Mass Action Kinetic Model Research Articles

Basal State Calibration of a Chemical Reaction Network Model for Autophagy.

The modulation of autophagy plays a dual role in tumor cells, with the potential to both promote and suppress tumor proliferation. In order to gain a deeper understanding of the nature of autophagy, we have developed a chemical reaction kinetic model of autophagy and apoptosis based on the mass action kinetic models that have been previously described in the literature. It is regrettable that the authors did not provide all of the information necessary to reconstruct their model, which made their simulation results irreproducible. In this study, based on an extensive literature review, we have identified concentrations for each species in the stress-free, homeostatic state. These ranges were randomly sampled to generate sets of initial concentrations, from which the simulations were run. In every case, abnormal behavior was observed, with apoptosis and autophagy being activated, even in the absence of stress. Consequently, the model failed to reproduce even the basal conditions. Detailed examination of the model revealed erroneous reactions, which were corrected. The influential kinetic parameters of the corrected model were identified and optimized using the Optima++ code. The model is now capable of simulating homeostatic states, and provides a suitable basis for further model development to describe cell response to various stresses.

Evaluating the risk of data loss due to particle radiation damage in a DNA data storage system

DNA data storage is a potential alternative to magnetic tape for archival storage purposes, promising substantial gains in information density. Critical to the success of DNA as a storage media is an understanding of the role of environmental factors on the longevity of the stored information. In this paper, we evaluate the effect of exposure to ionizing particle radiation, a cause of data loss in traditional magnetic media, on the longevity of data in DNA data storage pools. We develop a mass action kinetics model to estimate the rate of damage accumulation in DNA strands due to neutron interactions with both nucleotides and residual water molecules, then utilize the model to evaluate the effect several design parameters of a typical DNA data storage scheme have on expected data longevity. Finally, we experimentally validate our model by exposing dried DNA samples to different levels of neutron irradiation and analyzing the resulting error profile. Our results show that particle radiation is not a significant contributor to data loss in DNA data storage pools under typical storage conditions.

Probabilistic and maximum entropy modeling of chemical reaction systems: Characteristics and comparisons to mass action kinetic models.

We demonstrate and characterize a first-principles approach to modeling the mass action dynamics of metabolism. Starting from a basic definition of entropy expressed as a multinomial probability density using Boltzmann probabilities with standard chemical potentials, we derive and compare the free energy dissipation and the entropy production rates. We express the relation between entropy production and the chemical master equation for modeling metabolism, which unifies chemical kinetics and chemical thermodynamics. Because prediction uncertainty with respect to parameter variability is frequently a concern with mass action models utilizing rate constants, we compare and contrast the maximum entropy model, which has its own set of rate parameters, to a population of standard mass action models in which the rate constants are randomly chosen. We show that a maximum entropy model is characterized by a high probability of free energy dissipation rate and likewise entropy production rate, relative to other models. We then characterize the variability of the maximum entropy model predictions with respect to uncertainties in parameters (standard free energies of formation) and with respect to ionic strengths typically found in a cell.

Discovering optimal kinetic pathways for self-assembly using automatic differentiation

Macromolecular complexes are often composed of diverse subunits. The self-assembly of these subunits is inherently nonequilibrium and must avoid kinetic traps to achieve high yield over feasible timescales. We show how the kinetics of self-assembly benefits from diversity in subunits because it generates an expansive parameter space that naturally improves the "expressivity" of self-assembly, much like a deeper neural network. By using automatic differentiation algorithms commonly used in deep learning, we searched the parameter spaces of mass-action kinetic models to identify classes of kinetic protocols that mimic biological solutions for productive self-assembly. Our results reveal how high-yield complexes that easily become kinetically trapped in incomplete intermediates can instead be steered by internal design of rate-constants or external and active control of subunits to efficiently assemble. Internal design of a hierarchy of subunit binding rates generates self-assembly that can robustly avoid kinetic traps for all concentrations and energetics, but it places strict constraints on selection of relative rates. External control via subunit titration is more versatile, avoiding kinetic traps for any system without requiring molecular engineering of binding rates, albeit less efficiently and robustly. We derive theoretical expressions for the timescales of kinetic traps, and we demonstrate our optimization method applies not just for design but inference, extracting intersubunit binding rates from observations of yield-vs.-time for a heterotetramer. Overall, we identify optimal kinetic protocols for self-assembly as a powerful mechanism to achieve efficient and high-yield assembly in synthetic systems whether robustness or ease of "designability" is preferred.

