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Network biology is a powerful framework for studying the structure, function, and dynamics of biological systems, offering insights into the balance between health and disease states. The field is seeing rapid progress in all of its aspects: data availability, network synthesis, network analytics, and impactful applications in medicine and drug development. We review the most recent and significant results in network biomedicine, with a focus on the latest data, analytics, software resources, and applications in medicine. We also discuss what in our view are the likely directions of impactful development over the next few years.

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Control theory has seen recently impactful applications in network science, especially in connections with applications in network medicine. A key topic of research is that of finding minimal external interventions that offer control over the dynamics of a given network, a problem known as network controllability. We propose in this article a new solution for this problem based on genetic algorithms. We tailor our solution for applications in computational drug repurposing, seeking to maximize its use of FDA-approved drug targets in a given disease-specific protein-protein interaction network. We demonstrate our algorithm on several cancer networks and on several random networks with their edges distributed according to the Erdos-Renyi, the Scale-Free, and the Small World properties. Overall, we show that our new algorithm is more efficient in identifying relevant drug targets in a disease network, advancing the computational solutions needed for new therapeutic and drug repurposing approaches.

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In a recent study, Spencer et al. 2021, we have proposed a computational modeling framework for DNA multi strand dynamics implemented using the agent- and rule-based modeling methodology. While this modeling methodology allows for compact representations for systems with large numbers of different species and complexes, such as the case of self-assembly systems, one of its main drawbacks concerns its scalability. Since each agent is individually represented and modeled in the system, the framework becomes slow when dealing with tens- and hundreds of thousands of individual components. In this study we introduce a method to parallelize the computational modeling process by distributing it over several CPU's. We show that such multi-thread models remain equivalent to their sequential counterpart, while the speedup of the computational process can reach even a one-fold increase.

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To better understand the potential of drug repurposing in COVID-19, we analyzed control strategies over essential host factors for SARS-CoV-2 infection. We constructed comprehensive directed protein-protein interaction (PPI) networks integrating the top-ranked host factors, the drug target proteins and directed PPI data. We analyzed the networks to identify drug targets and combinations thereof that offer efficient control over the host factors. We validated our findings against clinical studies data and bioinformatics studies. Our method offers a new insight into the molecular details of the disease and into potentially new therapy targets for it. Our approach for drug repurposing is significant beyond COVID-19 and may be applied also to other diseases.

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We discuss in this chapter several network modelling methods and their applicability to precision medicine. We review several network centrality methods (degree centrality, closeness centrality, eccentricity centrality, betweenness centrality, and eigenvector-based prestige) and two systems controllability methods (minimum dominating sets and network structural controllability). We demonstrate their applicability to precision medicine on three multiple myeloma patient disease networks. Each network consists of protein-protein interactions (PPI) built around a specific patient's mutated genes, around the targets of the drugs used in the standard of care in multiple myeloma, and around multiple myeloma-specific essential genes. For each network, we demonstrate how the network methods we discuss can be used to identify personalized, targeted drug combinations uniquely suited to that patient. © 2020 John Wiley & Sons, Inc. All rights reserved.

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The dynamics of nucleic-acids dynamical systems is intrinsically based on local interaction. The major acting mechanisms are that of Watson-Crick complementarity on one-hand, generating binding events, and thermal energy on the other, generating random motion and un-binding. It is thus predictable that such systems can be successfully captured by computational modeling paradigms based on local interactions, such as the rule-based modeling methodology. In this research we introduce the Virtual DNA Lab (VDNA-Lab) a simulation tool which provides an easy to use graphical interface for creating, running and visualizing synthetic simulations for DNA assembly systems, such as assembly of DNA nanostructures, strand displacement cascades systems, DNA-tile assembly etc. It employs a custom designed model, implemented in the BioNetGen Language (BNGL) formalism, to capture the DNA dynamics, as well as the NFsim computational modeling engine to run simulations and generate outputs. These outputs can be visualized using the VDNA-Lab's own visualization tool, which allows also for further analysis and filtering. The software is freely available at https://github.com/Frankie-Spencer/virtual dna lab.

