in effectively reusing data. The AWG also led to the development of the Radiation Biology Ontology (RBO), ensuring radiation metadata are efficiently captured, connected, and interoperable. Feedback from the AWG provided design input toward the new single point-of-entry data submission portal for all investigators to submit, curate, and share their research data. Space biological data is now maximally open access, collected-curated with rich metadata, and formatted for interoperability to enable systems biology, meta-analysis, knowledge graphs, machine learning, modeling, and other reuse approaches. With potential for further federation of OSDR for data mining with traditional biological and medical databases (NIH, NCI, EBI, etc.), a new era for space biology has begun to support the knowledge discovery necessary for Lunar and Martian missions.

Ryan T Scott↗

NASA NTRS1987

USSR Space Life Sciences Digest, issue 13

This is the thirteenth issue of NASA's USSR Space Life Sciences Digest. It contains abstracts of 39 papers recently published in Russian-language periodicals and bound collections, two papers delivered at an international life sciences symposium, and three new Soviet monographs. Selected abstracts are illustrated with figures and tables from the original. Also included is a review of a recent Soviet-French symposium on Space Cytology. Current Soviet Life Sciences titles available in English are cited. The materials included in this issue have been identified as relevant to 31 areas of aerospace medicine and space biology. These areas are: adaptation, biological rhythms, body fluids, botany, cardiovascular and respiratory systems, cosmonaut training, cytology, developmental biology, endocrinology, enzymology, equipment and instrumentation, gastrointestinal systems, genetics, habitability and environment effects, hematology, human performance, immunology, life support systems, mathematical modeling, metabolism, microbiology, musculoskeletal system, neurophysiology, nutrition, operational medicine, perception, personnel selection, psychology, radiobiology, space biology, and space medicine.

Hooke, Lydia Razran↗

NASA NTRS2001

A Structural and Molecular Approach for the Study Biomarkers

Investigation of the nucleation and growth of crystals in both abiotic and biotic systems is critical to seemingly diverse disciplines of geology, biology, environmental science, and astrobiology. While there are abundant studies devoted to the determination of the structure and composition of inorganic crystals, as well as to the development of thermodynamic and kinetic models, it is only recently that research efforts have been directed towards understanding mineralization in biological systems (i.e., biomineralization). Biomineralization refers to the processes by which living organisms form inorganic solids. Studies of the processes of biomineralization under low temperature aqueous conditions have focused primarily on magnetite forming bacteria and shell forming marine organisms. Many of the biological building materials consist of inorganic minerals (calcium carbonate, calcium phosphate, silica or iron oxide) intricately combined with organic polymers (like proteins). More recently, efforts have been undertaken to explore the nature of biological activities in ancient rocks. In the absence of well-preserved microorganisms or genetic material required for the polmerase chain reaction (PCR) method in molecular phylogenetic studies, using biominerals as biomarkers offers an alternative approach for the recognition of biogenic activity in both terrestrial and extraterrestrial environments. The primary driving force in biomineralization is the interaction between organic and inorganic phases. Thus, the investigation of the ultrastructure and the nature of reactions at the molecular level occurring at the interface between inorganic and organic phases is essential to understanding the processes leading to the nucleation and growth of crystals. It is recognized that crystal surfaces can serve as the substrate for the organization of organic molecules that lead to the formation of polymers and other complex organic molecules, and in discussions of the origins of life, is referred to as organic synthesis on mineral surfaces. Furthermore, it is suggested that the interaction between mineral surfaces and simple organic molecules resulted in the formation of amino acids, RNA, and perhaps other more complex molecules such as proteins. On the other hand, in natural systems, it is recognized that functional groups on cell walls or membranes of microorganisms serve as sites of nucleation and crystallization. The precise replication of biominerals with controlled structure, morphology, size and texture is not confined to higher organisms as it also occurs in primitive prokaryotic cells such as magnetotactic bacteria and cyanobacteria. This suggests that the principal strategies of biomineralization were established early on in the evolutionary history of organisms. It is critical, therefore, to search for common mechanisms within diverse biological systems. One such common factor is the capability for organization and self-assembly. Organic macromolecules such as proteins and lipids can aggregate and polymerize forming membranes or extracellular matrix. At the organic-inorganic interface, several factors such as lattice geometry, polarity, stereochemistry and topography may act in concert to control nucleation and growth of crystals. Although several models have been proposed that discuss the significance of these factors for biomineralization, no comprehensive experimental data are available. In contrast to crystallization in exclusively inorganic systems, the kinetics of reaction and structural relationships between organic and inorganic phases in biominerals or biomimetic material is poorly understood. For example, it is not clear if the concept of epitactic growth (geometrical matching of unit cells at the interface of a secondary crystal growing on a primary crystal) applies to organic-inorganic systems. In contrast to inorganic templates that often have a smooth and rigid surface that promotes epitactic growth, biological substrates are usually rough and result in a large degree of mismatch. It is apparent that factors controlling the reaction at the crystal-matrix interface are strongly dependent upon the nature of the substrate. Therefore, characterization of the assembled organic surface and surface structure of the inorganic phase is crucial to understanding the processes of biomineralization. The focus of our research is the investigation of the processes leading to the nucleation and growth of crystals on both natural and synthetic systems through an interdisciplinary approach that integrates molecular biology, morphology and mineralogy using advanced preparation and analytical techniques. We have studied run-products, particularly magnetite, siderite and other carbonates, that resulted from extracellular biomineralization by extremophiles isolated from a variety of extreme environments ranging from permafrost to hydrothermal vent systems. The results of this study are critical to recognizing biomarkers in terrestrial and extraterrestrial environments.

