Ultrasensitivity in phosphorylation-dephosphorylation cycles with little substrate

Cellular decision-making is driven by dynamic behaviours, such as the preparations for sunrise enabled by circadian rhythms and the choice of cell fates enabled by positive feedback. Such behaviours are often built upon ultrasensitive responses where a linear change in input generates a sigmoidal change in output. Phosphorylation-dephosphorylation cycles are one means to generate ultrasensitivity. Using bioinformatics, we show that in vivo levels of kinases and phosphatases frequently exceed the levels of their corresponding substrates in budding yeast. This result is in contrast to the conditions often required by zero-order ultrasensitivity, perhaps the most well known means for how such cycles become ultrasensitive. We therefore introduce a mechanism to generate ultrasensitivity when numbers of enzymes are higher than numbers of substrates. Our model combines distributive and non-distributive actions of the enzymes with two-stage binding and concerted allosteric transitions of the substrate. We use analytical and numerical methods to calculate the Hill number of the response. For a substrate with [Formula: see text] phosphosites, we find an upper bound of the Hill number of [Formula: see text], and so even systems with a single phosphosite can be ultrasensitive. Two-stage binding, where an enzyme must first bind to a binding site on the substrate before it can access the substrate's phosphosites, allows the enzymes to sequester the substrate. Such sequestration combined with competition for each phosphosite provides an intuitive explanation for the sigmoidal shifts in levels of phosphorylated substrate. Additionally, we find cases for which the response is not monotonic, but shows instead a peak at intermediate levels of input. Given its generality, we expect the mechanism described by our model to often underlay decision-making circuits in eukaryotic cells

Computational Model of Vascular Endothelial Growth Factor Spatial Distribution in Muscle and Pro-Angiogenic Cell Therapy

Members of the vascular endothelial growth factor (VEGF) family of proteins are critical regulators of angiogenesis. VEGF concentration gradients are important for activation and chemotactic guidance of capillary sprouting, but measurement of these gradients in vivo is not currently possible. We have constructed a biophysically and molecularly detailed computational model to study microenvironmental transport of two isoforms of VEGF in rat extensor digitorum longus skeletal muscle under in vivo conditions. Using parameters based on experimental measurements, the model includes: VEGF secretion from muscle fibers; binding to the extracellular matrix; binding to and activation of endothelial cell surface VEGF receptors; and internalization. For 2-D cross sections of tissue, we analyzed predicted VEGF distributions, gradients, and receptor binding. Significant VEGF gradients (up to 12% change in VEGF concentration over 10 μm) were predicted in resting skeletal muscle with uniform VEGF secretion, due to non-uniform capillary distribution. These relative VEGF gradients were not sensitive to extracellular matrix composition, or to the overall VEGF expression level, but were dependent on VEGF receptor density and affinity, and internalization rate parameters. VEGF upregulation in a subset of fibers increased VEGF gradients, simulating transplantation of pro-angiogenic myoblasts, a possible therapy for ischemic diseases. The number and relative position of overexpressing fibers determined the VEGF gradients and distribution of VEGF receptor activation. With total VEGF expression level in the tissue unchanged, concentrating overexpression into a small number of adjacent fibers can increase the number of capillaries activated. The VEGF concentration gradients predicted for resting muscle (average 3% VEGF/10 μm) is sufficient for cellular sensing; the tip cell of a vessel sprout is approximately 50 μm long. The VEGF gradients also result in heterogeneity in the activation of blood vessel VEGF receptors. This first model of VEGF tissue transport and heterogeneity provides a platform for the design and evaluation of therapeutic approaches

The Presence of VEGF Receptors on the Luminal Surface of Endothelial Cells Affects VEGF Distribution and VEGF Signaling

Vascular endothelial growth factor (VEGF) is a potent cytokine that binds to specific receptors on the endothelial cells lining blood vessels. The signaling cascade triggered eventually leads to the formation of new capillaries, a process called angiogenesis. Distributions of VEGF receptors and VEGF ligands are therefore crucial determinants of angiogenic events and, to our knowledge, no quantification of abluminal vs. luminal receptors has been performed. We formulate a molecular-based compartment model to investigate the VEGF distribution in blood and tissue in humans and show that such quantification would lead to new insights on angiogenesis and VEGF-dependent diseases. Our multiscale model includes two major isoforms of VEGF (VEGF121 and VEGF165), as well as their receptors (VEGFR1 and VEGFR2) and the non-signaling co-receptor neuropilin-1 (NRP1). VEGF can be transported between tissue and blood via transendothelial permeability and the lymphatics. VEGF receptors are located on both the luminal and abluminal sides of the endothelial cells. In this study, we analyze the effects of the VEGF receptor localization on the endothelial cells as well as of the lymphatic transport. We show that the VEGF distribution is affected by the luminal receptor density. We predict that the receptor signaling occurs mostly on the abluminal endothelial surface, assuming that VEGF is secreted by parenchymal cells. However, for a low abluminal but high luminal receptor density, VEGF binds predominantly to VEGFR1 on the abluminal surface and VEGFR2 on the luminal surface. Such findings would be pertinent to pathological conditions and therapies related to VEGF receptor imbalance and overexpression on the endothelial cells and will hopefully encourage experimental receptor quantification for both luminal and abluminal surfaces on endothelial cells

