Quantifying the phosphorylation timescales of receptor-ligand complexes: a Markovian matrix-analytic approach.

Cells interact with the extracellular environment by means of receptor molecules on their surface. Receptors can bind different ligands, leading to the formation of receptor-ligand complexes. For a subset of receptors, called receptor tyrosine kinases, binding to ligand enables sequential phosphorylation of intra-cellular residues, which initiates a signalling cascade that regulates cellular function and fate. Most mathematical modelling approaches employed to analyse receptor signalling are deterministic, especially when studying scenarios of high ligand concentration or large receptor numbers. There exist, however, biological scenarios where low copy numbers of ligands and/or receptors need to be considered, or where signalling by a few bound receptor-ligand complexes is enough to initiate a cellular response. Under these conditions stochastic approaches are appropriate, and in fact, different attempts have been made in the literature to measure the timescales of receptor signalling initiation in receptor-ligand systems. However, these approaches have made use of numerical simulations or approximations, such as moment-closure techniques. In this paper, we study, from an analytical perspective, the stochastic times to reach a given signalling threshold for two receptor-ligand models. We identify this time as an extinction time for a conveniently defined auxiliary absorbing continuous time Markov process, since receptor-ligand association/dissociation events can be analysed in terms of quasi-birth-and-death processes. We implement algorithmic techniques to compute the different order moments of this time, as well as the steady-state probability distribution of the system. A novel feature of the approach introduced here is that it allows one to quantify the role played by each kinetic rate in the timescales of signal initiation, and in the steady-state probability distribution of the system. Finally, we illustrate our approach by carrying out numerical studies for the vascular endothelial growth factor and one of its receptors, the vascular endothelial growth factor receptor of human endothelial cells.

Computational assessment of thioether isosteres.

Replacement of the sulfur atom in biologically active diaryl and heteroaryl thioethers (Ar-S-Ar', HAr-S-Ar, and HAr-S-HAr') with any of several one-atom or two-atom linkers can be expected to reduce the susceptibility of the analogue to metabolic oxidation, a well-documented problem for thioethers intended for medicinal chemistry applications. Ab initio calculations indicate how well various proposed thioether isosteric groups, including some new and unusual ones, may perform structurally and electronically in replacing the bridging sulfur atom. Four of these are calculationally evaluated as proposed substructures in Axitinib analogues. The predicted binding behavior of the latter within two different previously crystallographically characterized protein-Axitinib binding sites (VEGFR2 kinase and ABL1 T315I gatekeeper mutant kinase), and an assessment of their suitability and anticipated shortcomings, are presented.

Intravitreal Ziv-Aflibercept: Clinical Effects and Economic Impact.

During the past decade, drugs that inhibit the actions of vascular endothelial growth factor (VEGF) have become standard-of-care treatment for a variety of chorioretinal vascular conditions. The off-label, intravitreal use of ziv-aflibercept (Zaltrap) has provided clinicians with an additional cost-effective drug. The commercial preparation of ziv-aflibercept contains the same aflibercept (VEGF-trap) molecule as Eylea but has a much higher osmolarity (1000 mOsm/kg vs 300 mOsm/kg). Initial concerns regarding cytotoxicity and long-term safety of intravitreal ziv-aflibercept have been largely negated after a series of publications failed to identify adverse ocular and systemic side effects. Both treatment-naive and anti-VEGF‒resistant cases of neovascular age-related macular degeneration (nAMD), diabetic macular edema (DME), retinal vein occlusion (RVO), and choroidal neovascular membrane (CNVM) may respond as well to ziv-aflibercept as to aflibercept. A higher dose of ziv-aflibercept (2 mg in 0.08 mL) does not cause any adverse effects during short-term follow-up period (1 month). Data from various sources suggest that ziv-aflibercept may be as cost effective as bevacizumab, thereby making it an attractive treatment option in low- and middle-income countries. However, problems with off-label use, compounding, and counterfeiting limit its availability in many countries. Data from prospective, randomized, multicenter clinical trials are still required to convince physicians and regulatory bodies of its clinical efficacy and potential as early therapy.

Modulation, bioinformatic screening, and assessment of small molecular peptides targeting the vascular endothelial growth factor receptor.

Vascular endothelial growth factor (VEGF) and VEGF receptor (VEGFR) are important factors in tumor growth and metastasis. Molecular probes or drugs designed to target VEGF/VEGFR interactions are crucial in tumor molecular imaging and targeted therapy. Bioinformatic methods enable molecular design based on the structure of bio-macromolecules and their interactions. This study was aimed to identify tumor-targeting small-molecule peptides with high affinity for VEGFR using bioinformatics screening. The VEGFR extracellular immunoglobulin-like modules Ig1-Ig3 were used as the target to systematically alter the primary peptide sequence of VEGF125-136. Molecular docking and surface functional group interaction methods were combined in an in silico screen for polypeptides, which in theory, would have higher affinities for VEGFR. In vitro receptor competition binding assays were used to assess the affinity of the putative VEGFR-binding polypeptides. Rhodamine-conjugated peptides were used to label and visualize peptide-binding sites on A549 cells. Using bioinformatic screening, we identified 20 polypeptides with potentially higher affinity for VEGFR. The polypeptides were capable of inhibiting the binding of (125)I-VEGF to VEGFR in a dose-dependent manner. The IC50 values of QKRKRKKSRKKH and RKRKRKKSRYIVLS (80 and 185 nmol/L, respectively) were significantly lower than that of VEGF125-136 (464 nmol/L); thus, the affinity of these peptides for VEGFR was 6- and 2.5-fold higher, respectively, than that of VEGF125-136. Rhodamine labeling of A549 cells revealed peptide binding mainly on the plasma membrane and in the cytoplasm. Bioinformatic approaches hold promise for the development of molecular imaging probes. Using this approach, we designed two peptides that showed higher affinity toward VEGFR. These polypeptides may be used as molecular probes or drugs targeting VEGFR, which can be utilized in molecular imaging and targeted therapy of certain tumors.

Monte Carlo simulations of VEGF binding to cell surface receptors in vitro.

The vascular endothelial growth factor (VEGF) family binds multiple endothelial cell surface receptors. Our goal is to build comprehensive models of these interactions for the purpose of simulating angiogenesis. In view of low concentrations of growth factors in vivo and in vitro, stochastic modeling of molecular interactions may be necessary. Here, we compare Monte Carlo simulations of the stochastic binding of VEGF and two of its major receptors on cells in vitro to equivalent deterministic simulations. In the range of typical VEGF concentrations, the stochastic and deterministic models are in agreement. However, we observe significant variability in receptor binding, which may be linked to biological stochastic events, e.g., blood vessel sprout initiation. We study patches of cell surface of varying sizes to investigate spatial integration of the signal by the cell, which impacts directly the variability of binding, and find significant variability up to the single-cell level. Dimerization of VEGF receptors does not significantly alter the variability in ligand binding. A 'sliding window' approach demonstrated no reduction in the variability of binding by temporal integration. The variability is expected to be more prominent in in vivo situations where the number of ligand molecules available for binding is less.