Thomas-Keprta, Kathie↗

NASA NTRS1999

Applications of amorphous track models in radiation biology

The average or amorphous track model uses the response of a system to gamma-rays and the radial distribution of dose about an ion's path to describe survival and other cellular endpoints from proton, heavy ion, and neutron irradiation. This model has been used for over 30 years to successfully fit many radiobiology data sets. We review several extensions of this approach that address objections to the original model, and consider applications of interest in radiobiology and space radiation risk assessment. In the light of present views of important cellular targets, the role of target size as manifested through the relative contributions from ion-kill (intra-track) and gamma-kill (inter-track) remains a critical question in understanding the success of the amorphous track model. Several variations of the amorphous model are discussed, including ones that consider the radial distribution of event-sizes rather than average electron dose, damage clusters rather than multiple targets, and a role for repair or damage processing.

NASA Discipline Radiation Health↗

NASA NTRS2002

Modeling and control for closed environment plant production systems

A computer program was developed to study multiple crop production and control in controlled environment plant production systems. The program simulates crop growth and development under nominal and off-nominal environments. Time-series crop models for wheat (Triticum aestivum), soybean (Glycine max), and white potato (Solanum tuberosum) are integrated with a model-based predictive controller. The controller evaluates and compensates for effects of environmental disturbances on crop production scheduling. The crop models consist of a set of nonlinear polynomial equations, six for each crop, developed using multivariate polynomial regression (MPR). Simulated data from DSSAT crop models, previously modified for crop production in controlled environments with hydroponics under elevated atmospheric carbon dioxide concentration, were used for the MPR fitting. The model-based predictive controller adjusts light intensity, air temperature, and carbon dioxide concentration set points in response to environmental perturbations. Control signals are determined from minimization of a cost function, which is based on the weighted control effort and squared-error between the system response and desired reference signal.

NASA Discipline Life Support Systems↗

NASA NTRS1986

USSR Space Life Sciences Digest, issue 6

This is the sixth issue of NASA's USSR Space Life Sciences Digest. It contains abstracts of 54 papers recently published in Russian language periodicals and bound collections and of 10 new Soviet monographs. Selected abstracts are illustrated with figures and tables from the original. Additional features include a table of Soviet EVAs and information about English translations of Soviet materials available to readers. The topics covered in this issue have been identified as relevant to 26 areas of aerospace medicine and space biology. These areas are adaptation, biospherics, body fluids, botany, cardiovascular and respiratory systems, developmental biology, endocrinology, enzymology, exobiology, genetics, habitability and environment effects, health and medical treatment, hematology, human performance, immunology, life support systems, mathematical modeling, metabolism., microbiology, morphology and cytology, musculoskeletal system, neurophysiology, nutrition, perception, personnel selection, psychology, radiobiology, reproductive biology, and space medicine.

