Discrete Logic Modelling Optimization to Contextualize Prior Knowledge Networks Using PRUNET

High-throughput technologies have led to the generation of an increasing amount of data in different areas of biology. Datasets capturing the cell’s response to its intra- and extra-cellular microenvironment allows such data to be incorporated as signed and directed graphs or influence networks. These prior knowledge networks (PKNs) represent our current knowledge of the causality of cellular signal transduction. New signalling data is often examined and interpreted in conjunction with PKNs. However, different biological contexts, such as cell type or disease states, may have distinct variants of signalling pathways, resulting in the misinterpretation of new data. The identification of inconsistencies between measured data and signalling topologies, as well as the training of PKNs using context specific datasets (PKN contextualization), are necessary conditions to construct reliable, predictive models, which are current challenges in the systems biology of cell signalling. Here we present PRUNET, a user-friendly software tool designed to address the contextualization of a PKNs to specific experimental conditions. As the input, the algorithm takes a PKN and the expression profile of two given stable steady states or cellular phenotypes. The PKN is iteratively pruned using an evolutionary algorithm to perform an optimization process. This optimization rests in a match between predicted attractors in a discrete logic model (Boolean) and a Booleanized representation of the phenotypes, within a population of alternative subnetworks that evolves iteratively. We validated the algorithm applying PRUNET to four biological examples and using the resulting contextualized networks to predict missing expression values and to simulate well-characterized perturbations. PRUNET constitutes a tool for the automatic curation of a PKN to make it suitable for describing biological processes under particular experimental conditions. The general applicability of the implemented algorithm makes PRUNET suitable for a variety of biological processes, for instance cellular reprogramming or transitions between healthy and disease states.     

Inferring Intracellular Signal Transduction Circuitry from Molecular Perturbation Experiments

The development of network inference methodologies that accurately predict connectivity in dysregulated pathways may enable the rational selection of patient therapies. Accurately inferring an intracellular network from data remains a very challenging problem in molecular systems biology. Living cells integrate extremely robust circuits that exhibit significant heterogeneity, but still respond to external stimuli in predictable ways. This phenomenon allows us to introduce a network inference methodology that integrates measurements of protein activation from perturbation experiments. The methodology relies on logic-based networks to provide a predictive approximation of the transfer of signals in a network. The approach presented was validated in silico with a set of test networks and applied to investigate the epidermal growth factor receptor signaling of a breast epithelial cell line, MFC10A. In our analysis, we predict the potential signaling circuitry most likely responsible for the experimental readouts of several proteins in the mitogen-activated protein kinase and phosphatidylinositol-3 kinase pathways. The approach can also be used to identify additional necessary perturbation experiments to distinguish between a set of possible candidate networks.     

Interplay between Graph Topology and Correlations of Third Order in Spiking Neuronal Networks

The study of processes evolving on networks has recently become a very popular research field, not only because of the rich mathematical theory that underpins it, but also because of its many possible applications, a number of them in the field of biology. Indeed, molecular signaling pathways, gene regulation, predator-prey interactions and the communication between neurons in the brain can be seen as examples of networks with complex dynamics. The properties of such dynamics depend largely on the topology of the underlying network graph. In this work, we want to answer the following question: Knowing network connectivity, what can be said about the level of third-order correlations that will characterize the network dynamics? We consider a linear point process as a model for pulse-coded, or spiking activity in a neuronal network. Using recent results from theory of such processes, we study third-order correlations between spike trains in such a system and explain which features of the network graph (i.e. which topological motifs) are responsible for their emergence. Comparing two different models of network topology—random networks of Erdős-Rényi type and networks with highly interconnected hubs—we find that, in random networks, the average measure of third-order correlations does not depend on the local connectivity properties, but rather on global parameters, such as the connection probability. This, however, ceases to be the case in networks with a geometric out-degree distribution, where topological specificities have a strong impact on average correlations.     

