The efficiency of reactant site sampling in network-free simulation of rule-based models for biochemical systems

Rule-based models, which are typically formulated to represent cell signaling systems, can now be simulated via various network-free simulation methods. In a network-free method, reaction rates are calculated for rules that characterize molecular interactions, and these rule rates, which each correspond to the cumulative rate of all reactions implied by a rule, are used to perform a stochastic simulation of reaction kinetics. Network-free methods, which can be viewed as generalizations of Gillespie's method, are so named because these methods do not require that a list of individual reactions implied by a set of rules be explicitly generated, which is a requirement of other methods for simulating rule-based models. This requirement is impractical for rule sets that imply large reaction networks (i.e. long lists of individual reactions), as reaction network generation is expensive. Here, we compare the network-free simulation methods implemented in RuleMonkey and NFsim, general-purpose software tools for simulating rule-based models encoded in the BioNetGen language. The method implemented in NFsim uses rejection sampling to correct overestimates of rule rates, which introduces null events (i.e. time steps that do not change the state of the system being simulated). The method implemented in RuleMonkey uses iterative updates to track rule rates exactly, which avoids null events. To ensure a fair comparison of the two methods, we developed implementations of the rejection and rejection-free methods specific to a particular class of kinetic models for multivalent ligand-receptor interactions. These implementations were written with the intention of making them as much alike as possible, minimizing the contribution of irrelevant coding differences to efficiency differences. Simulation results show that performance of the rejection method is equal to or better than that of the rejection-free method over wide parameter ranges. However, when parameter values are such that ligand-induced aggregation of receptors yields a large connected receptor cluster, the rejection-free method is more efficient.     

Steric effects on multivalent ligand-receptor binding: exclusion of ligand sites by bound cell surface receptors.

Steric effects can influence the binding of a cell surface receptor to a multivalent ligand. To account for steric effects arising from the size of a receptor and from the spacing of binding sites on a ligand, we extend a standard mathematical model for ligand-receptor interactions by introducing a steric hindrance factor. This factor gives the fraction of unbound ligand sites that are accessible to receptors, and thus available for binding, as a function of ligand site occupancy. We derive expressions for the steric hindrance factor for various cases in which the receptor covers a compact region on the ligand surface and the ligand expresses sites that are distributed regularly or randomly in one or two dimensions. These expressions are relevant for ligands such as linear polymers, proteins, and viruses. We also present numerical algorithms that can be used to calculate steric hindrance factors for other cases. These theoretical results allow us to quantify the effects of steric hindrance on ligand-receptor kinetics and equilibria.     

Monkey hybrid stem cells develop cellular features of Huntington's disease

Background  

Pluripotent stem cells that are capable of differentiating into different cell types and develop robust hallmark cellular features are useful tools for clarifying the impact of developmental events on neurodegenerative diseases such as Huntington's disease. Additionally, a Huntington's cell model that develops robust pathological features of Huntington's disease would be valuable for drug discovery research.     

Modeling the Effect of APC Truncation on Destruction Complex Function in Colorectal Cancer Cells

In colorectal cancer cells, APC, a tumor suppressor protein, is commonly expressed in truncated form. Truncation of APC is believed to disrupt degradation of β—catenin, which is regulated by a multiprotein complex called the destruction complex. The destruction complex comprises APC, Axin, β—catenin, serine/threonine kinases, and other proteins. The kinases and , which are recruited by Axin, mediate phosphorylation of β—catenin, which initiates its ubiquitination and proteosomal degradation. The mechanism of regulation of β—catenin degradation by the destruction complex and the role of truncation of APC in colorectal cancer are not entirely understood. Through formulation and analysis of a rule-based computational model, we investigated the regulation of β—catenin phosphorylation and degradation by APC and the effect of APC truncation on function of the destruction complex. The model integrates available mechanistic knowledge about site-specific interactions and phosphorylation of destruction complex components and is consistent with an array of published data. We find that the phosphorylated truncated form of APC can outcompete Axin for binding to β—catenin, provided that Axin is limiting, and thereby sequester β—catenin away from Axin and the Axin-recruited kinases and . Full-length APC also competes with Axin for binding to β—catenin; however, full-length APC is able, through its SAMP repeats, which bind Axin and which are missing in truncated oncogenic forms of APC, to bring β—catenin into indirect association with Axin and Axin-recruited kinases. Because our model indicates that the positive effects of truncated APC on β—catenin levels depend on phosphorylation of APC, at the first 20-amino acid repeat, and because phosphorylation of this site is mediated by , we suggest that is a potential target for therapeutic intervention in colorectal cancer. Specific inhibition of is predicted to limit binding of β—catenin to truncated APC and thereby to reverse the effect of APC truncation.     