An Accurate Algebraic Closed Form Solution for Drug Transport Kinetics through P-Glycoprotein Expressing Confluent Cell Monolayers by Fitting Our Experimentally Derived Empirical Fitting Function with the Elementary Rate Constants of 370 Virtual P-gp subs

The kinetics of transport by P-gp through confluent cell monolayers is typically modelled by a version of the Michaelis-Menten equations within PBPK mechanistic models1-5. The quasi-steady-state Michaelis-Menten equation was solved by the Lambert W-function, which is an infinite summation series that can only be evaluated in Matlab, Maple and a few other math programs6. Our Structural Mass Action Kinetic Model (SMAKM) for P-gp transport through confluent cell monolayers was built from a more accurate set of mass action kinetic equations. Its most significant departure from PBPK mechanistic models was that P-gp can only bind drug that has partitioned from the cytosol into the cytosolic monolayer, according to its molar partition coefficient KPC, since that is where P-gp’s substrate binding site resides. Our analysis of P-gp transport for many drugs using SMAKM has shown that most, if not all, commonly used P-gp expressing cells also express basolateral and apical uptake transporters for many, if not all, P-gp substrates. An algebraic Closed Form Solution for P-gp transport has been built by fitting the elementary rate constants of 370 Virtual P-gp substrates to an algebraic equation we started building in 2005 to fit our experimental drug transport kinetics through P-gp expressing confluent cell monolayers. The resultant algebraic Closed Form Solution clearly shows how each of P-gp’s elementary rate constants contributes to transport. It is currently used, within Excel, to predict the upper and lower bounds required to fit the elementary rate constants of new experimental drug transport data using Matlab’s Particle Swarm program.

Utilization of first-order mass action kinetic models to elucidate the mechanism of methane fermentation of glycerol

Knowledge-driven models can aid in understanding the underlying mechanism of methane fermentation, however, these models are often too complex. We proposed to utilize first-order mass action kinetic models as a simpler alternative to conventional knowledge-driven models for gaining some insights on the mechanism of methane fermentation. The data used for model fitting were obtained from a methane fermentation experiment using anaerobic sequencing batch reactor (ASBR) with glycerol as a substrate. Incorporation of substrate feeding profile into the model improved fitness to the data especially during the early stage of the feeding cycle. Model with the assumption that glycerol was metabolized into both propionic and acetic acid and methane was produced via both propionic and acetic acid showed the best fit (root-mean square error = 0.0012), which suggested that the mechanism of the glycerol methane fermentation might follow that particular path. The difference in the applicability of the models on several feed profiles used in this experiment suggested that the mechanism can be different for each feed profile, which was supported by the microbial consortium data. These findings showed the possibility to use first-order mass action kinetic models as a simpler alternative to study the mechanism of methane fermentation of glycerol.

The susceptible–infected–recovered model as a tool to motivate and teach differential equations: an analytic approach

Since the introduction by Kermack and McKendrick in 1927, the Susceptible–Infected–Recovered (SIR) epidemic model has been a foundational model to comprehend and predict the dynamics of infectious diseases. Almost for a century, the SIR model has been modified and extended to meet the needs of different characteristics of various infectious diseases including recent COVID-19 breakouts, which stimulates the advance in mathematical epidemiology theory significantly. Some of the mathematical ideas and techniques developed are also relevant to motivate teaching various topics in differential equations by connecting students' life experiences with current pandemics to meaningful classroom learning activities. Here, various pedagogically relevant topics from the SIR model are provided for undergraduate differential equation class, which includes (1) compartmental modelling and mass action kinetic modelling, (2) conservation rule and model reduction, (3) introduction to phase plane by removing time variable to derive trajectory equations, (4) transformation of equations to equivalent forms, (5) transformation of second-order system to second-order ODE, (6) deriving an analytic solution to the SIR equation by solving Bernoulli's equation, (7) deriving an analytic solution to the SIR equation from trajectory equations and (8) deriving an analytic solution to the SIR equation from exponential substitutions.

