Rapid and sustained nuclear–cytoplasmic ERK oscillations induced by epidermal growth factor

Although the ERK pathway has a central role in the response of cells to growth factors, its regulatory structure and dynamics are incompletely understood. To investigate ERK activation in real time, we expressed an ERK–GFP fusion protein in human mammary epithelial cells. On EGF stimulation, we observed sustained oscillations of the ERK–GFP fusion protein between the nucleus and cytoplasm with a periodicity of ∼15 min. The oscillations were persistent (>45 cycles), independent of cell cycle phase, and were highly dependent on cell density, essentially disappearing at confluency. Oscillations occurred even at ligand doses that elicited very low levels of ERK phosphorylation, and could be detected biochemically in both transfected and nontransfected cells. Mathematical modeling revealed that negative feedback from phosphorylated ERK to the cascade input was necessary to match the robustness of the oscillation characteristics observed over a broad range of ligand concentrations. Our characterization of single-cell ERK dynamics provides a quantitative foundation for understanding the regulatory structure of this signaling cascade

Coupled Systems of Differential-Algebraic and Kinetic Equations with Application to the Mathematical Modelling of Muscle Tissue

We consider a coupled system composed of a linear differential-algebraic equation (DAE) and a linear large-scale system of ordinary differential equations where the latter stands for the dynamics of numerous identical particles. Replacing the discrete particles by a kinetic equation for a particle density, we obtain in the mean-field limit the new class of partially kinetic systems. We investigate the influence of constraints on the kinetic theory of those systems and present necessary adjustments. We adapt the mean-field limit to the DAE model and show that index reduction and the mean-field limit commute. As a main result, we prove Dobrushin's stability estimate for linear systems. The estimate implies convergence of the mean-field limit and provides a rigorous link between the particle dynamics and their kinetic description. Our research is inspired by mathematical models for muscle tissue where the macroscopic behaviour is governed by the equations of continuum mechanics, often discretised by the finite element method, and the microscopic muscle contraction process is described by Huxley's sliding filament theory. The latter represents a kinetic equation that characterises the state of the actin-myosin bindings in the muscle filaments. Linear partially kinetic systems are a simplified version of such models, with focus on the constraints.Comment: 32 pages, 18 figure

Targeted Drug Delivery by Gemtuzumab Ozogamicin: Mechanism-Based Mathematical Model for Treatment Strategy Improvement and Therapy Individualization

Gemtuzumab ozogamicin (GO) is a chemotherapy-conjugated anti-CD33 monoclonal antibody effective in some patients with acute myeloid leukemia (AML). The optimal treatment schedule and optimal timing of GO administration relative to other agents remains unknown. Conventional pharmacokinetic analysis has been of limited insight for the schedule optimization. We developed a mechanism-based mathematical model and employed it to analyze the time-course of free and GO-bound CD33 molecules on the lekemic blasts in individual AML patients treated with GO. We calculated expected intravascular drug exposure (I-AUC) as a surrogate marker for the response to the drug. A high CD33 production rate and low drug efflux were the most important determinants of high I-AUC, characterizing patients with favorable pharmacokinetic profile and, hence, improved response. I-AUC was insensitive to other studied parameters within biologically relevant ranges, including internalization rate and dissociation constant. Our computations suggested that even moderate blast burden reduction prior to drug administration enables lowering of GO doses without significantly compromising intracellular drug exposure. These findings indicate that GO may optimally be used after cyto-reductive chemotherapy, rather than before, or concomitantly with it, and that GO efficacy can be maintained by dose reduction to 6 mg/m2 and a dosing interval of 7 days. Model predictions are validated by comparison with the results of EORTC-GIMEMA AML19 clinical trial, where two different GO schedules were administered. We suggest that incorporation of our results in clinical practice can serve identification of the subpopulation of elderly patients who can benefit most of the GO treatment and enable return of the currently suspended drug to clinic

Spatio-Temporal Dependence of the Signaling Response in Immune-Receptor Trafficking Networks Regulated by Cell Density: A Theoretical Model

Cell signaling processes involve receptor trafficking through highly connected networks of interacting components. The binding of surface receptors to their specific ligands is a key factor for the control and triggering of signaling pathways. In most experimental systems, ligand concentration and cell density vary within a wide range of values. Dependence of the signal response on cell density is related with the extracellular volume available per cell. This dependence has previously been studied using non-spatial models which assume that signaling components are well mixed and uniformly distributed in a single compartment. In this paper, a mathematical model that shows the influence exerted by cell density on the spatio-temporal evolution of ligands, cell surface receptors, and intracellular signaling molecules is developed. To this end, partial differential equations were used to model ligand and receptor trafficking dynamics through the different domains of the whole system. This enabled us to analyze several interesting features involved with these systems, namely: a) how the perturbation caused by the signaling response propagates through the system; b) receptor internalization dynamics and how cell density affects the robustness of dose-response curves upon variation of the binding affinity; and c) that enhanced correlations between ligand input and system response are obtained under conditions that result in larger perturbations of the equilibrium . Finally, the results are compared with those obtained by considering that the above components are well mixed in a single compartment

An empirical Bayesian approach for model-based inference of cellular signaling networks