Functional Brain Networks Develop from a “Local to Distributed” Organization

The mature human brain is organized into a collection of specialized functional networks that flexibly interact to support various cognitive functions. Studies of development often attempt to identify the organizing principles that guide the maturation of these functional networks. In this report, we combine resting state functional connectivity MRI (rs-fcMRI), graph analysis, community detection, and spring-embedding visualization techniques to analyze four separate networks defined in earlier studies. As we have previously reported, we find, across development, a trend toward ‘segregation’ (a general decrease in correlation strength) between regions close in anatomical space and ‘integration’ (an increased correlation strength) between selected regions distant in space. The generalization of these earlier trends across multiple networks suggests that this is a general developmental principle for changes in functional connectivity that would extend to large-scale graph theoretic analyses of large-scale brain networks. Communities in children are predominantly arranged by anatomical proximity, while communities in adults predominantly reflect functional relationships, as defined from adult fMRI studies. In sum, over development, the organization of multiple functional networks shifts from a local anatomical emphasis in children to a more “distributed” architecture in young adults. We argue that this “local to distributed” developmental characterization has important implications for understanding the development of neural systems underlying cognition. Further, graph metrics (e.g., clustering coefficients and average path lengths) are similar in child and adult graphs, with both showing “small-world”-like properties, while community detection by modularity optimization reveals stable communities within the graphs that are clearly different between young children and young adults. These observations suggest that early school age children and adults both have relatively efficient systems that may solve similar information processing problems in divergent ways.     

Functional Brain Networks Develop from a “Local to Distributed” Organization

The mature human brain is organized into a collection of specialized functional networks that flexibly interact to support various cognitive functions. Studies of development often attempt to identify the organizing principles that guide the maturation of these functional networks. In this report, we combine resting state functional connectivity MRI (rs-fcMRI), graph analysis, community detection, and spring-embedding visualization techniques to analyze four separate networks defined in earlier studies. As we have previously reported, we find, across development, a trend toward ‘segregation’ (a general decrease in correlation strength) between regions close in anatomical space and ‘integration’ (an increased correlation strength) between selected regions distant in space. The generalization of these earlier trends across multiple networks suggests that this is a general developmental principle for changes in functional connectivity that would extend to large-scale graph theoretic analyses of large-scale brain networks. Communities in children are predominantly arranged by anatomical proximity, while communities in adults predominantly reflect functional relationships, as defined from adult fMRI studies. In sum, over development, the organization of multiple functional networks shifts from a local anatomical emphasis in children to a more “distributed” architecture in young adults. We argue that this “local to distributed” developmental characterization has important implications for understanding the development of neural systems underlying cognition. Further, graph metrics (e.g., clustering coefficients and average path lengths) are similar in child and adult graphs, with both showing “small-world”-like properties, while community detection by modularity optimization reveals stable communities within the graphs that are clearly different between young children and young adults. These observations suggest that early school age children and adults both have relatively efficient systems that may solve similar information processing problems in divergent ways.     

Context-specific network modeling identifies new crosstalk in β-adrenergic cardiac hypertrophy

Cardiac hypertrophy is a context-dependent phenomenon wherein a myriad of biochemical and biomechanical factors regulate myocardial growth through a complex large-scale signaling network. Although numerous studies have investigated hypertrophic signaling pathways, less is known about hypertrophy signaling as a whole network and how this network acts in a context-dependent manner. Here, we developed a systematic approach, CLASSED (Context-specific Logic-bASed Signaling nEtwork Development), to revise a large-scale signaling model based on context-specific data and identify main reactions and new crosstalks regulating context-specific response. CLASSED involves four sequential stages with an automated validation module as a core which builds a logic-based ODE model from the interaction graph and outputs the model validation percent. The context-specific model is developed by estimation of default parameters, classified qualitative validation, hybrid Morris-Sobol global sensitivity analysis, and discovery of missing context-dependent crosstalks. Applying this pipeline to our prior-knowledge hypertrophy network with context-specific data revealed key signaling reactions which distinctly regulate cell response to isoproterenol, phenylephrine, angiotensin II and stretch. Furthermore, with CLASSED we developed a context-specific model of β-adrenergic cardiac hypertrophy. The model predicted new crosstalks between calcium/calmodulin-dependent pathways and upstream signaling of Ras in the ISO-specific context. Experiments in cardiomyocytes validated the model’s predictions on the role of CaMKII-Gβγ and CaN-Gβγ interactions in mediating hypertrophic signals in ISO-specific context and revealed a difference in the phosphorylation magnitude and translocation of ERK1/2 between cardiac myocytes and fibroblasts. CLASSED is a systematic approach for developing context-specific large-scale signaling networks, yielding insights into new-found crosstalks in β-adrenergic cardiac hypertrophy.     

