Node embedding is a powerful approach for representing the structural role of each node in a graph. $textit{Node2vec}$ is a widely used method for node embedding that works by exploring the local neighborhoods via biased random walks on the graph. Ho
wever, $textit{node2vec}$ does not consider edge weights when computing walk biases. This intrinsic limitation prevents $textit{node2vec}$ from leveraging all the information in weighted graphs and, in turn, limits its application to many real-world networks that are weighted and dense. Here, we naturally extend $textit{node2vec}$ to $textit{node2vec+}$ in a way that accounts for edge weights when calculating walk biases, but which reduces to $textit{node2vec}$ in the cases of unweighted graphs or unbiased walks. We empirically show that $textit{node2vec+}$ is more robust to additive noise than $textit{node2vec}$ in weighted graphs using two synthetic datasets. We also demonstrate that $textit{node2vec+}$ significantly outperforms $textit{node2vec}$ on a commonly benchmarked multi-label dataset (Wikipedia). Furthermore, we test $textit{node2vec+}$ against GCN and GraphSAGE using various challenging gene classification tasks on two protein-protein interaction networks. Despite some clear advantages of GCN and GraphSAGE, they show comparable performance with $textit{node2vec+}$. Finally, $textit{node2vec+}$ can be used as a general approach for generating biased random walks, benefiting all existing methods built on top of $textit{node2vec}$. $textit{Node2vec+}$ is implemented as part of $texttt{PecanPy}$, which is available at https://github.com/krishnanlab/PecanPy .
There are many mathematical models of biochemical cell signaling pathways that contain a large number of elements (species and reactions). This is sometimes a big issue for identifying critical model elements and describing the model dynamics. Thus,
techniques of model reduction can be used as a mathematical tool in order to minimize the number of variables and parameters. In this thesis, we review some well-known methods of model reduction for cell signaling pathways. We have also developed some approaches that provide us a great step forward in model reduction. The techniques are quasi steady state approximation (QSSA), quasi equilibrium approximation (QEA), lumping of species and entropy production analysis. They are applied on protein translation pathways with microRNA mechanisms, chemical reaction networks, extracellular signal regulated kinase (ERK) pathways, NFkB signal transduction pathways, elongation factors EFTu and EFTs signaling pathways and Dihydrofolate reductase (DHFR) pathways. The main aim of this thesis is to reduce the complex cell signaling pathway models. This provides one a better understanding of the dynamics of such models and gives an accurate approximate solution. Results show that there is a good agreement between the original models and the simplified models.
A decomposition of a chemical reaction network (CRN) is produced by partitioning its set of reactions. The partition induces networks, called subnetworks, that are smaller than the given CRN which, at this point, can be called parent network. A compl
ex is called a common complex if it occurs in at least two subnetworks in a decomposition. A decomposition is said to be incidence independent if the image of the incidence map of the parent network is the direct sum of the images of the subnetworks incidence maps. It has been recently discovered that the complex balanced equilibria of the parent network and its subnetworks are fundamentally connected in an incidence independent decomposition. In this paper, we utilized the set of common complexes and a developed criterion to investigate decompositions incidence independence properties. A framework was also developed to analyze decomposition classes with similar structure and incidence independence properties. We identified decomposition classes that can be characterized by their sets of common complexes and studied their incidence independence. Some of these decomposition classes occur in some biological and chemical models. Finally, a sufficient condition was obtained for the complex balancing of some power law kinetic (PLK) systems with incidence independent and complex balanced decompositions. This condition led to a generalization of the Defficiency Zero Theorem for some PLK systems.
In cellular reprogramming, almost all epigenetic memories of differentiated cells are erased by the overexpression of few genes, regaining pluripotency, potentiality for differentiation. Considering the interplay between oscillatory gene expression a
nd slower epigenetic modifications, such reprogramming is perceived as an unintuitive, global attraction to the unstable manifold of a saddle, which represents pluripotency. The universality of this scheme is confirmed by the repressilator model, and by gene regulatory networks randomly generated and those extracted from embryonic stem cells.
