Mathematical modeling of drug-induced receptor internalization in the HER2-positive SKBR3 breast cancer cell-line

About 20% of breast cancer tumors over-express the HER2 receptor. Trastuzumab, an approved drug to treat this type of breast cancer, is a monoclonal antibody directly binding at the HER2 receptor and ultimately inhibiting cancer cell growth. The goal of our study was to understand the early impact of trastuzumab on HER2 internalization and recycling in the HER2-overexpressing breast cancer cell line SKBR3. To this end, fluorescence microscopy, monitoring the amount of HER2 expression in the plasma membrane, was combined with mathematical modeling to derive the flux of HER2 receptors from and to the membrane. We constructed a dynamic multi-compartment model based on ordinary differential equations. To account for cancer cell heterogeneity, a first, dynamic model was expanded to a second model including two distinct cell phenotypes, with implications for different conformational states of HER2, i.e. monomeric or homodimeric. Our mathematical model shows that the hypothesis of fast constitutive HER2 recycling back to the plasma membrane does not match the experimental data. It conclusively describes the experimental observation that trastuzumab induces sustained receptor internalization in cells with membrane ruffles. It is also concluded that for rare, non-ruffled (flat) cells, HER2 internalization occurs three orders of magnitude slower than for the bulk, ruffled cell population

Dynamic Modeling, Parameter Estimation, and Uncertainty Analysis in R

In a wide variety of research fields, dynamic modeling is employed as an instrument to learn and understand complex systems. The differential equations involved in this process are usually non-linear and depend on many parameters whose values determine the characteristics of the emergent system. The inverse problem, i.e., the inference or estimation of parameter values from observed data, is of interest from two points of view. First, the existence point of view, dealing with the question whether the system is able to reproduce the observed dynamics for any parameter values. Second, the identifiability point of view, investigating invariance of the prediction under change of parameter values, as well as the quantification of parameter uncertainty. In this paper, we present the R package dMod providing a framework for dealing with the inverse problem in dynamic systems modeled by ordinary differential equations. The uniqueness of the approach taken by dMod is to provide and propagate accurate derivatives computed from symbolic expressions wherever possible. This derivative information highly supports the convergence of optimization routines and enhances their numerical stability, a requirement for the applicability of sophisticated uncertainty analysis methods. Computational efficiency is achieved by automatic generation and execution of C code. The framework is object-oriented (S3) and provides a variety of functions to set up ordinary differential equation models, observation functions and parameter transformations for multi-conditional parameter estimation. The key elements of the framework and the methodology implemented in dMod are highlighted by an application on a three-compartment transporter model

A new security approach in telecom infrastructures: The RESISTO concept

Communications play a fundamental role in the economic and social well-being of the citizens and on operations of most of the critical infrastructures (CIs).Extreme weather events, natural disasters and criminal attacks represent a challenge due to their increase in frequency and intensity requiring smarter resilience of the Communication CIs, which are extremely vulnerable due to the ever-increasing complexity of the architecture also in light of the evolution towards 5G, the extensive use of programmable platforms and exponential growth of connected devices. In this paper, we present the aim of RESISTO H2020 EU-funded project, which constitutes an innovative solution for Communication Cis holistic situation awareness and enhanced resilience

Plant-type phytoene desaturase: Functional evaluation of structural implications

<div><p>Phytoene desaturase (PDS) is an essential plant carotenoid biosynthetic enzyme and a prominent target of certain inhibitors, such as norflurazon, acting as bleaching herbicides. PDS catalyzes the introduction of two double bonds into 15-<i>cis</i>-phytoene, yielding 9,15,9'-tri-<i>cis</i>-ζ-carotene via the intermediate 9,15-di-<i>cis</i>-phytofluene. We present the necessary data to scrutinize functional implications inferred from the recently resolved crystal structure of <i>Oryza sativa</i> PDS in a complex with norflurazon. Using dynamic mathematical modeling of reaction time courses, we support the relevance of homotetrameric assembly of the enzyme observed <i>in crystallo</i> by providing evidence for substrate channeling of the intermediate phytofluene between individual subunits at membrane surfaces. Kinetic investigations are compatible with an ordered ping-pong bi-bi kinetic mechanism in which the carotene and the quinone electron acceptor successively occupy the same catalytic site. The mutagenesis of a conserved arginine that forms a hydrogen bond with norflurazon, the latter competing with plastoquinone, corroborates the possibility of engineering herbicide resistance, however, at the expense of diminished catalytic activity. This mutagenesis also supports a “flavin only” mechanism of carotene desaturation not requiring charged residues in the active site. Evidence for the role of the central 15-<i>cis</i> double bond of phytoene in determining regio-specificity of carotene desaturation is presented.</p></div

Kinetic scheme of the substrate channeling model and dynamic modeling of PDS reaction time courses.

