Controlling receptor/ligand trafficking: effects of cellular and molecular properties on endosomal sorting

Computer-assembled cross-species/cross-modalities two-pore physiologically based pharmacokinetic model for biologics in mice and rats

Two-pore physiologically-based pharmacokinetic (PBPK) models can be expected to describe the tissue distribution and elimination kinetics of soluble proteins, endogenous or dosed, as function of their size. In this work, we amalgamated our previous two-pore PBPK model for an inert domain antibody (dAb) in mice with the cross-species platform PBPK model for monoclonal antibodies described in literature into a unified two-pore platform that describes protein modalities of different sizes and includes neonatal Fc receptor (FcRn) mediated recycling. This unified PBPK model was parametrized for organ-specific lymph flow rates and the endosomal recycling rate constant using an extended tissue distribution time-course dataset that included an inert dAb, albumin and IgG in rats and mice. The model was evaluated by comparing the ab initio predictions for the tissue distribution and elimination properties of albumin-binding dAbs (AlbudAbs^TM) in mice and rats with the experimental observations. Due to the large number of molecular species and reactions involved in large-scale PBPK models, we have also developed and deployed a Matlab^TM script for automating the assembly of SimBiology^TM-based two-pore biologics PBPK models which drastically cuts the time and effort required for model building.

Integrative meta-modeling identifies endocytic vesicles, late endosome and the nucleus as the cellular compartments primarily directing RTK signaling

Recently, intracellular receptor signaling has been identified as a key component mediating cell responses for various receptor tyrosine kinases (RTKs). However, the extent each endocytic compartment (endocytic vesicle, early endosome, recycling endosome, late endosome, lysosome and nucleus) contributes to receptor signaling has not been quantified. Furthermore, our understanding of endocytosis and receptor signaling is complicated by cell- or receptor-specific endocytosis mechanisms. Therefore, towards understanding the differential endocytic compartment signaling roles, and identifying how to achieve signal transduction control for RTKs, we delineate how endocytosis regulates RTK signaling. We achieve this via a meta-analysis across eight RTKs, integrating computational modeling with experimentally derived cell (compartment volume, trafficking kinetics and pH) and ligand-receptor (ligand/receptor concentration and interaction kinetics) physiology. Our simulations predict the abundance of signaling from eight RTKs, identifying the following hierarchy in RTK signaling: PDGFRβ > IGFR1 > EGFR > PDGFRα > VEGFR1 > VEGFR2 > Tie2 > FGFR1. We find that endocytic vesicles are the primary cell signaling compartment; over 43% of total receptor signaling occurs within the endocytic vesicle compartment for these eight RTKs. Mechanistically, we found that high RTK signaling within endocytic vesicles may be attributed to their low volume (5.3 × 10^-19 L) which facilitates an enriched ligand concentration (3.2 μM per ligand molecule within the endocytic vesicle). Under the analyzed physiological conditions, we identified extracellular ligand concentration as the most sensitive parameter to change; hence the most significant one to modify when regulating absolute compartment signaling. We also found that the late endosome and nucleus compartments are important contributors to receptor signaling, where 26% and 18%, respectively, of average receptor signaling occurs across the eight RTKs. Conversely, we found very low membrane-based receptor signaling, exhibiting <1% of the total receptor signaling for these eight RTKs. Moreover, we found that nuclear translocation, mechanistically, requires late endosomal transport; when we blocked receptor trafficking from late endosomes to the nucleus we found a 57% reduction in nuclear translocation. In summary, our research has elucidated the significance of endocytic vesicles, late endosomes and the nucleus in RTK signal propagation.