A compartment model of VEGF distribution in blood, healthy and diseased tissues

<p>Abstract</p> <p>Background</p> <p>Angiogenesis is a process by which new capillaries are formed from pre-existing blood vessels in physiological (e.g., exercise, wound healing) or pathological (e.g., ischemic limb as in peripheral arterial disease, cancer) contexts. This neovascular mechanism is mediated by the vascular endothelial growth factor (VEGF) family of cytokines. Although VEGF is often targeted in anti-angiogenic therapies, there is little knowledge about how its concentration may vary between tissues and the vascular system. A compartment model is constructed to study the VEGF distribution in the tissue (including matrix-bound, cell surface receptor-bound and free VEGF isoforms) and in the blood. We analyze the sensitivity of this distribution to the secretion rate, clearance rate and vascular permeability of VEGF.</p> <p>Results</p> <p>We find that, in a physiological context, VEGF concentration varies approximately linearly with the VEGF secretion rate. VEGF concentration in blood but not in tissue is dependent on the vascular permeability of healthy tissue. Model simulations suggest that relative VEGF increases are similar in blood and tissue during exercise and return to baseline within several hours. In a pathological context (tumor), we find that blood VEGF concentration is relatively insensitive to increased vascular permeability in tumors, to the secretion rate of VEGF by tumors and to the clearance. However, it is sensitive to the vascular permeability in the healthy tissue. Finally, the VEGF distribution profile in healthy tissue reveals that about half of the VEGF is complexed with the receptor tyrosine kinase VEGFR2 and the co-receptor Neuropilin-1. In diseased tissues, this binding can be reduced to 15% while VEGF bound to the extracellular matrix and basement membranes increases.</p> <p>Conclusion</p> <p>The results are of importance for physiological conditions (e.g., exercise) and pathological conditions (e.g., peripheral arterial disease, coronary artery disease, cancer). This mathematical model can serve as a tool for understanding the VEGF distribution in physiological and pathological contexts as well as a foundation to investigate pro- or anti-angiogenic strategies.</p

Integration of experimental and computational approaches to sprouting angiogenesis

We summarize recent experimental and computational studies that investigate molecular and cellular mechanisms of sprouting angiogenesis. We discuss how experimental tools have unveiled new opportunities for computational modeling by providing detailed phenomenological descriptions and conceptual models of cell-level behaviors underpinned by high-quality molecular data. Using recent examples, we show how new understanding results from bridging computational and experimental approaches

Computational Modeling of Interacting VEGF and Soluble VEGF Receptor Concentration Gradients

Experimental data indicates that soluble vascular endothelial growth factor (VEGF) receptor 1 (sFlt-1) modulates the guidance cues provided to sprouting blood vessels by VEGF-A. To better delineate the role of sFlt-1 in VEGF signaling, we have developed an experimentally based computational model. This model describes dynamic spatial transport of VEGF, and its binding to receptors Flt-1 and Flk-1, in a mouse embryonic stem cell model of vessel morphogenesis. The model represents the local environment of a single blood vessel. Our simulations predict that blood vessel secretion of sFlt-1 and increased local sFlt-1 sequestration of VEGF results in decreased VEGF–Flk-1 levels on the sprout surface. In addition, the model predicts that sFlt-1 secretion increases the relative gradient of VEGF–Flk-1 along the sprout surface, which could alter endothelial cell perception of directionality cues. We also show that the proximity of neighboring sprouts may alter VEGF gradients, VEGF receptor binding, and the directionality of sprout growth. As sprout distances decrease, the probability that the sprouts will move in divergent directions increases. This model is a useful tool for determining how local sFlt-1 and VEGF gradients contribute to the spatial distribution of VEGF receptor binding, and can be used in conjunction with experimental data to explore how multi-cellular interactions and relationships between local growth factor gradients drive angiogenesis

Integrated computational and Drosophila cancer model platform captures previously unappreciated chemicals perturbing a kinase network

Drosophila provides an inexpensive and quantitative platform for measuring whole animal drug response. A complementary approach is virtual screening, where chemical libraries can be efficiently screened against protein target(s). Here, we present a unique discovery platform integrating structure-based modeling with Drosophila biology and organic synthesis. We demonstrate this platform by developing chemicals targeting a Drosophila model of Medullary Thyroid Cancer (MTC) characterized by a transformation network activated by oncogenic dRetM955T. Structural models for kinases relevant to MTC were generated for virtual screening to identify unique preliminary hits that suppressed dRetM955T-induced transformation. We then combined features from our hits with those of known inhibitors to create a ‘hybrid’ molecule with improved suppression of dRetM955T transformation. Our platform provides a framework to efficiently explore novel kinase inhibitors outside of explored inhibitor chemical space that are effective in inhibiting cancer networks while minimizing whole body toxicity

Flt-1 (VEGFR-1) coordinates discrete stages of blood vessel formation

In developing blood vessel networks, the overall level of vessel branching often correlates with angiogenic sprout initiations, but in some pathological situations, increased sprout initiations paradoxically lead to reduced vessel branching and impaired vascular function. We examine the hypothesis that defects in the discrete stages of angiogenesis can uniquely contribute to vessel branching outcomes