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Endothelial cells, which line the lumen of blood vessels, locally sense and respond to blood flow. In response to altered blood flow dynamics during early embryonic development, these cells undergo shape changes that directly affect vessel geometry: In the dorsal aorta of zebrafish embryos, elongation of endothelial cells in the direction of flow between 48 and 72 hours post fertilization (hpf) reduces the vessel's diameter. This remodeling process requires Endoglin; excessive endothelial cell growth in the protein's absence results in vessel diameter increases. To understand how these changes in vessel geometry emerge from morphological changes of individual endothelial cells, we developed a novel mathematical approach that allows 3D reconstruction and quantification of both dorsal aorta geometry and endothelial cell surface morphology. Based on fluorescently marked endothelial cell contours, we inferred cross-sections of the dorsal aorta that accounted for dorsal flattening of the vessel. By projection of endothelial cell contours onto the estimated cross-sections and subsequent triangulation, we finally reconstructed 3D surfaces of the individual cells. By simultaneously reconstructing vessel cross-sections and cell surfaces, we found in an exploratory analysis that morphology varied between endothelial cells located in different sectors of the dorsal aorta in both wild-type and Endoglin-deficient zebrafish embryos: In wild-types, ventral endothelial cells were smaller and more elongated in flow direction than dorsal endothelial cells at both 48 hpf and 72 hpf. Although dorsal and ventral endothelial cells in Endoglin-deficient embryos had similar sizes at 48 hpf, dorsal endothelial cells were much larger at 72 hpf. In Endoglin-deficient embryos, elongation in flow direction increased between 48 hpf and 72 hpf in ventral endothelial cells but hardly changed in dorsal endothelial cells. Hereby, we provide evidence that dorsal endothelial cells contribute most to the disparate changes in dorsal aorta diameter in wild-type and Endoglin-deficient embryos between 48 hpf and 72 hpf. Author summary: Endothelial cells, which form the innermost layer of each blood vessel, sense and respond to blood flow. During early embryonic development in zebrafish, endothelial cells of the dorsal aorta elongate in the direction of blood flow and hereby decrease the vessel's diameter. To understand how these changes in vessel geometry emerge from morphological changes of individual endothelial cells, it is critical to precisely quantify both vessel geometry and cell morphology. To this end, we developed a novel mathematical approach that leverages information from fluorescently marked endothelial cell contours to reconstruct the dorsal aorta's surface in 3D. In an exploratory analysis, we applied this method to wild-type and mutant zebrafish embryos lacking functional Endoglin that is required for the physiological vessel diameter decrease. By quantifying vessel geometry and cell morphology in these embryos, we found that size and elongation in the direction of blood flow varied between endothelial cells located in different vessel sectors. Notably, we determined a subgroup of endothelial cells that contributed most to the vessel diameter increases in the absence of Endoglin. Future studies can investigate whether variability in endothelial cell behavior also contributes to the onset of human vascular malformations occurring due to a loss of Endoglin. [ABSTRACT FROM AUTHOR]

In systems biology and pharmacology, large-scale kinetic models are used to study the dynamic response of a system to a specific input or stimulus. While in many applications, a deeper understanding of the input-response behaviour is highly desirable, it is often hindered by the large number of molecular species and the complexity of the interactions. An approach that identifies key molecular species for a given input-response relationship and characterises dynamic properties of states is therefore highly desirable. We introduce the concept of index analysis; it is based on different time- and state-dependent quantities (indices) to identify important dynamic characteristics of molecular species. All indices are defined for a specific pair of input and response variables as well as for a specific magnitude of the input. In application to a large-scale kinetic model of the EGFR signalling cascade, we identified different phases of signal transduction, the peculiar role of Phosphatase3 during signal activation and Ras recycling during signal onset. In addition, we discuss the challenges and pitfalls of interpreting the relevance of molecular species based on knock-out simulation studies, and provide an alternative view on conflicting results on the importance of parallel EGFR downstream pathways. Beyond the applications in model interpretation, index analysis is envisioned to be a valuable tool in model reduction. Author summary: In systems biology, the response of signalling networks to various molecular stimuli is studied through large and complex kinetic models. Prominent examples include the epidermal growth factor receptor signalling cascade and its response to growth factors or therapeutic interventions by small molecules and therapeutic protein drugs. The design of targeted interventions requires a detailed understanding of the signalling cascade, the identification of key molecular constituents and their functional role in propagating the signal. A quantitative analysis of such systems, however, is challenging due the size of the model and the complexity of molecular interactions. We present an approach based on time- and state dependent quantities that are called indices and quantify different characteristic dynamic features of the molecular constituents. This allows for a more in-depth understanding of how the signal propagates through the network and elicits its response. Our findings for the epidermal growth factor receptor signalling cascade provide new insights on the dynamic interplay of key molecular players. [ABSTRACT FROM AUTHOR]