<p>(A) Substrate channeling model, accounting for substrate channeling between PDS homotetramers. Symbols are as given in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0187628#pone.0187628.g004" target="_blank">Fig 4A</a>. Two species of phytofluene, i.e. phytofluene fates, coexist. Left; nascent phytofluene (pf*) that is produced from phytoene (p) can be restricted in its diffusion into the membrane residing in a microdomain in proximity to the PDS homotetramer, as indicated by the bent arrow. It can be channeled into a second PDS subunit of the homotetramer containing FAD_ox, allowing rapid conversion to ζ-carotene (z) with the rate constant <i>k</i>_pf*. Right; pf* can alternatively diffuse into PDS-distant membrane areas with rate constant <i>k</i>_diff, this defining the species pf. From there it can be taken up by another monomeric PDS subunit and be converted into ζ-carotene (z) with rate constant <i>k</i>_pf. Rate constant <i>k</i>_age represents enzyme inactivation which refers to both the reduced and oxidized enzyme states. (B-G) Dynamic modeling of reaction time courses of phytoene and phytofluene conversion by PDS. Reaction time courses were conducted with 1.3 nmol phytoene (p low; B), and 3.7 nmol phytoene (p high; C). In addition, liposomes containing 5.2 nmol phytofluene were used (pf; D). The observables are given as data points (black, phytoene, p; red, phytofluene, pf; blue, ζ-carotene, z). The model fit, represented by lines, is based on Eqs <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0187628#pone.0187628.e013" target="_blank">1</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0187628#pone.0187628.e018" target="_blank">6</a>–<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0187628#pone.0187628.e022" target="_blank">10</a> with simultaneous parameter estimation for all three reaction time courses. Shadowed areas indicate one standard deviation as estimated by the error model (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0187628#sec002" target="_blank">Methods</a>). Measurements were carried out in triplicate. (E) Prediction of the amount of oxidized, active PDS (ox) and reduced PDS (red) over time, indicating a rapid decrease in oxidized and reduced PDS levels due to enzyme inactivation. (F,G) Deduced carotene fluxes through the different sub-processes labeled with their rate constants (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0187628#pone.0187628.g004" target="_blank">Fig 4</a>). Note the different scaling in F and G. Flux predictions are based on the phytoene conversion reaction time course “p high” (C).</p

Observed and estimated apparent K_M and V_max values for PDS substrates.

<p>Observed and estimated apparent K_M and V_max values for PDS substrates.</p

Kinetic scheme of the monomeric model and dynamic modeling of PDS reaction time courses.

<p>(A) Monomeric model. PDS monomeric subunits (orange and blue rectangles) within the homotetramer are assumed to work independently. Orange/blue color denotes reduced/oxidized half sides of phytoene (p), phytofluene (pf) and ζ-carotene (z) and the respective redox state of the PDS-bound FAD. The overall reaction comprises the three main processes phytoene desaturation (i), phytofluene desaturation (ii) and plastoquinone reduction (iii) with the rate constants <i>k</i>_p, <i>k</i>_pf and <i>k</i>_rox, respectively. Each rate constant encompasses the three equilibria represented by the reaction arrows associated to each of the three main processes which are highlighted by shadowed areas: association-dissociation of enzyme and substrate, desaturation-saturation of substrate and dissociation-association of enzyme and product. All hydrophobic carotene substrates and DPQ (Q) are soluble in the hydrophobic core of liposomal membranes. Progressive inactivation of PDS by denaturation (iv) is a process to be considered. (B-D) Reaction time courses of phytoene and phytofluene conversion by PDS. Reaction time courses were initiated [p] = 3.7 nmol (p high; B), [p] = 1.3 nmol (p low; C) and [pf] = 5.2 nmol (pf; D). The observables are given as data points (black, phytoene, p; red, phytofluene, pf; blue, ζ-carotene, pf), the model fit (obtained with model I; ODE 1–5) is represented by lines. The modeling was either based on simultaneous parameter estimation for all three reaction time courses (solid lines) or on simultaneous estimation of <i>k</i>_p, <i>k</i>_rox and <i>k</i>_age and individual estimation of <i>k</i>_pf (dashed line). Measurements were carried out in triplicate.</p