Generalized Poisson-Nernst-Planck-Based Physical Model of the O2∣LSM∣YSZ Electrode

The paper presents a generalized Poisson-Nernst-Planck model of an yttria-stabilized zirconia electrolyte developed from first principles of nonequilibrium thermodynamics which allows for spatial resolution of the space charge layer. It takes into account limitations in oxide ion concentrations due to the limited availability of oxygen vacancies. The electrolyte model is coupled with a reaction kinetic model describing the triple phase boundary with electron conducting lanthanum strontium manganite and gaseous phase oxygen. By comparing the outcome of numerical simulations based on different formulations of the kinetic Eqs. with the results of EIS and CV measurements we attempt to discern the existence of separate surface lattice sites for oxygen adatoms and surface oxides from the assumption of shared ones. Moreover, we show that the mass-action kinetics model is sensitive to oxygen partial pressure unlike exponential kinetics models. The resulting model is fitted to a dataset of EIS and CVs spanning multiple temperatures and pressures, using various relative weights of EIS and CV data in the fitness function. The model successfully describes the physics of the interface around the OCV.

A structural property for reduction of biochemical networks

Large-scale biochemical models are of increasing sizes due to the consideration of interacting organisms and tissues. Model reduction approaches that preserve the flux phenotypes can simplify the analysis and predictions of steady-state metabolic phenotypes. However, existing approaches either restrict functionality of reduced models or do not lead to significant decreases in the number of modelled metabolites. Here, we introduce an approach for model reduction based on the structural property of balancing of complexes that preserves the steady-state fluxes supported by the network and can be efficiently determined at genome scale. Using two large-scale mass-action kinetic models of Escherichia coli, we show that our approach results in a substantial reduction of 99% of metabolites. Applications to genome-scale metabolic models across kingdoms of life result in up to 55% and 85% reduction in the number of metabolites when arbitrary and mass-action kinetics is assumed, respectively. We also show that predictions of the specific growth rate from the reduced models match those based on the original models. Since steady-state flux phenotypes from the original model are preserved in the reduced, the approach paves the way for analysing other metabolic phenotypes in large-scale biochemical networks.

Mathematical Models of Blood-Brain Barrier Transport of Monoclonal Antibodies Targeting the Transferrin Receptor and the Insulin Receptor.

We develop and analyze mathematical models for receptor-mediated transcytosis of monoclonal antibodies (MAb) targeting the transferrin receptor (TfR) or the insulin receptor (IR), which are expressed at the blood-brain barrier (BBB). The mass-action kinetic model for both the TfR and IR antibodies were solved numerically to generate predictions for the concentrations of all species in all compartments considered. Using these models, we estimated the rates of MAb endocytosis into brain capillary endothelium, which forms the BBB in vivo, the rates of MAb exocytosis from the intra-endothelial compartment into brain extracellular space, and the rates of receptor recycling from the endothelial space back to the luminal endothelial plasma membrane. Our analysis highlights the optimal rates of MAb association with the targeted receptor. An important role of the endogenous ligand, transferrin (Tf) or insulin, in receptor-mediated-transport (RMT) of the associated MAb was found and was attributed to the five order magnitude difference between plasma concentrations of Tf (25,000 nM) and insulin (0.3 nM). Our modeling shows that the very high plasma concentration of Tf leads to only 5% of the endothelial TfR expressed on the luminal endothelial membrane.

Case Study 8: Status of the Structural Mass Action Kinetic Model of P-gp-Mediated Transport Through Confluent Cell Monolayers.