Mathematical modeling of mutant transferrin-CRM107 molecular conjugates for cancer therapy

The transferrin (Tf) trafficking pathway is a promising mechanism for use in targeted cancer therapy due to the overexpression of transferrin receptors (TfRs) on cancerous cells. We have previously developed a mathematical model of the Tf/TfR trafficking pathway to improve the efficiency of Tf as a drug carrier. By using diphtheria toxin (DT) as a model toxin, we found that mutating the Tf protein to change its iron release rate improves cellular association and efficacy of the drug. Though this is an improvement upon using wild-type Tf as the targeting ligand, conjugated toxins like DT are unfortunately still highly cytotoxic at off-target sites. In this work, we address this hurdle in cancer research by developing a mathematical model to predict the efficacy and selectivity of Tf conjugates that use an alternative toxin. For this purpose, we have chosen to study a mutant of DT, cross-reacting material 107 (CRM107). First, we developed a mathematical model of the Tf-DT trafficking pathway by extending our Tf/TfR model to include intracellular trafficking via DT and DT receptors. Using this mathematical model, we subsequently investigated the efficacy of several conjugates in cancer cells: DT and CRM107 conjugated to wild-type Tf, as well as to our engineered mutant Tf proteins (K206E/R632A Tf and K206E/R534A Tf). We also investigated the selectivity of mutant Tf-CRM107 against non-neoplastic cells. Through the use of our mathematical model, we predicted that (i) mutant Tf-CRM107 exhibits a greater cytotoxicity than wild-type Tf-CRM107 against cancerous cells, (ii) this improvement was more drastic with CRM107 conjugates than with DT conjugates, and (iii) mutant Tf-CRM107 conjugates were selective against non-neoplastic cells. These predictions were validated with in vitro cytotoxicity experiments, demonstrating that mutant Tf-CRM107 conjugates is indeed a more suitable therapeutic agent. Validation from in vitro experiments also confirmed that such whole-cell kinetic models can be useful in cancer therapeutic design.

The AXL Receptor is a Sensor of Ligand Spatial Heterogeneity

The AXL receptor is a TAM (Tyro3, AXL, MerTK) receptor tyrosine kinase (RTK) important in physiological inflammatory processes such as blood clotting, viral infection, and innate immune-mediated cell clearance. Overexpression of the receptor in a number of solid tumors is increasingly appreciated as a key drug resistance and tumor dissemination mechanism. Although the ligand-receptor (Gas6-AXL) complex structure is known, literature reports on ligand-mediated signaling have provided conflicting conclusions regarding the influence of other factors such as phosphatidylserine binding, and a detailed, mechanistic picture of AXL activation has not emerged. Integrating quantitative experiments with mathematical modeling, we show here that AXL operates to sense local spatial heterogeneity in ligand concentration, a feature consistent with its physiological role in inflammatory cell responses. This effect arises as a result of an intricate reaction-diffusion interaction. Our results demonstrate that AXL functions distinctly from other RTK families, a vital insight for envisioned design of AXL-targeted therapeutic intervention.

Two independent histidines, one in human prolactin and one in its receptor, are critical for pH-dependent receptor recognition and activation

Human prolactin (hPRL), a member of the family of hematopoietic cytokines, functions as both an endocrine hormone and autocrine/paracrine growth factor. We have previously demonstrated that recognition of the hPRL·receptor depends strongly on solution acidity over the physiologic range from pH 6 to pH 8. The hPRL·receptor binding interface contains four histidines whose protonation is hypothesized to regulate pH-dependent receptor recognition. Here, we systematically dissect its molecular origin by characterizing the consequences of His to Ala mutations on pH-dependent receptor binding kinetics, site-specific histidine protonation, and high resolution structures of the intermolecular interface. Thermodynamic modeling of the pH dependence to receptor binding affinity reveals large changes in site-specific protonation constants for a majority of interface histidines upon complexation. Removal of individual His imidazoles reduces these perturbations in protonation constants, which is most likely explained by the introduction of solvent-filled, buried cavities in the crystallographic structures without inducing significant conformational rearrangements.