Hooke, L. R.↗

DOE OSTI2025

In vitro toxicity assessment of uranium particulates on different human lung epithelial cell models

Inhalation of uranium aerosols produced via human activities such as mining can pose a threat to human respiratory systems. Uranium oxide particulates emit short-range alpha particles that elicit DNA and direct damage, beyond associated physiochemical heavy-metal toxicity, to internal epithelial tissues. The availability of reliable in vitro models to study radiation exposure can greatly enhance our ability to understand and combat the biological impacts of exposure. However, the toxicological effects of alpha emissions and/or the oxidation states of uranium particulates vary across different human lung epithelial cell models and have not been systematically compared. We have endeavored to address this limitation by comparing impacts in three different human lung cell models: primary human bronchial and tracheal epithelial cells, primary human small airway epithelial cells, and human adenocarcinoma alveolar basal epithelial cells. Other studies have mainly investigated the toxicity of depleted uranium. Here, we compared the exposure of uranium oxide particulates (U 3 O 8 and UO 3 ) of different enrichment states on the chosen cell systems. Each cell model was exposed to 0.1, 1, 10, 50, 100, and 500 µg/mL of depleted U 3 O 8 , highly-enriched U 3 O 8 , and natural UO 3 particulates for 24 hours in submerged monolayer cultures. We compared viability and superoxide dismutase activity results across cell lines and uranium enrichment/ oxidative states. The results showed that 1) the oxide state of the particulates affected cell viability, implying that uranium’s different oxidation states contribute to different toxicological responses, and 2) each cell model reacts differently when exposed to uranium oxides, which may provide insights into the mechanistic processes associated with the exposure of radiological particulates on different biological systems. For instance, increased uranium enrichment corresponds to increased toxicity for the primary cells, but not for the immortalized cells. Our study shows that a holistic approach that incorporates similarities between model systems and types of radionuclides is required to truly develop empirical solutions for radiation exposure.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2020

Pattern formation in a coupled membrane-bulk reaction-diffusion model for intracellular polarization and oscillations

Reaction-diffusion systems have been widely used to study spatio-temporal phenomena in cell biology, such as cell polarization. Coupled bulk-surface models naturally include compartmentalization of cytosolic and membrane-bound polarity molecules. Here we study the distribution of the polarity protein Cdc42 in a mass-conserved membrane-bulk model, and explore the effects of diffusion and spatial dimensionality on spatio-temporal pattern formation. We first analyze a one-dimensional (1-D) model for Cdc42 oscillations in fission yeast, consisting of two diffusion equations in the bulk domain coupled to nonlinear ODEs for binding kinetics at each end of the cell. In 1-D, our analysis reveals the existence of symmetric and asymmetric steady states, as well as anti-phase relaxation oscillations typical of slow-fast systems. We then extend our analysis to a two-dimensional (2-D) model with circular bulk geometry, for which species can either diffuse inside the cell or become bound to the membrane and undergo a nonlinear reaction-diffusion process. We also consider a nonlocal system of PDEs approximating the dynamics of the 2-D membrane-bulk model in the limit of fast bulk diffusion. In all three model variants we find that mass conservation selects perturbations of spatial modes that simply redistribute mass. In 1-D, only anti-phase oscillations between the two ends of the cell can occur, and in-phase oscillations are excluded. In higher dimensions, no radially symmetric oscillations are observed. Instead, the only instabilities are symmetry-breaking, either corresponding to stationary Turing instabilities, leading to the formation of stationary patterns, or to oscillatory Turing instabilities, leading to traveling and standing waves. Codimension-two Bogdanov—Takens bifurcations occur when the two distinct instabilities coincide, causing traveling waves to slow down and to eventually become stationary patterns. Our work clarifies the effect of geometry and dimensionality on behaviors observed in ma.ss-conserved cell polarity models.

97 MATHEMATICS AND COMPUTING↗