In the first edition of this book, we presented the basics of explicitly incorporating the lipid biochemistry into a confluent cell monolayer transport model and the novel findings of this model up to 2013, including the use of global optimization to fit the elementary rate constants and the efflux active P-glycoprotein (P-gp) membrane concentrations for the transport of four P-gp substrates across MDCKII-hMDR1-NKI confluent cell monolayers. This chapter is an update on that model, which has been focused primarily on discovering how microvilli morphology regulates the efflux active P-gp and the existence of, as yet, unidentified uptake transporters of P-gp substrates in all of the commonly used P-gp expressing cell lines used in the pharmaceutical industry, thereby adding new players to DDI predictions and IVIVE. The structural mass action kinetic model uses the general mass action reactions for P-gp binding and efflux, with the membrane structural parameters for the confluent cell monolayer to predict drug transport over time. Binding of drug to P-gp occurs within the cytosolic monolayer of the apical membrane, according to (a) the molar partition coefficient of the drug to the cytosolic monolayer and (b) the association rate constant, k1 (M-1s-1), of the drug from the basolateral or apical outer monolayers into the P-gp binding site. Release of substrate from P-gp back into the cytosolic monolayer occurs with a dissociation rate constant kr (s-1) or, much less frequently, into the apical aqueous chamber with an efflux rate constant k2 (s-1). The model fits the efflux active P-gp concentration, T(0), i.e., the P-gp whose effluxed drug actuallyreaches the apical aqueous chamber, as opposed to the majority of P-gp whose effluxed drug is reabsorbed back into the same or neighboring microvilli prior to reaching the apical aqueous chamber. Efflux active P-gp largely resides near the tips of the microvilli. We have shown using kinetics and structured illumination microscopy that: (a) efflux active P-gp is controlled by microvilli morphology; (b) there are apical (AT) and basolateral (BT) uptake transporters for P-gp substrates in most, if not all, P-gp expressing cell lines used in the pharmaceutical industry, whichexist, but which remain unidentified; (c) the lab-to-lab variability in P-gp IC50 values observed in the P-gp IC50 initiative was due to the conflated inhibition of P-gp and the basolateral digoxin uptake transporters by all 15 P-gp substrates tested in that study; (d)even the IC50 values for P-gp inhibition alone do not obey the Cheng-Prusoff relationship; (e) the fitted elementary rate constants and the molecular dissociation constant Ki for this kinetic model are system independent; and (f) the time dependence of product formation for these confluent cell monolayers is correlated withthe P-gp Vmax/Km, whendefined by its fitted elementary rate constants and uptake transporter clearances, without any steady-state assumptions.

Mass Action Kinetic Model of Apoptosis by TRAIL-Functionalized Leukocytes

Background: Metastasis through the bloodstream contributes to poor prognosis in many types of cancer. A unique approach to target and kill colon, prostate, and other epithelial-type cancer cells in the blood has been recently developed that uses circulating leukocytes to present the cancer-specific, liposome-bound Tumor Necrosis Factor (TNF)-related apoptosis inducing ligand (TRAIL) on their surface along with E − selectin adhesion receptors. This approach, demonstrated both in vitro with human blood and in mice, mimics the cytotoxic activity of natural killer cells. The resulting liposomal TRAIL-coated leukocytes hold promise as an effective means to neutralize circulating tumor cells that enter the bloodstream with the potential to form new metastases.Methods: The computational biology study reported here examines the mechanism of this effective signal delivery, by considering the kinetics of the coupled reaction cascade, from TRAIL binding death receptor to eventual apoptosis. In this study, a collision of bound TRAIL with circulating tumor cells (CTCs) is considered and compared to a prolonged exposure of CTCs to soluble TRAIL. An existing computational model of soluble TRAIL treatment was modified to represent the kinetics from a diffusion-limited 3D reference frame into a 2D collision frame with advection and adhesion to mimic the E − selectin and membrane bound TRAIL treatment. Thus, the current model recreates the new approach of targeting cancer cells within the blood. The model was found to faithfully reproduce representative observations from experiments of liposomal TRAIL treatment under shear.Results: The model predicts apoptosis of CTCs within 2 h when treated with membrane bound TRAIL, while apoptosis in CTCs treated with soluble TRAIL proceeds much more slowly over the course of 10 h, consistent with previous experiments. Given the clearance rate of soluble TRAIL in vivo, this model predicts that the soluble TRAIL method would be rendered ineffective, as found in previous experiments.Conclusion: This study therefore indicates that the kinetics of the coupled reaction cascade of liposomal E − selectin and membrane bound TRAIL colliding with CTCs can explain why this new approach to target and kill cancer cells in blood is much more effective than its soluble counterpart.

Derivation of a System-Independent Ki for P-glycoprotein Mediated Digoxin Transport from System-Dependent IC50 Data.