SPEACH_AF: Sampling protein ensembles and conformational heterogeneity with Alphafold2

The unprecedented performance of Deepmind’s Alphafold2 in predicting protein structure in CASP XIV and the creation of a database of structures for multiple proteomes and protein sequence repositories is reshaping structural biology. However, because this database returns a single structure, it brought into question Alphafold’s ability to capture the intrinsic conformational flexibility of proteins. Here we present a general approach to drive Alphafold2 to model alternate protein conformations through simple manipulation of the multiple sequence alignment via in silico mutagenesis. The approach is grounded in the hypothesis that the multiple sequence alignment must also encode for protein structural heterogeneity, thus its rational manipulation will enable Alphafold2 to sample alternate conformations. A systematic modeling pipeline is benchmarked against canonical examples of protein conformational flexibility and applied to interrogate the conformational landscape of membrane proteins. This work broadens the applicability of Alphafold2 by generating multiple protein conformations to be tested biologically, biochemically, biophysically, and for use in structure-based drug design.     

Site recognition and substrate screens for PKN family proteins

The PRKs [protein kinase C-related kinases; also referred to as PKNs (protein kinase Ns)] are a kinase family important in diverse functions including migration and cytokinesis. In the present study, we have re-evaluated and compared the specificity of PKN1 and PKN3 and assessed the predictive value in substrates. We analysed the phosphorylation consensus motif of PKNs using a peptide library approach and demonstrate that both PKN1 and PKN3 phosphorylate serine residues in sequence contexts that have an arginine residue in position -3. In contrast, PKN1 and PKN3 do not tolerate arginine residues in position +1 and -1 respectively. To test the predictive value of this motif, site analysis was performed on the PKN substrate CLIP-170 (cytoplasmic linker protein of 170 kDa); a PKN target site was identified that conformed to the predicted pattern. Using a protein array, we identified 22 further substrates for PKN1, of which 20 were previously undescribed substrates. To evaluate further the recognition signature, the site on one of these hits, EGFR (epidermal growth factor receptor), was identified. This identified Thr??? in EGFR as the PKN1 phosphorylation site and this retains an arginine residue at the -3 position. Finally, the constitutive phosphorylation of EGFR on Thr??? is shown to be modulated by PKN in vivo.     

Disentangling the Complexity of HGF Signaling by Combining Qualitative and Quantitative Modeling

Signaling pathways are characterized by crosstalk, feedback and feedforward mechanisms giving rise to highly complex and cell-context specific signaling networks. Dissecting the underlying relations is crucial to predict the impact of targeted perturbations. However, a major challenge in identifying cell-context specific signaling networks is the enormous number of potentially possible interactions. Here, we report a novel hybrid mathematical modeling strategy to systematically unravel hepatocyte growth factor (HGF) stimulated phosphoinositide-3-kinase (PI3K) and mitogen activated protein kinase (MAPK) signaling, which critically contribute to liver regeneration. By combining time-resolved quantitative experimental data generated in primary mouse hepatocytes with interaction graph and ordinary differential equation modeling, we identify and experimentally validate a network structure that represents the experimental data best and indicates specific crosstalk mechanisms. Whereas the identified network is robust against single perturbations, combinatorial inhibition strategies are predicted that result in strong reduction of Akt and ERK activation. Thus, by capitalizing on the advantages of the two modeling approaches, we reduce the high combinatorial complexity and identify cell-context specific signaling networks.     

Regimes and mechanisms of transient amplification in abstract and biological neural networks

Neuronal networks encode information through patterns of activity that define the networks’ function. The neurons’ activity relies on specific connectivity structures, yet the link between structure and function is not fully understood. Here, we tackle this structure-function problem with a new conceptual approach. Instead of manipulating the connectivity directly, we focus on upper triangular matrices, which represent the network dynamics in a given orthonormal basis obtained by the Schur decomposition. This abstraction allows us to independently manipulate the eigenspectrum and feedforward structures of a connectivity matrix. Using this method, we describe a diverse repertoire of non-normal transient amplification, and to complement the analysis of the dynamical regimes, we quantify the geometry of output trajectories through the effective rank of both the eigenvector and the dynamics matrices. Counter-intuitively, we find that shrinking the eigenspectrum’s imaginary distribution leads to highly amplifying regimes in linear and long-lasting dynamics in nonlinear networks. We also find a trade-off between amplification and dimensionality of neuronal dynamics, i.e., trajectories in neuronal state-space. Networks that can amplify a large number of orthogonal initial conditions produce neuronal trajectories that lie in the same subspace of the neuronal state-space. Finally, we examine networks of excitatory and inhibitory neurons. We find that the strength of global inhibition is directly linked with the amplitude of amplification, such that weakening inhibitory weights also decreases amplification, and that the eigenspectrum’s imaginary distribution grows with an increase in the ratio between excitatory-to-inhibitory and excitatory-to-excitatory connectivity strengths. Consequently, the strength of global inhibition reveals itself as a strong signature for amplification and a potential control mechanism to switch dynamical regimes. Our results shed a light on how biological networks, i.e., networks constrained by Dale’s law, may be optimised for specific dynamical regimes.     