Combination antibody treatment down-regulates epidermal growth factor receptor by inhibiting endosomal recycling

Due to its common dysregulation in epithelial-based cancers and extensive characterization of its role in tumor growth, epidermal growth factor receptor (EGFR) is a highly validated target for anticancer therapies. There has been particular interest in the development of monoclonal antibodies (mAbs) targeting EGFR, resulting in two approved mAb-based drugs and several others in clinical trials. It has recently been reported that treatment with combinations of noncompetitive mAbs can induce receptor clustering, leading to synergistic receptor down-regulation. We elucidate three key aspects of this phenomenon. First, we show that highly potent combinations consisting of two noncompetitive mAbs that target EGFR domain 3 reduce surface receptor levels by up to 80% with a halftime of 0.5-5 h in both normal and transformed human cell lines to an extent inversely proportional to receptor density. Second, we find the mechanism underlying down-regulation to be consistent with recycling inhibition. Third, in contrast to the agonism associated with ligand-induced down-regulation, we demonstrate that mAb-induced down-regulation does not activate EGFR or its downstream effectors and it leads to synergistic reduction in migration and proliferation of cells that secrete autocrine ligand. These new insights will aid in ongoing rational design of EGFR-targeted antibody therapeutics.

Systems approach to therapeutics design

A general methodology is described for improving the therapeutic properties of protein drugs by engineering novel intracellular trafficking pathways. Procedures for cellular trafficking experiments and mathematical modeling of trafficking pathways are presented. Previous work on the engineering of the transferrin trafficking pathway will be used to illustrate how each step of the methodology can be applied.

Endosomal receptor kinetics determine the stability of intracellular growth factor signalling complexes

There is an emerging paradigm that growth factor signalling continues in the endosome and that cell response to a growth factor is defined by the integration of cell surface and endosomal events. As activated receptors in the endosome are exposed to a different set of binding partners, they probably elicit differential signals compared with when they are at the cell surface. As such, complete appreciation of growth factor signalling requires understanding of growth factor-receptor binding and trafficking kinetics both at the cell surface and in endosomes. Growth factor binding to surface receptors is well characterized, and endosomal binding is assumed to follow surface kinetics if one accounts for changes in pH. Yet, specific binding kinetics within the endosome has not been examined in detail. To parse the factors governing the binding state of endosomal receptors we analysed a whole-cell mathematical model of epidermal growth factor receptor trafficking and binding. We discovered that the stability of growth factor-receptor complexes within endosomes is governed by three primary independent factors: the endosomal dissociation constant, total endosomal volume and the number of endosomal receptors. These factors were combined into a single dimensionless parameter that determines the endosomal binding state of the growth factor-receptor complex and can distinguish different growth factors from each other and different cell states. Our findings indicate that growth factor binding within endosomal compartments cannot be appreciated solely on the basis of the pH-dependence of the dissociation constant and that the concentration of receptors in the endosomal compartment must also be considered.

Inhibition of transferrin iron release increases in vitro drug carrier efficacy

Transferrin (Tf) conjugates of CRM107 are currently being tested in clinical trials for treatment of malignant gliomas. However, the rapid cellular recycling of Tf limits its efficiency as a drug carrier. We have developed a mathematical model of the Tf/TfR trafficking cycle and have identified the Tf iron release rate as a previously unreported factor governing the degree of Tf cellular association. The release of iron from Tf is inhibited by replacing the synergistic carbonate anion with oxalate. Trafficking patterns for oxalate Tf and native Tf are compared by measuring their cellular association with HeLa cells. The amount of Tf associated with the cells is an average of 51% greater for oxalate Tf than for native Tf over a two hour period at Tf concentrations of 0.1 nM and 1 nM. Importantly, diphtheria toxin (DT) conjugates of oxalate Tf are more cytotoxic against HeLa cells than conjugates of native Tf. Conjugate IC(50) values were determined to be 0.06 nM for the oxalate Tf conjugate vs. 0.22 nM for the native Tf conjugate. Thus, we show that inhibition of Tf iron release improves the efficacy of Tf as a drug carrier through increased association with cells expressing TfR.