It has been previously demonstrated that IC50 values for inhibition of digoxin transport across confluent polarized cell monolayers are system-dependent. Digoxin IC50 data from five laboratories participating in the P-glycoprotein (P-gp) IC50 Initiative, using Caco-2, MDCKII-hMDR1 or LLC-PK1-hMDR1 cells, were fitted by the structural mass action kinetic model for P-gp-mediated transport across confluent cell monolayers. We determined their efflux-active P-gp concentration [T(0)], inhibitor elementary dissociation rate constant from P-gp (krQ), digoxin basolateral uptake clearance (kB), and inhibitor binding affinity to the digoxin basolateral uptake transporter (KQB). We also fitted the IC50 data for inhibition of digoxin transport through monolayers of primary human proximal tubule cells (HPTCs). All cell systems kinetically required a basolateral uptake transporter for digoxin, which also bound to all inhibitors. The inhibitor krQ was cell system-independent, thereby allowing calculation of a system-independent Ki. The variability in efflux-active P-gp concentrations and basolateral uptake clearances in the five laboratories was about an order of magnitude. These laboratory-to-laboratory variabilities can explain more than 60% of the IC50 variability found in the principal component analysis plot in a previous study, supporting the hypothesis that the observed IC50 variability is primarily due to differences in expression levels of efflux-active P-gp and the basolateral digoxin uptake transporter. HPTCs had 10- to 100-fold lower efflux-active P-gp concentrations than the overexpressing cell lines, whereas their digoxin basolateral uptake clearances were similar. HPTC basolateral uptake of digoxin was inhibited 50% by 10 μM ouabain, suggesting involvement of OATP4C1.

Three-dimensional stochastic model of actin-myosin binding in the sarcomere lattice.

The effect of molecule tethering in three-dimensional (3-D) space on bimolecular binding kinetics is rarely addressed and only occasionally incorporated into models of cell motility. The simplest system that can quantitatively determine this effect is the 3-D sarcomere lattice of the striated muscle, where tethered myosin in thick filaments can only bind to a relatively small number of available sites on the actin filament, positioned within a limited range of thermal movement of the myosin head. Here we implement spatially explicit actomyosin interactions into the multiscale Monte Carlo platform MUSICO, specifically defining how geometrical constraints on tethered myosins can modulate state transition rates in the actomyosin cycle. The simulations provide the distribution of myosin bound to sites on actin, ensure conservation of the number of interacting myosins and actin monomers, and most importantly, the departure in behavior of tethered myosin molecules from unconstrained myosin interactions with actin. In addition, MUSICO determines the number of cross-bridges in each actomyosin cycle state, the force and number of attached cross-bridges per myosin filament, the range of cross-bridge forces and accounts for energy consumption. At the macroscopic scale, MUSICO simulations show large differences in predicted force-velocity curves and in the response during early force recovery phase after a step change in length comparing to the two simplest mass action kinetic models. The origin of these differences is rooted in the different fluxes of myosin binding and corresponding instantaneous cross-bridge distributions and quantitatively reflects a major flaw of the mathematical description in all mass action kinetic models. Consequently, this new approach shows that accurate recapitulation of experimental data requires significantly different binding rates, number of actomyosin states, and cross-bridge elasticity than typically used in mass action kinetic models to correctly describe the biochemical reactions of tethered molecules and their interaction energetics.

Extrapolation of Elementary Rate Constants of P-glycoprotein-Mediated Transport from MDCKII-hMDR1-NKI to Caco-2 Cells.

The best parameters for incorporation into mechanistic physiologically based pharmacokinetic models for transporters are system-independent kinetic parameters and active (not total) transporter levels. Previously, we determined the elementary rate constants for P-glycoprotein (P-gp)-mediated transport (on- and off-rate constants from membrane to P-gp binding pocket and efflux rate constant into the apical chamber) using the structural mass action kinetic model in confluent MDCKII-hMDR1-NKI cell monolayers. In the present work, we extended the kinetic analysis to Caco-2 cells for the first time and showed that the elementary rate constants are very similar compared with MDCKII-hMDR1-NKI cells, suggesting they primarily depend on the interaction of the compound with P-gp and are therefore mostly independent of the in vitro system used. The level of efflux active (not total) P-gp is also fitted by our model. The estimated level of efflux active P-gp was 5.0 ± 1.4-fold lower in Caco-2 cells than in MDCKII-hMDR1-NKI cells. We also kinetically identified the involvement of a basolateral uptake transporter for both digoxin and loperamide in Caco-2 cells, as found previously in MDCKII-hMDR1-NKI cells, due to their low passive permeability. This demonstrates the value of our P-gp structural model as a diagnostic tool in detecting the importance of other transporters, which cannot be unambiguously done by the Michaelis-Menten approach. The system-independent elementary rate constants for P-gp obtained in vitro are more fundamental parameters than those obtained using Michaelis-Menten steady-state equations. This suggests they will be more robust mechanistic parameters for incorporation into physiologically based pharmacokinetic models for transporters.