RNA 3D architectures are stabilized by sophisticated networks of (non-canonical) base pair interactions, which can be conveniently encoded as multi-relational graphs and efficiently exploited by graph theoretical approaches and recent progresses in m
achine learning techniques. RNAglib is a library that eases the use of this representation, by providing clean data, methods to load it in machine learning pipelines and graph-based deep learning models suited for this representation. RNAglib also offers other utilities to model RNA with 2.5D graphs, such as drawing tools, comparison functions or baseline performances on RNA applications. The method and data is distributed as a fully documented pip package. Availability: https://rnaglib.cs.mcgill.ca
We are concerned with polynomial ordinary differential systems that arise from modelling chemical reaction networks. For such systems, which may be of high dimension and may depend on many parameters, it is frequently of interest to obtain a reductio
n of dimension in certain parameter ranges. Singular perturbation theory, as initiated by Tikhonov and Fenichel, provides a path toward such reductions. In the present paper we discuss parameter values that lead to singular perturbation reductions (so-called Tikhonov-Fenichel parameter values, or TFPVs). An algorithmic approach is known, but it is feasible for small dimensions only. Here we characterize conditions for classes of reaction networks for which TFPVs arise by turning off reactions (by setting rate parameters to zero), or by removing certain species (which relates to the classical quasi-steady state approach to model reduction). In particular, we obtain definitive results for the class of complex balanced reaction networks (of deficiency zero) and first order reaction networks.
Autocatalysis underlies the ability of chemical and biochemical systems to replicate. Recently, Blokhuis et al. gave a stoechiometric definition of autocatalysis for reaction networks, stating the existence of a combination of reactions such that the
balance for all autocatalytic species is strictly positive, and investigated minimal autocatalytic networks, called {em autocatalytic cores}. By contrast, spontaneous autocatalysis -- namely, exponential amplification of all species internal to a reaction network, starting from a diluted regime, i.e. low concentrations -- is a dynamical property. We introduce here a topological condition (Top) for autocatalysis, namely: restricting the reaction network description to highly diluted species, we assume existence of a strongly connected component possessing at least one reaction with multiple products (including multiple copies of a single species). We find this condition to be necessary and sufficient for stoechiometric autocatalysis. When degradation reactions have small enough rates, the topological condition further ensures dynamical autocatalysis, characterized by a strictly positive Lyapunov exponent giving the instantaneous exponential growth rate of the system. The proof is generally based on the study of auxiliary Markov chains. We provide as examples general autocatalytic cores of Type I and Type III in the typology of Blokhuis et al. In a companion article, Lyapunov exponents and the behavior in the growth regime are studied quantitatively beyond the present diluted regime .
We prove that nested canalizing functions are the minimum-sensitivity Boolean functions for any given activity ratio and we characterize the sensitivity boundary which has a nontrivial fractal structure. We further observe, on an extensive database o
f regulatory functions curated from the literature, that this bound severely constrains the robustness of biological networks. Our findings suggest that the accumulation near the edge of chaos in these systems is a natural consequence of a drive towards maximum stability while maintaining plasticity in transcriptional activity.
Inferring functional relationships within complex networks from static snapshots of a subset of variables is a ubiquitous problem in science. For example, a key challenge of systems biology is to translate cellular heterogeneity data obtained from si
ngle-cell sequencing or flow-cytometry experiments into regulatory dynamics. We show how static population snapshots of co-variability can be exploited to rigorously infer properties of gene expression dynamics when gene expression reporters probe their upstream dynamics on separate time-scales. This can be experimentally exploited in dual-reporter experiments with fluorescent proteins of unequal maturation times, thus turning an experimental bug into an analysis feature. We derive correlation conditions that detect the presence of closed-loop feedback regulation in gene regulatory networks. Furthermore, we show how genes with cell-cycle dependent transcription rates can be identified from the variability of co-regulated fluorescent proteins. Similar correlation constraints might prove useful in other areas of science in which static correlation snapshots are used to infer causal connections between dynamically interacting components.
The novel coronavirus SARS-CoV-2 has resulted in a global pandemic with worldwide 6-digital infection rates and thousands death tolls daily. Enormeous effords are undertaken to achieve high coverage of immunization in order to reach herd immunity to
stop spreading of SARS-CoV-2 infection. Several SARS-CoV-2 vaccines, based either on mRNA, viral vectors, or inactivated SARS-CoV-2 virus have been approved and are being applied worldwide. However, recently increased numbers of normally very rare types of thromboses associated with thrombocytopenia have been reported in particular in the context of the adenoviral vector vaccine ChAdOx1 nCoV-19 from Astra Zeneca. While statistical prevalence of these side effects seem to correlate with this particular vaccine type, i.e. adenonoviral vector based vaccines, the exact molecular mechanisms are still not clear. The present review summarizes current data and hypotheses for molecular and cellular mechanisms into one integrated hypothesis indicating that coagulopathies, including thromboses, thrombocytopenia and other related side effects are correlated to an interplay of the two components in the vaccine, i.e. the spike antigen and the adenoviral vector, with the innate and immune system which under certain circumstances can imitate the picture of a limited COVID-19 pathological picture.