Hyperdigraph-theoretic analysis of the EGFR signaling network: initial steps leading to GTP:Ras complex formation

We construct an algebraic-combinatorial model of the SOS compartment of the EGFR biochemical network. A Petri net is used to construct an initial representation of the biochemical decision making network, which in turn defines a hyperdigraph. We observe that the linear algebraic structure of each hyperdigraph admits a canonical set of algebraic-combinatorial invariants that correspond to the information flow conservation laws governing a molecular kinetic reaction network. The linear algebraic structure of the hyperdigraph and its sets of invariants can be generalized to define a discrete algebraic-geometric structure, which is referred to as an oriented matroid. Oriented matroids define a polyhedral optimization geometry that is used to determine optimal subpaths that span the nullspace of a set of kinetic chemical reaction equations. Sets of constrained submodular path optimizations on the hyperdigraph are objectively obtained as a spanning tree of minimum cycle paths. This complete set of subcircuits is used to identify the network pinch points and invariant flow subpaths. We demonstrate that this family of minimal circuits also characteristically identifies additional significant biochemical reaction pattern features. We use the SOS Compartment A of the EGFR biochemical pathway to develop and demonstrate the application of our algebraic-combinatorial mathematical modeling methodology.

Simulating the impact of a molecular 'decision-process' on cellular phenotype and multicellular patterns in brain tumors

Experimental evidence indicates that human brain cancer cells proliferate or migrate, yet do not display both phenotypes at the same time. Here, we present a novel computational model simulating this cellular decision-process leading up to either phenotype based on a molecular interaction network of genes and proteins. The model's regulatory network consists of the epidermal growth factor receptor (EGFR), its ligand transforming growth factor-alpha (TGF alpha), the downstream enzyme phospholipaseC-gamma (PLC gamma) and a mitosis-associated response pathway. This network is activated by autocrine TGF alpha secretion, and the EGFR-dependent downstream signaling this step triggers, as well as modulated by an extrinsic nutritive glucose gradient. Employing a framework of mass action kinetics within a multiscale agent-based environment, we analyse both the emergent multicellular behavior of tumor growth and the single-cell molecular profiles that change over time and space. Our results show that one can indeed simulate the dichotomy between cell migration and proliferation based solely on an EGFR decision network. It turns out that these behavioral decisions on the single cell level impact the spatial dynamics of the entire cancerous system. Furthermore, the simulation results yield intriguing experimentally testable hypotheses also on the sub-cellular level such as spatial cytosolic polarization of PLC gamma towards an extrinsic chemotactic gradient. Implications of these results for future works, both on the modeling and experimental side are discussed.

HER2-mediated effects on EGFR endosomal sorting: analysis of biophysical mechanisms

Overexpression of HER2, a receptor-like tyrosine kinase and signaling partner for the epidermal growth factor receptor (EGFR), has been implicated in numerous experimental and clinical studies as promoting the progression of many types of cancer. One avenue by which HER2 overexpression may dysregulate EGFR-mediated cell responses, such as proliferation and migration, downstream of EGF family ligand binding, is by its modulation on EGFR endocytic trafficking dynamics. EGFR signaling is regulated by downregulation and compartmental relocalization arising from endocytic internalization and endosomal sorting to degradation versus recycling fates. HER2 overexpression influences both of these processes. At the endosomal sorting stage, increased HER2 levels elicit enhanced EGFR recycling outcomes, but the mechanism by which this transpires is poorly understood. Here, we determine whether alternative mechanisms for HER2-mediated enhancement of EGFR recycling can be distinguished by comparison of corresponding mathematical models to experimental literature data. Indeed, we find that the experimental data are clearly most consistent with a mechanism in which HER2 directly competes with EGFR for a stoichiometrically-limited quantity of endosomal retention components (ERCs), thereby reducing degradation of ERC-coupled EGFR. Model predictions based on this mechanism exhibited qualitative trends highly similar to data on the fraction of EGF/EGFR complexes sorted to recycling fate as a function of the amount of internalized EGF/EGFR complexes. In contrast, model predictions for alternative mechanisms-blocking of EGFR/ERC coupling, or altering EGF/EGFR dissociation-were inconsistent with the qualitative trends of the experimental data.