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Current advances in computational modelling and simulation have led to the inclusion of computer scientists as partners in the process of engineering of new nanomaterials and nanodevices. This trend is now, more than ever, visible in the field of deoxyribonucleic acid (DNA)-based nanotechnology, as DNA's intrinsic principle of self-assembly has been proven to be highly algorithmic and programmable. As a raw material, DNA is a rather unremarkable fabric. However, as a way to achieve patterns, dynamic behavior, or nano-shape reconstruction, DNA has been proven to be one of the most functional nanomaterials. It would thus be of great potential to pair up DNA's highly functional assembly characteristics with the mechanic properties of other well-known bio-nanomaterials, such as graphene, cellulos, or fibroin. In the current study, we perform projections regarding the structural properties of a fibril mesh (or filter) for which assembly would be guided by the controlled aggregation of DNA scaffold subunits. The formation of such a 2D fibril mesh structure is ensured by the mechanistic assembly properties borrowed from the DNA assembly apparatus. For generating inexpensive pre-experimental assessments regarding the efficiency of various assembly strategies, we introduced in this study a computational model for the simulation of fibril mesh assembly dynamical systems. Our approach was based on providing solutions towards two main circumstances. First, we created a functional computational model that is restrictive enough to be able to numerically simulate the controlled aggregation of up to 1000s of elementary fibril elements yet rich enough to provide actionable insides on the structural characteristics for the generated assembly. Second, we used the provided numerical model in order to generate projections regarding effective ways of manipulating one of the the key structural properties of such generated filters, namely the average size of the openings (gaps) within these meshes, also known as the filter's aperture. This work is a continuation of Amarioarei et al., 2018, where a preliminary version of this research was discussed.

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Motivation: There is an increasing amount of data coming from genome-wide studies identifying disease-specific survivability-essential proteins and host factors critical to a cell becoming infected. Targeting such proteins has a strong potential for targeted, precision therapies. Typically however, too few of them are drug targetable. An alternative approach is to influence them through drug targetable proteins upstream of them. Structural target network controllability is a suitable solution to this problem. It aims to discover suitable source nodes (e.g. drug targetable proteins) in a directed interaction network that can control (through a suitable set of input functions) a desired set of targets. Results: We introduce NetControl4BioMed, a free open-source web-based application that allows users to generate or upload directed protein-protein interaction networks and to perform target structural network controllability analyses on them. The analyses can be customized to focus the search on drug targetable source nodes, thus providing drug therapeutic suggestions. The application integrates protein data from HGNC, Ensemble, UniProt, NCBI and InnateDB, directed interaction data from InnateDB, Omnipath and SIGNOR, cell-line data from COLT and DepMap, and drug-target data from DrugBank.

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In a recent paper, using one of the algorithmic assembly formalisms of DNA nanotechnology, we proved that one tile can self-assemble length n structures and n x n squares, which are basic shapes in the study of DNA origami. This new result within a classic Tile Assembly Model (TAM) would not have been possible without the following programming topics: how can we simulate one-dimensional staged self-assembly using the signal-passing TAM, and how can we program staged self-assembly using the available software? We provide probabilistic approaches for investigating the assembly of tile-based one-dimensional structures. We obtain a probabilistic proof of Han's hook length formula in Enumerative Combinatorics. We identify algebraic and combinatorial structures underlying these algorithmic and information theory results.

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Since its introduction in the early 2000s, DNA origami had a big impact on the development of nanotechnology by gathering numerous applications. During this time, many tools were designed and used to generate arbitrary shapes capable of self-assembly which make this technique more approachable. In this paper, we have created the map of Romania at nanoscale dimensions by using a new open-source software - PERDIX. For this purpose, we used a scaffold strand with a length of 6959 nucleotides and 162 staple strands with a variable length ranging between 20 and 63 nucleotides. All the computational tools that were used in this experiment are open-source and user-friendly.

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We describe two new discrete symmetries of the inviscid Burgers (or Riemann–Hopf) equation ut+uux=0. We derived both of them using a local, formal approach of Hopf algebraic renormalization, a tool recently used in algorithmic computations. We prove that one of them is a Lie point transformation. Symmetries generate new exact solutions from the known solutions and provide useful frames of reference in the study of shock wave formation. © 2020 The Author(s)

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We give examples of 2-parameter bounded quadratic dynamical systems with 3 finite singularities, which have at least 4 limit cycles around a singularity (in the (4,0)-configuration)-the first example of this type - and in a (3,1)-configuration. The paper mentions the Nanobiotechnological origins of these experimentally discovered systems with interesting properties.

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We give examples of 2-parameter bounded quadratic dynamical systems with 3 finite singularities, which have at least 4 limit cycles around a singularity (in the (4,0)-configuration) - the first example of this type - and in a (3,1)-configuration. The paper mentions the Nanobiotechnological origins of these experimentally discovered systems with interesting properties. © 2019 University of Kragujevac, Faculty of Science. All rights reserved.

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The Tile Assembly Model, and its many variants, is one of the most fundamental algorithmic assembly formalism within DNA nanotechnology. Most of the research in this field is focused on the complexity of assembling different shapes and patterns. In many cases, the assembly process is intrinsically deterministic and the final product is unique, while the assembly process might evolve through several possible assembly strategies. In this study we consider the controlled assembly of one dimensional tile structures according to predefined assembly graphs. We provide algorithmic approaches for developing such controlled assembly protocols, using the signal-passing Tile Assembly Model, as well as probabilistic approaches for investigating the assembly of such tile-based one-dimensional structures. As a byproduct, we build a generalized TAS (tile assembly system) which generate specific non-local non-associative algebraic computations and we assamble n x n squares using only one tile, which is a better efficiency compared to the staged assembly model. (C) 2019 The Authors. Published by Elsevier B.V.