Quantification of cellular and nuclear uptake rates of polymeric gene delivery nanoparticles and DNA plasmids via flow cytometry

Non-viral, biomaterial-mediated gene delivery has the potential to treat many diseases, but is limited by low efficacy. Elucidating the bottlenecks of plasmid mass transfer can enable an improved understanding of biomaterial structure–function relationships, leading to next-generation rationally designed non-viral gene delivery vectors. As proof of principle, we transfected human primary glioblastoma cells using a poly(beta-amino ester) complexed with eGFP plasmid DNA. The polyplexes transfected 70.6±0.6% of the cells with 101±3% viability. The amount of DNA within the cytoplasm, nuclear envelope, and nuclei was assessed at multiple time points using fluorescent dye conjugated plasmid up to 24h post-transfection using a quantitative multi-well plate-based flow cytometry assay. Conversion to plasmid counts and degradation kinetics were accounted for via quantitative PCR (plasmid degradation rate constants were determined to be 0.62h−1 and 0.084h−1 for fast and slow phases respectively). Quantitative cellular uptake, nuclear association, and nuclear uptake rate constants were determined by using a four-compartment first order mass-action model. The rate limiting step for these poly(beta-amino ester)/DNA polyplex nanoparticles was determined to be cellular uptake (7.5×10−4h−1) and only 0.1% of the added dose was taken up by the human brain cancer cells, whereas 12% of internalized DNA successfully entered the nucleus (the rate of nuclear internalization of nuclear associated plasmid was 1.1h−1). We describe an efficient new method for assessing cellular and nuclear uptake rates of non-viral gene delivery nanoparticles using flow cytometry to improve understanding and design of polymeric gene delivery nanoparticles. Statement of SignificanceIn this work, a quantitative high throughput flow cytometry-based assay and computational modeling approach was developed for assessing cellular and nuclear uptake rates of non-viral gene delivery nanoparticles. This method is significant as it can be used to elucidate structure–function relationships of gene delivery nanoparticles and improve their efficiency. This method was applied to a particular type of biodegradable polymer, a poly(beta-amino ester), that transfected human brain cancer cells with high efficacy and without cytotoxicity. A four-compartment first order mass-action kinetics model was found to model the experimental transport data well without requiring external fitting parameters. Quantitative rate constants were identified for the intracellular transport, including DNA degradation rate from polyplexes, cellular uptake rate, and nuclear uptake rate, with cellular uptake identified as the rate-limiting step.

Models of cancer growth

In this paper we present a simple mathematical model of cancer growth. The model is discrete, it is a linear map (T) on three dimensional Eucledian vector space. But for some values of the parameters there exists a linear vector field on three dimensional Eucledian vector space whose time one map is T. We can analyze what happens to the flow of this vector field on one of the coordinate hyperplanes (see Fig. 5 in Sect. 4). In words this figure depicts, that if you have a bad ratio of growth inhibitor to growth factor cancer grows and if you have a good ratio cancer is eradicated. We can modify the dynamical system to model giving chemo therapy or immune therapy and discuss the consequences. We fit the model predictions to a Gompertz function and this gives a good fit for some values of the parameters (see Figs. 1, 2, 3 and 4). A main topic of the present paper is a mass action kinetic model for cancer growth. This gives a three dimensional ODE model, for which the first orthant is positively invariant. We discretize the linearization of this nonlinear ODE and with appropriate parameter definitions we recover the model T of Sect. 1. For some parameter values the model T induces a two dimensional map of the plane, see Sect. 5 .