An Approach for Identifying Brainstem Dopaminergic Pathways Using Resting State Functional MRI

Here, we present an approach for identifying brainstem dopaminergic pathways using resting state functional MRI. In a group of healthy individuals, we searched for significant functional connectivity between dopamine-rich midbrain areas (substantia nigra; ventral tegmental area) and a striatal region (caudate) that was modulated by both a pharmacological challenge (the administration of the dopaminergic agonist bromocriptine) and a dopamine-sensitive cognitive trait (an individual’s working memory capacity). A significant inverted-U shaped connectivity pattern was found in a subset of midbrain-striatal connections, demonstrating that resting state fMRI data is sufficiently powerful to identify brainstem neuromodulatory brain networks.     

Learning the rules of collective cell migration using deep attention networks

Collective, coordinated cellular motions underpin key processes in all multicellular organisms, yet it has been difficult to simultaneously express the ‘rules’ behind these motions in clear, interpretable forms that effectively capture high-dimensional cell-cell interaction dynamics in a manner that is intuitive to the researcher. Here we apply deep attention networks to analyze several canonical living tissues systems and present the underlying collective migration rules for each tissue type using only cell migration trajectory data. We use these networks to learn the behaviors of key tissue types with distinct collective behaviors—epithelial, endothelial, and metastatic breast cancer cells—and show how the results complement traditional biophysical approaches. In particular, we present attention maps indicating the relative influence of neighboring cells to the learned turning decisions of a ‘focal cell’–the primary cell of interest in a collective setting. Colloquially, we refer to this learned relative influence as ‘attention’, as it serves as a proxy for the physical parameters modifying the focal cell’s future motion as a function of each neighbor cell. These attention networks reveal distinct patterns of influence and attention unique to each model tissue. Endothelial cells exhibit tightly focused attention on their immediate forward-most neighbors, while cells in more expansile epithelial tissues are more broadly influenced by neighbors in a relatively large forward sector. Attention maps of ensembles of more mesenchymal, metastatic cells reveal completely symmetric attention patterns, indicating the lack of any particular coordination or direction of interest. Moreover, we show how attention networks are capable of detecting and learning how these rules change based on biophysical context, such as location within the tissue and cellular crowding. That these results require only cellular trajectories and no modeling assumptions highlights the potential of attention networks for providing further biological insights into complex cellular systems.     

Identification of Potential Pathway Mediation Targets in Toll-like Receptor Signaling

Recent advances in reconstruction and analytical methods for signaling networks have spurred the development of large-scale models that incorporate fully functional and biologically relevant features. An extended reconstruction of the human Toll-like receptor signaling network is presented herein. This reconstruction contains an extensive complement of kinases, phosphatases, and other associated proteins that mediate the signaling cascade along with a delineation of their associated chemical reactions. A computational framework based on the methods of large-scale convex analysis was developed and applied to this network to characterize input–output relationships. The input–output relationships enabled significant modularization of the network into ten pathways. The analysis identified potential candidates for inhibitory mediation of TLR signaling with respect to their specificity and potency. Subsequently, we were able to identify eight novel inhibition targets through constraint-based modeling methods. The results of this study are expected to yield meaningful avenues for further research in the task of mediating the Toll-like receptor signaling network and its effects.     

The Logic of EGFR/ErbB Signaling: Theoretical Properties and Analysis of High-Throughput Data