Amoeboid cell motility is relevant in a wide variety of biomedical processes such as wound healing, cancer metastasis, and embryonic morphogenesis. It is characterized by pronounced changes of the cell shape associated with expansions and retractions of the cell membrane, which result in a crawling kind of locomotion. Despite existing computational models of amoeboid motion, the inference of expansion and retraction components of individual cells, the corresponding classification of cells, and the a priori specification of the parameter regime to achieve a specific motility behavior remain challenging open problems. We propose a novel model of the spatio-temporal evolution of two-dimensional cell contours comprising three biophysiologically motivated components: a stochastic term accounting for membrane protrusions and two deterministic terms accounting for membrane retractions by regularizing the shape and area of the contour. Mathematically, these correspond to the intensity of a self-exciting Poisson point process, the area-preserving curve-shortening flow, and an area adjustment flow. The model is used to generate contour data for a variety of qualitatively different, e.g., polarized and non-polarized, cell tracks that visually resemble experimental data very closely. In application to experimental cell tracks, we inferred the protrusion component and examined its correlation to common biomarkers: the F-actin density close to the membrane and its local motion. Due to the low model complexity, parameter estimation is fast, straightforward, and offers a simple way to classify contour dynamics based on two locomotion types: the amoeboid and a so-called fan-shaped type. For both types, we use cell tracks segmented from fluorescence imaging data of the model organism Dictyostelium discoideum. An implementation of the model is provided within the open-source software package AmoePy, a Python-based toolbox for analyzing and simulating amoeboid cell motility. [ABSTRACT FROM AUTHOR]

Amoeboid cell motility is essential for a wide range of biological processes including wound healing, embryonic morphogenesis, and cancer metastasis. It relies on complex dynamical patterns of cell shape changes that pose long-standing challenges to mathematical modeling and raise a need for automated and reproducible approaches to extract quantitative morphological features from image sequences. Here, we introduce a theoretical framework and a computational method for obtaining smooth representations of the spatiotemporal contour dynamics from stacks of segmented microscopy images. Based on a Gaussian process regression we propose a one-parameter family of regularized contour flows that allows us to continuously track reference points (virtual markers) between successive cell contours. We use this approach to define a coordinate system on the moving cell boundary and to represent different local geometric quantities in this frame of reference. In particular, we introduce the local marker dispersion as a measure to identify localized membrane expansions and provide a fully automated way to extract the properties of such expansions, including their area and growth time. The methods are available as an open-source software package called AmoePy, a Python-based toolbox for analyzing amoeboid cell motility (based on time-lapse microscopy data), including a graphical user interface and detailed documentation. Due to the mathematical rigor of our framework, we envision it to be of use for the development of novel cell motility models. We mainly use experimental data of the social amoeba Dictyostelium discoideum to illustrate and validate our approach. Author summary: Amoeboid motion is a crawling-like cell migration that plays an important key role in multiple biological processes such as wound healing and cancer metastasis. This type of cell motility results from expanding and simultaneously contracting parts of the cell membrane. From fluorescence images, we obtain a sequence of points, representing the cell membrane, for each time step. By using regression analysis on these sequences, we derive smooth representations, so-called contours, of the membrane. Since the number of measurements is discrete and often limited, the question is raised of how to link consecutive contours with each other. In this work, we present a novel mathematical framework in which these links are described by regularized flows allowing a certain degree of concentration or stretching of neighboring reference points on the same contour. This stretching rate, the so-called local dispersion, is used to identify expansions and contractions of the cell membrane providing a fully automated way of extracting properties of these cell shape changes. We applied our methods to time-lapse microscopy data of the social amoeba Dictyostelium discoideum. [ABSTRACT FROM AUTHOR]

Despite the success of highly active antiretroviral therapy (HAART) in the management of human immunodeficiency virus (HIV)-1 infection, virological failure due to drug resistance development remains a major challenge. Resistant mutants display reduced drug susceptibilities, but in the absence of drug, they generally have a lower fitness than the wild type, owing to a mutation-incurred cost. The interaction between these fitness costs and drug resistance dictates the appearance of mutants and influences viral suppression and therapeutic success. Assessing in vivo viral fitness is a challenging task and yet one that has significant clinical relevance. Here, we present a new computational modelling approach for estimating viral fitness that relies on common sparse cross-sectional clinical data by combining statistical approaches to learn drug-specific mutational pathways and resistance factors with viral dynamics models to represent the host-virus interaction and actions of drug mechanistically. We estimate in vivo fitness characteristics of mutant genotypes for two antiretroviral drugs, the reverse transcriptase inhibitor zidovudine (ZDV) and the protease inhibitor indinavir (IDV). Well-known features of HIV-1 fitness landscapes are recovered, both in the absence and presence of drugs. We quantify the complex interplay between fitness costs and resistance by computing selective advantages for different mutants. Our approach extends naturally to multiple drugs and we illustrate this by simulating a dual therapy with ZDV and IDV to assess therapy failure. The combined statistical and dynamical modelling approach may help in dissecting the effects of fitness costs and resistance with the ultimate aim of assisting the choice of salvage therapies after treatment failure. [ABSTRACT FROM AUTHOR]