Background A common challenge in systems biology is to infer mechanistic descriptions of biological process given limited observations of a biological system. Mathematical models are frequently used to represent a belief about the causal relationships among proteins within a signaling network. Bayesian methods provide an attractive framework for inferring the validity of those beliefs in the context of the available data. However, efficient sampling of high-dimensional parameter space and appropriate convergence criteria provide barriers for implementing an empirical Bayesian approach. The objective of this study was to apply an Adaptive Markov chain Monte Carlo technique to a typical study of cellular signaling pathways. Results As an illustrative example, a kinetic model for the early signaling events associated with the epidermal growth factor (EGF) signaling network was calibrated against dynamic measurements observed in primary rat hepatocytes. A convergence criterion, based upon the Gelman-Rubin potential scale reduction factor, was applied to the model predictions. The posterior distributions of the parameters exhibited complicated structure, including significant covariance between specific parameters and a broad range of variance among the parameters. The model predictions, in contrast, were narrowly distributed and were used to identify areas of agreement among a collection of experimental studies. Conclusion In summary, an empirical Bayesian approach was developed for inferring the confidence that one can place in a particular model that describes signal transduction mechanisms and for inferring inconsistencies in experimental measurements

Phosphoproteomics-Based Modeling Defines the Regulatory Mechanism Underlying Aberrant EGFR Signaling

BACKGROUND: Mutation of the epidermal growth factor receptor (EGFR) results in a discordant cell signaling, leading to the development of various diseases. However, the mechanism underlying the alteration of downstream signaling due to such mutation has not yet been completely understood at the system level. Here, we report a phosphoproteomics-based methodology for characterizing the regulatory mechanism underlying aberrant EGFR signaling using computational network modeling. METHODOLOGY/PRINCIPAL FINDINGS: Our phosphoproteomic analysis of the mutation at tyrosine 992 (Y992), one of the multifunctional docking sites of EGFR, revealed network-wide effects of the mutation on EGF signaling in a time-resolved manner. Computational modeling based on the temporal activation profiles enabled us to not only rediscover already-known protein interactions with Y992 and internalization property of mutated EGFR but also further gain model-driven insights into the effect of cellular content and the regulation of EGFR degradation. Our kinetic model also suggested critical reactions facilitating the reconstruction of the diverse effects of the mutation on phosphoproteome dynamics. CONCLUSIONS/SIGNIFICANCE: Our integrative approach provided a mechanistic description of the disorders of mutated EGFR signaling networks, which could facilitate the development of a systematic strategy toward controlling disease-related cell signaling

Transcriptional Regulation: Effects of Promoter Proximal Pausing on Speed, Synchrony and Reliability

Recent whole genome polymerase binding assays in the Drosophila embryo have shown that a substantial proportion of uninduced genes have pre-assembled RNA polymerase-II transcription initiation complex (PIC) bound to their promoters. These constitute a subset of promoter proximally paused genes for which mRNA elongation instead of promoter access is regulated. This difference can be described as a rearrangement of the regulatory topology to control the downstream transcriptional process of elongation rather than the upstream transcriptional initiation event. It has been shown experimentally that genes with the former mode of regulation tend to induce faster and more synchronously, and that promoter-proximal pausing is observed mainly in metazoans, in accord with a posited impact on synchrony. However, it has not been shown whether or not it is the change in the regulated step per se that is causal. We investigate this question by proposing and analyzing a continuous-time Markov chain model of PIC assembly regulated at one of two steps: initial polymerase association with DNA, or release from a paused, transcribing state. Our analysis demonstrates that, over a wide range of physical parameters, increased speed and synchrony are functional consequences of elongation control. Further, we make new predictions about the effect of elongation regulation on the consistent control of total transcript number between cells. We also identify which elements in the transcription induction pathway are most sensitive to molecular noise and thus possibly the most evolutionarily constrained. Our methods produce symbolic expressions for quantities of interest with reasonable computational effort and they can be used to explore the interplay between interaction topology and molecular noise in a broader class of biochemical networks. We provide general-purpose code implementing these methods

A domain-based approach to predict protein-protein interactions

<p>Abstract</p> <p>Background</p> <p>Knowing which proteins exist in a certain organism or cell type and how these proteins interact with each other are necessary for the understanding of biological processes at the whole cell level. The determination of the protein-protein interaction (PPI) networks has been the subject of extensive research. Despite the development of reasonably successful methods, serious technical difficulties still exist. In this paper we present DomainGA, a quantitative computational approach that uses the information about the domain-domain interactions to predict the interactions between proteins.</p> <p>Results</p> <p>DomainGA is a multi-parameter optimization method in which the available PPI information is used to derive a quantitative scoring scheme for the domain-domain pairs. Obtained domain interaction scores are then used to predict whether a pair of proteins interacts. Using the yeast PPI data and a series of tests, we show the robustness and insensitivity of the DomainGA method to the selection of the parameter sets, score ranges, and detection rules. Our DomainGA method achieves very high explanation ratios for the positive and negative PPIs in yeast. Based on our cross-verification tests on human PPIs, comparison of the optimized scores with the structurally observed domain interactions obtained from the iPFAM database, and sensitivity and specificity analysis; we conclude that our DomainGA method shows great promise to be applicable across multiple organisms.</p> <p>Conclusion</p> <p>We envision the DomainGA as a first step of a multiple tier approach to constructing organism specific PPIs. As it is based on fundamental structural information, the DomainGA approach can be used to create potential PPIs and the accuracy of the constructed interaction template can be further improved using complementary methods. Explanation ratios obtained in the reported test case studies clearly show that the false prediction rates of the template networks constructed using the DomainGA scores are reasonably low, and the erroneous predictions can be filtered further using supplementary approaches such as those based on literature search or other prediction methods.</p