The epidermal growth factor receptor (EGFR) signaling pathway is probably the best-studied receptor system in mammalian cells, and it also has become a popular example for employing mathematical modeling to cellular signaling networks. Dynamic models have the highest explanatory and predictive potential; however, the lack of kinetic information restricts current models of EGFR signaling to smaller sub-networks. This work aims to provide a large-scale qualitative model that comprises the main and also the side routes of EGFR/ErbB signaling and that still enables one to derive important functional properties and predictions. Using a recently introduced logical modeling framework, we first examined general topological properties and the qualitative stimulus-response behavior of the network. With species equivalence classes, we introduce a new technique for logical networks that reveals sets of nodes strongly coupled in their behavior. We also analyzed a model variant which explicitly accounts for uncertainties regarding the logical combination of signals in the model. The predictive power of this model is still high, indicating highly redundant sub-structures in the network. Finally, one key advance of this work is the introduction of new techniques for assessing high-throughput data with logical models (and their underlying interaction graph). By employing these techniques for phospho-proteomic data from primary hepatocytes and the HepG2 cell line, we demonstrate that our approach enables one to uncover inconsistencies between experimental results and our current qualitative knowledge and to generate new hypotheses and conclusions. Our results strongly suggest that the Rac/Cdc42 induced p38 and JNK cascades are independent of PI3K in both primary hepatocytes and HepG2. Furthermore, we detected that the activation of JNK in response to neuregulin follows a PI3K-dependent signaling pathway.     

Interaction profiling methods to map protein and pathway targets of bioactive ligands

Recent advances in -omic profiling technologies have ushered in an era where we no longer want to merely measure the presence or absence of a biomolecule of interest, but instead hope to understand its function and interactions within larger signaling networks. Here, we review several emerging proteomic technologies capable of detecting protein interaction networks in live cells and their integration to draft holistic maps of proteins that respond to diverse stimuli, including bioactive small molecules. Moreover, we provide a conceptual framework to combine so-called ‘top-down’ and ‘bottom-up’ interaction profiling methods and ensuing proteomic profiles to directly identify binding targets of small molecule ligands, as well as for unbiased discovery of proteins and pathways that may be directly bound or influenced by those first responders. The integrated, interaction-based profiling methods discussed here have the potential to provide a unique and dynamic view into cellular signaling networks for both basic and translational biological studies.     

Enzyme kinetics and distinct modulation of the protein kinase N family of kinases by lipid activators and small molecule inhibitors

The PKN (protein kinase N) family of Ser/Thr protein kinases regulates a diverse set of cellular functions, such as cell migration and cytoskeletal organization. Inhibition of tumour PKN activity has been explored as an oncology therapeutic approach, with a PKN3-targeted RNAi (RNA interference)-derived therapeutic agent in Phase I clinical trials. To better understand this important family of kinases, we performed detailed enzymatic characterization, determining the kinetic mechanism and lipid sensitivity of each PKN isoform using full-length enzymes and synthetic peptide substrate. Steady-state kinetic analysis revealed that PKN1–3 follows a sequential ordered Bi–Bi kinetic mechanism, where peptide substrate binding is preceded by ATP binding. This kinetic mechanism was confirmed by additional kinetic studies for product inhibition and affinity of small molecule inhibitors. The known lipid effector, arachidonic acid, increased the catalytic efficiency of each isoform, mainly through an increase in k_cat for PKN1 and PKN2, and a decrease in peptide K_M for PKN3. In addition, a number of PKN inhibitors with various degrees of isoform selectivity, including potent (K_i<10 nM) and selective PKN3 inhibitors, were identified by testing commercial libraries of small molecule kinase inhibitors. This study provides a kinetic framework and useful chemical probes for understanding PKN biology and the discovery of isoform-selective PKN-targeted inhibitors.     

PRER: A patient representation with pairwise relative expression of proteins on biological networks

Changes in protein and gene expression levels are often used as features in predictive modeling such as survival prediction. A common strategy to aggregate information contained in individual proteins is to integrate the expression levels with the biological networks. In this work, we propose a novel patient representation where we integrate proteins’ expression levels with the protein-protein interaction (PPI) networks: Patient representation with PRER (Pairwise Relative Expressions with Random walks). PRER captures the dysregulation patterns of proteins based on the neighborhood of a protein in the PPI network. Specifically, PRER computes a feature vector for a patient by comparing the source protein’s expression level with other proteins’ levels that are within its neighborhood. The neighborhood of the source protein is derived by biased random-walk strategy on the network. We test PRER’s performance in survival prediction task in 10 different cancers using random forest survival models. PRER yields a statistically significant predictive performance in 9 out of 10 cancers when compared to the same model trained with features based on individual protein expressions. Furthermore, we identified the pairs of proteins that their interactions are predictive of patient survival but their individual expression levels are not. The set of identified relations provides a valuable collection of protein biomarkers with high prognostic value. PRER can be used for other complex diseases and prediction tasks that use molecular expression profiles as input. PRER is freely available at: https://github.com/hikuru/PRER.