Preliminary analysis to estimate the spatial distribution of benefits of P load reduction: Identifying the spatial influence of phosphorus loading from the Maumee River (USA) in western Lake Erie

Since the early 2000s, Lake Erie has been experiencing annual cyanobacterial blooms that often cover large portions of the western basin and even reach into the central basin. These blooms have affected several ecosystem services provided by Lake Erie to surrounding communities (notably drinking water quality). Several modeling efforts have identified the springtime total bioavailable phosphorus (TBP) load as a major driver of maximum cyanobacterial biomass in western Lake Erie, and on this basis, international water management bodies have set a phosphorus (P) reduction goal. This P reduction goal is intended to reduce maximum cyanobacterial biomass, but there has been very limited effort to identify the specific locations within the western basin of Lake Erie that will likely experience the most benefits. Here, we used pixel‐specific linear regression to identify where annual variation in spring TBP loads is most strongly associated with cyanobacterial abundance, as inferred from satellite imagery. Using this approach, we find that annual TBP loads are most strongly associated with cyanobacterial abundance in the central and southern areas of the western basin. At the location of the Toledo water intake, the association between TBP load and cyanobacterial abundance is moderate, and in Maumee Bay (near Toledo, Ohio), the association between TBP and cyanobacterial abundance is no better than a null model. Both of these locations are important for the delivery of specific ecosystem services, but this analysis indicates that P load reductions would not be expected to substantially improve maximum annual cyanobacterial abundance in these locations. These results are preliminary in the sense that only a limited set of models were tested in this analysis, but these results illustrate the importance of identifying whether the spatial distribution of management benefits (in this case P load reduction) matches the spatial distribution of management goals (reducing the effects of cyanobacteria on important ecosystem services).     

Use of Mechanistic Models to Integrate and Analyze Multiple Proteomic Datasets

Proteins in cell signaling networks tend to interact promiscuously through low-affinity interactions. Consequently, evaluating the physiological importance of mapped interactions can be difficult. Attempts to do so have tended to focus on single, measurable physicochemical factors, such as affinity or abundance. For example, interaction importance has been assessed on the basis of the relative affinities of binding partners for a protein of interest, such as a receptor. However, multiple factors can be expected to simultaneously influence the recruitment of proteins to a receptor (and the potential of these proteins to contribute to receptor signaling), including affinity, abundance, and competition, which is a network property. Here, we demonstrate that measurements of protein copy numbers and binding affinities can be integrated within the framework of a mechanistic, computational model that accounts for mass action and competition. We use cell line-specific models to rank the relative importance of protein-protein interactions in the epidermal growth factor receptor (EGFR) signaling network for 11 different cell lines. Each model accounts for experimentally characterized interactions of six autophosphorylation sites in EGFR with proteins containing a Src homology 2 and/or phosphotyrosine-binding domain. We measure importance as the predicted maximal extent of recruitment of a protein to EGFR following ligand-stimulated activation of EGFR signaling. We find that interactions ranked highly by this metric include experimentally detected interactions. Proteins with high importance rank in multiple cell lines include proteins with recognized, well-characterized roles in EGFR signaling, such as GRB2 and SHC1, as well as a protein with a less well-defined role, YES1. Our results reveal potential cell line-specific differences in recruitment.     

Mitochondrial Morphological Features Are Associated with Fission and Fusion Events

Mitochondria are dynamic organelles that undergo constant remodeling through the regulation of two opposing processes, mitochondrial fission and fusion. Although several key regulators and physiological stimuli have been identified to control mitochondrial fission and fusion, the role of mitochondrial morphology in the two processes remains to be determined. To address this knowledge gap, we investigated whether morphological features extracted from time-lapse live-cell images of mitochondria could be used to predict mitochondrial fate. That is, we asked if we could predict whether a mitochondrion is likely to participate in a fission or fusion event based on its current shape and local environment. Using live-cell microscopy, image analysis software, and supervised machine learning, we characterized mitochondrial dynamics with single-organelle resolution to identify features of mitochondria that are predictive of fission and fusion events. A random forest (RF) model was trained to correctly classify mitochondria poised for either fission or fusion based on a series of morphological and positional features for each organelle. Of the features we evaluated, mitochondrial perimeter positively correlated with mitochondria about to undergo a fission event. Similarly mitochondrial solidity (compact shape) positively correlated with mitochondria about to undergo a fusion event. Our results indicate that fission and fusion are positively correlated with mitochondrial morphological features; and therefore, mitochondrial fission and fusion may be influenced by the mechanical properties of mitochondrial membranes.