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Recent research has revealed new applications of network control science within bio-medicine, pharmacology, and medical therapeutics. These new insights and new applications generated in turn a rediscovery of some old, unresolved algorithmic questions, this time with a much stronger motivation for their tackling. One of these questions regards the so-called Structural Target Control optimization problem, known in previous literature also as Structural Output Controllability problem. Given a directed network (graph) and a target subset of nodes, the task is to select a small (or the smallest) set of nodes from which the target can be independently controlled, i.e., it can be driven from any given initial configuration to any desired final one, through a finite sequence of input values. In recent work, this problem has been shown to be NP-hard, and several heuristic algorithms were introduced and analyzed, both on randomly generated networks, and on bio-medical ones. In this paper, we show that the Structural Target Controllability problem is fixed parameter tractable when parameterized by the number of target nodes. We also prove that the problem is hard to approximate at a factor better than O(log n).

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This paper presents the latest trends and approaches used for constructing nanoscale structures of 2D objects through DNA folding based on the DNA origami technology developed by Rothemund. The Rothemund method has been used in the construction of various shapes, such as the development of the nanoscale structure for the United States map. Following the steps of Rothemund's technique, we simulate the construction of the Romanian map nanoscale 2D structure, embedding the number 100 into it.

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The TAM (Model Tile Assembly Model) is a mathematical paradigm for modeling DNA self-assembling according to various given shapes, using DNA-tiles (rectangular shape) with sticky ends on each of the four edges that bound together on various shapes desired by the researcher. Although there are various models in the literature, the focus in this manuscript is on a rule based model, specifically the authors present an overview of the one-dimensional hierarchical self-assembly model of DNA tiles. The authors also present the evolution of number of tiles in partial assemblies, the average assembly size and of the number of partial assemblies of sizes 2 through 10 over the total running time. All simulations were run using the NFSim simulator on a preset period of time.

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Control theory is a well-established approach in network science, with applications in bio-medicine and cancer research. We build on recent results for structural controllability of directed networks, which identifies a set of driver nodes able to control an a-priori defined part of the network. We develop a novel and efficient approach for the (targeted) structural controllability of cancer networks and demonstrate it for the analysis of breast, pancreatic, and ovarian cancer. We build in each case a protein-protein interaction network and focus on the survivability-essential proteins specific to each cancer type. We show that these essential proteins are efficiently controllable from a relatively small computable set of driver nodes. Moreover, we adjust the method to find the driver nodes among FDA-approved drug-target nodes. We find that, while many of the drugs acting on the driver nodes are part of known cancer therapies, some of them are not used for the cancer types analyzed here; some drug-target driver nodes identified by our algorithms are not known to be used in any cancer therapy. Overall we show that a better understanding of the control dynamics of cancer through computational modelling can pave the way for new efficient therapeutic approaches and personalized medicine.

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The (abstract) Tile Assembly Model (aTAM), is a mathematical paradigm for the study and algorithmic design of DNA self-assembly systems. It employs the use of so-called DNA tiles, which are abstractions of experimentally achievable DNA nanostructure complexes with similar inter-matching behaviours. To this day, there are about half-dozen different experimental implementations of DNA tiles and their sub-sequent algorithmic assembly into larger complexes, see e.g. Reif et al. (2012) [29]. In order to provide further insight into the assembly process, the aTAM model has been extended to a kinetic counterpart (kTAM). Although there is a wide abundance of different variants of the abstract model, e.g., stage, step, hierarchical, temperature-k, signal-passing, etc. (see e.g. Patitz (2012) [22]), numerical simulations of the kinetic counterpart have been performed only for a few types of these systems. This might be due to the fact that the numerical models and simulations of kTAM were almost exclusively implemented using classical stochastic simulation algorithms frameworks, which are not designed for capturing models with theoretically un-bounded number of species. In this paper we introduce an agent- and rule-based modelling approach for kTAM, and its implementation on NFsim, one of the available platfonris for such type of modelling. We show not only how the modelling of kTAM can be implemented, but we also explore the advantages of this modelling framework for kinetic simulations of kTAM and the easy way such models can be updated and modified. We present numerical comparisons both with classical numerical simulations of kTAM, as well as comparison in between four different kinetic variant of the TAM model, all implemented in NFsim as stand-alone rule-based models. (C) 2017 Elsevier B.V. All rights reserved.

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