An integrated model of epidermal growth factor receptor trafficking and signal transduction

Endocytic trafficking of many types of receptors can have profound effects on subsequent signaling events. Quantitative models of these processes, however, have usually considered trafficking and signaling independently. Here, we present an integrated model of both the trafficking and signaling pathway of the epidermal growth factor receptor (EGFR) using a probability weighted-dynamic Monte Carlo simulation. Our model consists of hundreds of distinct endocytic compartments and approximately 13,000 reactions/events that occur over a broad spatio-temporal range. By using a realistic multicompartment model, we can investigate the distribution of the receptors among cellular compartments as well as their potential signal transduction characteristics. Our new model also allows the incorporation of physiochemical aspects of ligand-receptor interactions, such as pH-dependent binding in different endosomal compartments. To determine the utility of this approach, we simulated the differential activation of the EGFR by two of its ligands, epidermal growth factor (EGF) and transforming growth factor-alpha (TGF-alpha). Our simulations predict that when EGFR is activated with TGF-alpha, receptor activation is biased toward the cell surface whereas EGF produces a signaling bias toward the endosomal compartment. Experiments confirm these predictions from our model and simulations. Our model accurately predicts the kinetics and extent of receptor downregulation induced by either EGF or TGF-alpha. Our results suggest that receptor trafficking controls the compartmental bias of signal transduction, rather than simply modulating signal magnitude. Our model provides a new approach to evaluating the complex effect of receptor trafficking on signal transduction. Importantly, the stochastic and compartmental nature of the simulation allows these models to be directly tested by high-throughput approaches, such as quantitative image analysis.

Metabotropic receptor activation, desensitization and sequestration-I: modelling calcium and inositol 1,4,5-trisphosphate dynamics following receptor activation

A mathematical account is given of the processes governing the time courses of calcium ions (Ca2+), inositol 1,4,5-trisphosphate (IP(3)) and phosphatidylinositol 4,5-bisphosphate (PIP(2)) in single cells following the application of external agonist to metabotropic receptors. A model is constructed that incorporates the regulation of metabotropic receptor activity, the G-protein cascade and the Ca2+ dynamics in the cytosol. It is subsequently used to reproduce observations on the extent of desensitization and sequestration of the P(2)Y(2) receptor following its activation by uridine triphosphate (UTP). The theory predicts the dependence on agonist concentration of the change in the number of receptors in the membrane as well as the time course of disappearance of receptors from the plasmalemma, upon exposure to agonist. In addition, the extent of activation and desensitization of the receptor, using the calcium transients in cells initiated by exposure to agonist, is also predicted. Model predictions show the significance of membrane PIP(2) depletion and resupply on the time course of IP(3) and Ca2+ levels. Results of the modelling also reveal the importance of receptor recycling and PIP(2) resupply for maintaining Ca2+ and IP(3) levels during sustained application of agonist.

pH Dependence of structural stability of interleukin-2 and granulocyte colony-stimulating factor

After a cytokine binds to its receptor on the cell surface (pH approximately 7), the complex is internalized into acidic endosomal compartments (pH approximately 5-6), where partially unfolded intermediates can form. The nature of these structural transitions was studied for wild-type interleukin-2 (IL-2) and wild-type granulocyte colony-stimulating factor (G-CSF). A noncoincidence of denaturation transitions in the secondary and tertiary structure of IL-2 and tertiary structural perturbations in G-CSF suggest the presence of an intermediate state for each, a common feature of this structural family of four-helical bundle proteins. Unexpectedly, both IL-2 and G-CSF display monotonic increases in stability as the pH is decreased from 7 to 4. We hypothesize that such cytokines with cell-based clearance mechanisms in vivo may have evolved to help stabilize endosomal complexes for sorting to lysosomal degradation. We show that mutants of both IL-2 and G-CSF have differential stabilities to their wild-type counterparts as a function of pH, and that these differences may explain the differences in ligand trafficking and depletion. Further understanding of the structural changes accompanying unfolding may help guide cytokine design with respect to ligand binding, endocytic trafficking, and, consequently, therapeutic efficacy.

