Modelling mechanically dominated vasculature development

Vascular networks play a key role in the development, function, and survival of many organisms, facilitating transport of nutrients and other critical factors within and between systems. The development of these vessel networks has been thoroughly explored in a variety of in vivo, in vitro and in silico contexts. However, the role of interactions between the growing vasculature and its environment remains largely unresolved, particularly concerning mechanical effects. Motivated by this gap in understanding, we develop a computational framework that is tailored to exploring the role of the mechanical environment on the formation of vascular networks. Here, we describe, document, implement, and explore an agent-based modelling framework, resolving the growth of individual vessels and seeking to capture phenomenology and intuitive qualitative mechanisms. In our explorations, we demonstrate that such a model can successfully reproduce familiar network structures, whilst highlighting the roles that mechanical influences could play in vascular development. For instance, we illustrate how an external substrate could act as an effective shared memory for the periodic regrowth of vasculature. We also observe the emergence of a nuanced collective behaviour and clustered vessel growth, which results from mechanical characteristics of the external environment

A mathematical model of α-catenin dimerization at Adherens Junctions in polarized epithelial cells

Abstract The protein α-catenin is found as a monomer or homodimer. As a monomer, α-catenin can bind to β-catenin, which localizes to the plasma membrane at the site of Adherens Junctions (AJs) in polarized epithelial cells. As a dimer, α-catenin can bind to actin filaments, affecting the organization of the actin cytoskeleton. At usual cytoplasmic concentrations, α-catenin is found predominantly in monomeric form. It is currently thought that α-catenin can not simultaneously bind β-catenin and homodimerize, and that the dynamics of binding and unbinding from β-catenin, possibly coupled with lower diffusion near an AJ, are sufficient to locally accumulate α-catenin monomers and homodimers. Using a mathematical model of α-catenin dynamics, I show that α-catenin must transiently homodimerize while bound to β-catenin in order for homodimers to form, even in the presence of a spatial diffusion gradient

Topological data analysis approaches to uncovering the timing of ring structure onset in filamentous networks

Improvements in experimental and computational technologies have led to significant increases in data available for analysis. Topological data analysis (TDA) is an emerging area of mathematical research that can identify structures in these data sets. Here we develop a TDA method to detect physical structures in a cell that persist over time. In most cells, protein filaments (actin) interact with motor proteins (myosins) and organize into polymer networks and higher-order structures. An example of these structures are ring channels that maintain constant diameters over time and play key roles in processes such as cell division, development, and wound healing. The interactions of actin with myosin can be challenging to investigate experimentally in living systems, given limitations in filament visualization \textit{in vivo}. We therefore use complex agent-based models that simulate mechanical and chemical interactions of polymer proteins in cells. To understand how filaments organize into structures, we propose a TDA method that assesses effective ring generation in data consisting of simulated actin filament positions through time. We analyze the topological structure of point clouds sampled along these actin filaments and propose an algorithm for connecting significant topological features in time. We introduce visualization tools that allow the detection of dynamic ring structure formation. This method provides a rigorous way to investigate how specific interactions and parameters may impact the timing of filamentous network organization.Comment: 20 pages, 9 figure

Variation in Structure and Process of Care in Traumatic Brain Injury: Provider Profiles of European Neurotrauma Centers Participating in the CENTER-TBI Study.

INTRODUCTION: The strength of evidence underpinning care and treatment recommendations in traumatic brain injury (TBI) is low. Comparative effectiveness research (CER) has been proposed as a framework to provide evidence for optimal care for TBI patients. The first step in CER is to map the existing variation. The aim of current study is to quantify variation in general structural and process characteristics among centers participating in the Collaborative European NeuroTrauma Effectiveness Research in Traumatic Brain Injury (CENTER-TBI) study. METHODS: We designed a set of 11 provider profiling questionnaires with 321 questions about various aspects of TBI care, chosen based on literature and expert opinion. After pilot testing, questionnaires were disseminated to 71 centers from 20 countries participating in the CENTER-TBI study. Reliability of questionnaires was estimated by calculating a concordance rate among 5% duplicate questions. RESULTS: All 71 centers completed the questionnaires. Median concordance rate among duplicate questions was 0.85. The majority of centers were academic hospitals (n = 65, 92%), designated as a level I trauma center (n = 48, 68%) and situated in an urban location (n = 70, 99%). The availability of facilities for neuro-trauma care varied across centers; e.g. 40 (57%) had a dedicated neuro-intensive care unit (ICU), 36 (51%) had an in-hospital rehabilitation unit and the organization of the ICU was closed in 64% (n = 45) of the centers. In addition, we found wide variation in processes of care, such as the ICU admission policy and intracranial pressure monitoring policy among centers. CONCLUSION: Even among high-volume, specialized neurotrauma centers there is substantial variation in structures and processes of TBI care. This variation provides an opportunity to study effectiveness of specific aspects of TBI care and to identify best practices with CER approaches

Variation in neurosurgical management of traumatic brain injury

Background: Neurosurgical management of traumatic brain injury (TBI) is challenging, with only low-quality evidence. We aimed to explore differences in neurosurgical strategies for TBI across Europe. Methods: A survey was sent to 68 centers participating in the Collaborative European Neurotrauma Effectiveness Research in Traumatic Brain Injury (CENTER-TBI) study. The questionnaire contained 21 questions, including the decision when to operate (or not) on traumatic acute subdural hematoma (ASDH) and intracerebral hematoma (ICH), and when to perform a decompressive craniectomy (DC) in raised intracranial pressure (ICP). Results: The survey was completed by 68 centers (100%). On average, 10 neurosurgeons work in each trauma center. In all centers, a neurosurgeon was available within 30 min. Forty percent of responders reported a thickness or volume threshold for evacuation of an ASDH. Most responders (78%) decide on a primary DC in evacuating an ASDH during the operation, when swelling is present. For ICH, 3% would perform an evacuation directly to prevent secondary deterioration and 66% only in case of clinical deterioration. Most respondents (91%) reported to consider a DC for refractory high ICP. The reported cut-off ICP for DC in refractory high ICP, however, differed: 60% uses 25 mmHg, 18% 30 mmHg, and 17% 20 mmHg. Treatment strategies varied substantially between regions, specifically for the threshold for ASDH surgery and DC for refractory raised ICP. Also within center variation was present: 31% reported variation within the hospital for inserting an ICP monitor and 43% for evacuating mass lesions. Conclusion: Despite a homogeneous organization, considerable practice variation exists of neurosurgical strategies for TBI in Europe. These results provide an incentive for comparative effectiveness research to determine elements of effective neurosurgical care

Efficient parameter generation for constrained models using MCMC

Abstract Mathematical models of complex systems rely on parameter values to produce a desired behavior. As mathematical and computational models increase in complexity, it becomes correspondingly difficult to find parameter values that satisfy system constraints. We propose a Markov Chain Monte Carlo (MCMC) approach for the problem of constrained model parameter generation by designing a Markov chain that efficiently explores a model’s parameter space. We demonstrate the use of our proposed methodology to analyze responses of a newly constructed bistability-constrained model of protein phosphorylation to perturbations in the underlying protein network. Our results suggest that parameter generation for constrained models using MCMC provides powerful tools for modeling-aided analysis of complex natural processes

Stronger net posterior cortical forces and asymmetric microtubule arrays produce simultaneous centration and rotation of the pronuclear complex in the early Caenorhabditis elegans embryo

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