The human immunodeficiency virus (HIV) can be suppressed by highly active anti-retroviral therapy (HAART) in the majority of infected patients. Nevertheless, treatment interruptions inevitably result in viral rebounds from persistent, latently infected cells, necessitating lifelong treatment. Virological failure due to resistance development is a frequent event and the major threat to treatment success. Currently, it is recommended to change treatment after the confirmation of virological failure. However, at the moment virological failure is detected, drug resistant mutants already replicate in great numbers. They infect numerous cells, many of which will turn into latently infected cells. This pool of cells represents an archive of resistance, which has the potential of limiting future treatment options. The objective of this study was to design a treatment strategy for treatment-naive patients that decreases the likelihood of early treatment failure and preserves future treatment options. We propose to apply a single, pro-active treatment switch, following a period of treatment with an induction regimen. The main goal of the induction regimen is to decrease the abundance of randomly generated mutants that confer resistance to the maintenance regimen, thereby increasing subsequent treatment success. Treatment is switched before the overgrowth and archiving of mutant strains that carry resistance against the induction regimen and would limit its future re-use. In silico modelling shows that an optimal trade-off is achieved by switching treatment at ≈ 80 days after the initiation of antiviral therapy. Evaluation of the proposed treatment strategy demonstrated significant improvements in terms of resistance archiving and virological response, as compared to conventional HAART. While continuous pro-active treatment alternation improved the clinical outcome in a randomized trial, our results indicate that a similar improvement might also be reached after a single pro-active treatment switch. The clinical validity of this finding, however, remains to be shown by a corresponding trial. [ABSTRACT FROM AUTHOR]

Predictive markers linking drug efficacy to clinical outcome are a key component in the drug discovery and development process. In HIV infection, two different measures, viral load decay and phenotypic assays, are used to assess drug efficacy in vivo and in vitro. For the newly introduced class of integrase inhibitors, a huge discrepancy between these two measures of efficacy was observed. Hence, a thorough understanding of the relation between these two measures of drug efficacy is imperative for guiding future drug discovery and development activities in HIV. In this article, we developed a novel viral dynamics model, which allows for a mechanistic integration of the mode of action of all approved drugs and drugs in late clinical trials. Subsequently, we established a link between in vivo and in vitro measures of drug efficacy, and extract important determinants of drug efficacy in vivo. The analysis is based on a new quantity—the reproductive capacity—that represents in mathematical terms the in vivo analog of the read-out of a phenotypic assay. Our results suggest a drug-class specific impact of antivirals on the total amount of viral replication. Moreover, we showed that the (drug-)target half life, dominated by immune-system related clearance processes, is a key characteristic that affects both the emergence of resistance as well as the in vitro-in vivo correlation of efficacy measures in HIV treatment. We found that protease- and maturation inhibitors, due to their target half-life, decrease the total amount of viral replication and the emergence of resistance most efficiently. [ABSTRACT FROM AUTHOR]

The human immunodeficiency virus (HIV) can be suppressed by highly active anti-retroviral therapy (HAART) in the majority of infected patients. Nevertheless, treatment interruptions inevitably result in viral rebounds from persistent, latently infected cells, necessitating lifelong treatment. Virological failure due to resistance development is a frequent event and the major threat to treatment success. Currently, it is recommended to change treatment after the confirmation of virological failure. However, at the moment virological failure is detected, drug resistant mutants already replicate in great numbers. They infect numerous cells, many of which will turn into latently infected cells. This pool of cells represents an archive of resistance, which has the potential of limiting future treatment options. The objective of this study was to design a treatment strategy for treatment-naive patients that decreases the likelihood of early treatment failure and preserves future treatment options. We propose to apply a single, pro-active treatment switch, following a period of treatment with an induction regimen. The main goal of the induction regimen is to decrease the abundance of randomly generated mutants that confer resistance to the maintenance regimen, thereby increasing subsequent treatment success. Treatment is switched before the overgrowth and archiving of mutant strains that carry resistance against the induction regimen and would limit its future re-use. In silico modelling shows that an optimal trade-off is achieved by switching treatment at days after the initiation of antiviral therapy. Evaluation of the proposed treatment strategy demonstrated significant improvements in terms of resistance archiving and virological response, as compared to conventional HAART. While continuous pro-active treatment alternation improved the clinical outcome in a randomized trial, our results indicate that a similar improvement might also be reached after a single pro-active treatment switch. The clinical validity of this finding, however, remains to be shown by a corresponding trial.