Rational cytokine design for increased lifetime and enhanced potency using pH-activated "histidine switching"

We describe a method for the rational design of more effective therapeutic proteins using amino acid substitutions that reduce receptor binding affinity in intracellular endosomal compartments, thereby leading to increased recycling in the ligand-sorting process and consequently resulting in longer half-life in extracellular medium. We demonstrate this approach for granulocyte colony-stimulating factor by using computationally predicted histidine substitutions that switch protonation states between cell-surface and endosomal pH. Molecular modeling of binding electrostatics indicates two different single-histidine mutants that fulfill our design requirements; experimental assays demonstrate that each mutant indeed exhibits an order-of-magnitude increase in medium half-life along with enhanced potency due to increased endocytic recycling.

Receptor-mediated targeting of gene delivery vectors: insights from molecular mechanisms for improved vehicle design

One way to deliver transgenes to cells in a selective manner is to target the delivery vehicles, or vectors, to specific cell-surface receptors as a first step toward ultimate transport of the gene to the nucleus for expression. While selective delivery, although often to undesired cell types, occurs naturally for some viral vectors and can be achieved for nonviral vehicles, current understanding and control of the delivery mechanism is inadequate for many therapeutic applications. The complicated nature of receptor-mediated transgene uptake and transport requires improved analysis to more effectively evaluate delivery vehicles. As receptor-mediated pathways for gene delivery typically involve vector binding, internalization, subcellular trafficking, vesicular escape, nuclear translocation, and unpackaging for transcription, each of these processes offer mechanisms that can be exploited to enhance targeted gene delivery via properly designed vehicles. For the purpose of this review, current targeted gene delivery vehicles are divided into three approaches: viral, synthetic, and hybrid vectors. Each approach possesses advantages as well as disadvantages at the present time for in vitro and in vivo application, and provides particular challenges to overcome in order to gain significantly improved targeted delivery properties. Quantitative experiments and mathematical modeling of the gene delivery pathway will serve to provide insight into molecular mechanisms and rate-limiting steps for effective gene expression. Information on molecular mechanisms obtained by such methodologies can then be applied to specific vectors, whether viral, synthetic, or hybrid, allowing for the creation of targeted, effective, and safe gene therapeutics.

The receptor recycling pathway contains two distinct populations of early endosomes with different sorting functions

Receptor recycling involves two endosome populations, peripheral early endosomes and perinuclear recycling endosomes. In polarized epithelial cells, either or both populations must be able to sort apical from basolateral proteins, returning each to its appropriate plasma membrane domain. However, neither the roles of early versus recycling endosomes in polarity nor their relationship to each other has been quantitatively evaluated. Using a combined morphological, biochemical, and kinetic approach, we found these two endosome populations to represent physically and functionally distinct compartments. Early and recycling endosomes were resolved on Optiprep gradients and shown to be differentially associated with rab4, rab11, and transferrin receptor; rab4 was enriched on early endosomes and at least partially depleted from recycling endosomes, with the opposite being true for rab11 and transferrin receptor. The two populations were also pharmacologically distinct, with AlF4 selectively blocking export of transferrin receptor from recycling endosomes to the basolateral plasma membrane. We applied these observations to a detailed kinetic analysis of transferrin and dimeric IgA recycling and transcytosis. The data from these experiments permitted the construction of a testable, mathematical model which enabled a dissection of the roles of early and recycling endosomes in polarized receptor transport. Contrary to expectations, the majority (>65%) of recycling to the basolateral surface is likely to occur from early endosomes, but with relatively little sorting of apical from basolateral proteins. Instead, more complete segregation of basolateral receptors from receptors intended for transcytosis occurred upon delivery to recycling endosomes.