Quantitative analysis of insulin-like growth factor 2 receptor and insulin-like growth factor binding proteins to identify control mechanisms for insulin-like growth factor 1 receptor phosphorylation.

BackgroundThe insulin-like growth factor (IGF) system impacts cellular development by regulating proliferation, differentiation, and apoptosis, and is an attractive therapeutic target in cancer. The IGF system is complex, with two ligands (IGF1, IGF2), two receptors (IGF1R, IGF2R), and at least six high affinity IGF-binding proteins (IGFBPs) that regulate IGF ligand bioavailability. While the individual components of the IGF system are well studied, the question of how these different components integrate as a system to regulate cell behavior is less clear.ResultsTo analyze the relative importance of different mechanisms that control IGF network activity, we developed a mass-action kinetic model incorporating cell surface binding, phosphorylation, and intracellular trafficking events. The model was calibrated and validated using experimental data collected from OVCAR5, an immortalized ovarian cancer cell line. We then performed model analysis to examine the ability of IGF2R or IGFBPs to counteract phosphorylation of IGF1R, a critical step for IGF network activation. This analysis suggested that IGF2R levels would need to be 320-fold greater than IGF1R in order to decrease pIGF1R by 25 %, while IGFBP levels would need to be 390-fold greater. Analysis of The Cancer Genome Atlas (TCGA) data set suggested that this level of overexpression is unlikely for IGF2R in ovarian, breast, and colon cancer. In contrast, IGFBPs can likely reach these levels, suggesting that IGFBPs are the more critical regulator of IGF1R network activity. Levels of phosphorylated IGF1R were insensitive to changes in parameters regulating the IGF2R arm of the network.ConclusionsUsing a mass-action kinetic model, we determined that IGF2R plays a minor role in regulating the activity of IGF1R under a variety of conditions and that due to their high expression levels, IGFBPs are the dominant mechanism to regulating IGF network activation.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-016-0263-6) contains supplementary material, which is available to authorized users.

On the Relationship of Protein and mRNA Dynamics in Vertebrate Embryonic Development

A biochemical explanation of development from the fertilized egg to the adult requires an understanding of the proteins and RNAs expressed over time during embryogenesis. We present a comprehensive characterization of protein and mRNA dynamics across early development in Xenopus. Surprisingly, we find that most protein levels change little and duplicated genes are expressed similarly. While the correlation between protein and mRNA levels is poor, a mass action kinetics model parameterized using protein synthesis and degradation rates regresses protein dynamics to RNA dynamics, corrected for initial protein concentration. This study provides detailed data for absolute levels of ∼10,000 proteins and ∼28,000 transcripts via a convenient web portal, a rich resource for developmental biologists. It underscores the lasting impact of maternal dowry, finds surprisingly few cases where degradation alone drives a change in protein level, and highlights the importance of transcription in shaping the dynamics of the embryonic proteome.

A kinetic model identifies phosphorylated estrogen receptor‐α (ERα) as a critical regulator of ERα dynamics in breast cancer

Receptor levels are a key mechanism by which cells regulate their response to stimuli. The levels of estrogen receptor-α (ERα) impact breast cancer cell proliferation and are used to predict prognosis and sensitivity to endocrine therapy. Despite the clinical application of this information, it remains unclear how different cellular processes interact as a system to control ERα levels. To address this question, experimental results from the ERα-positive human breast cancer cell line (MCF-7) treated with 17-β-estradiol or vehicle control were used to develop a mass-action kinetic model of ERα regulation. Model analysis determined that RNA dynamics could be captured through phosphorylated ERα (pERα)-dependent feedback on transcription. Experimental analysis confirmed that pERα-S118 binds to the estrogen receptor-1 (ESR1) promoter, suggesting that pERα can feedback on ESR1 transcription. Protein dynamics required a separate mechanism in which the degradation rate for pERα was 8.3-fold higher than nonphosphorylated ERα. Using a model with both mechanisms, the root mean square error was 0.078. Sensitivity analysis of this combined model determined that while multiple mechanisms regulate ERα levels, pERα-dependent feedback elicited the strongest effect. Combined, our computational and experimental results identify phosphorylation of ERα as a critical decision point that coordinates the cellular circuitry to regulate ERα levels.