Mechanics of biological networks: from the cell cytoskeleton to connective tissue.

From the cell cytoskeleton to connective tissues, fibrous networks are ubiquitous in metazoan life as the key promoters of mechanical strength, support and integrity. In recent decades, the application of physics to biological systems has made substantial strides in elucidating the striking mechanical phenomena observed in such networks, explaining strain stiffening, power law rheology and cytoskeletal fluidisation - all key to the biological function of individual cells and tissues. In this review we focus on the current progress in the field, with a primer into the basic physics of individual filaments and the networks they form. This is followed by a discussion of biological networks in the context of a broad spread of recent in vitro and in vivo experiments.

GALANT: a Cytoscape plugin for visualizing data as functional landscapes projected onto biological networks

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Discriminating Different Classes of Biological Networks by Analyzing the Graphs Spectra Distribution

The brain's structural and functional systems, protein-protein interaction, and gene networks are examples of biological systems that share some features of complex networks, such as highly connected nodes, modularity, and small-world topology. Recent studies indicate that some pathologies present topological network alterations relative to norms seen in the general population. Therefore, methods to discriminate the processes that generate the different classes of networks (e. g., normal and disease) might be crucial for the diagnosis, prognosis, and treatment of the disease. It is known that several topological properties of a network (graph) can be described by the distribution of the spectrum of its adjacency matrix. Moreover, large networks generated by the same random process have the same spectrum distribution, allowing us to use it as a "fingerprint". Based on this relationship, we introduce and propose the entropy of a graph spectrum to measure the "uncertainty" of a random graph and the Kullback-Leibler and Jensen-Shannon divergences between graph spectra to compare networks. We also introduce general methods for model selection and network model parameter estimation, as well as a statistical procedure to test the nullity of divergence between two classes of complex networks. Finally, we demonstrate the usefulness of the proposed methods by applying them to (1) protein-protein interaction networks of different species and (2) on networks derived from children diagnosed with Attention Deficit Hyperactivity Disorder (ADHD) and typically developing children. We conclude that scale-free networks best describe all the protein-protein interactions. Also, we show that our proposed measures succeeded in the identification of topological changes in the network while other commonly used measures (number of edges, clustering coefficient, average path length) failed.

Comparison of module detection algorithms in protein networks and investigation of the biological meaning of predicted modules

Background
It is generally acknowledged that a functional understanding of a biological system can only be obtained by an understanding of the collective of molecular interactions in form of biological networks. Protein networks are one particular network type of special importance, because proteins form the functional base units of every biological cell. On a mesoscopic level of protein networks, modules are of significant importance because these building blocks may be the next elementary functional level above individual proteins allowing to gain insight into fundamental organizational principles of biological cells.
Results
In this paper, we provide a comparative analysis of five popular and four novel module detection algorithms. We study these module prediction methods for simulated benchmark networks as well as 10 biological protein interaction networks (PINs). A particular focus of our analysis is placed on the biological meaning of the predicted modules by utilizing the Gene Ontology (GO) database as gold standard for the definition of biological processes. Furthermore, we investigate the robustness of the results by perturbing the PINs simulating in this way our incomplete knowledge of protein networks.
Conclusions
Overall, our study reveals that there is a large heterogeneity among the different module prediction algorithms if one zooms-in the biological level of biological processes in the form of GO terms and all methods are severely affected by a slight perturbation of the networks. However, we also find pathways that are enriched in multiple modules, which could provide important information about the hierarchical organization of the system

Programming chemical kinetics: engineering dynamic reaction networks with DNA strand displacement

Over the last century, the silicon revolution has enabled us to build faster, smaller and more sophisticated computers. Today, these computers control phones, cars, satellites, assembly lines, and other electromechanical devices. Just as electrical wiring controls electromechanical devices, living organisms employ "chemical wiring" to make decisions about their environment and control physical processes. Currently, the big difference between these two substrates is that while we have the abstractions, design principles, verification and fabrication techniques in place for programming with silicon, we have no comparable understanding or expertise for programming chemistry.

In this thesis we take a small step towards the goal of learning how to systematically engineer prescribed non-equilibrium dynamical behaviors in chemical systems. We use the formalism of chemical reaction networks (CRNs), combined with mass-action kinetics, as our programming language for specifying dynamical behaviors. Leveraging the tools of nucleic acid nanotechnology (introduced in Chapter 1), we employ synthetic DNA molecules as our molecular architecture and toehold-mediated DNA strand displacement as our reaction primitive.

Abstraction, modular design and systematic fabrication can work only with well-understood and quantitatively characterized tools. Therefore, we embark on a detailed study of the "device physics" of DNA strand displacement (Chapter 2). We present a unified view of strand displacement biophysics and kinetics by studying the process at multiple levels of detail, using an intuitive model of a random walk on a 1-dimensional energy landscape, a secondary structure kinetics model with single base-pair steps, and a coarse-grained molecular model that incorporates three-dimensional geometric and steric effects. Further, we experimentally investigate the thermodynamics of three-way branch migration. Our findings are consistent with previously measured or inferred rates for hybridization, fraying, and branch migration, and provide a biophysical explanation of strand displacement kinetics. Our work paves the way for accurate modeling of strand displacement cascades, which would facilitate the simulation and construction of more complex molecular systems.

In Chapters 3 and 4, we identify and overcome the crucial experimental challenges involved in using our general DNA-based technology for engineering dynamical behaviors in the test tube. In this process, we identify important design rules that inform our choice of molecular motifs and our algorithms for designing and verifying DNA sequences for our molecular implementation. We also develop flexible molecular strategies for "tuning" our reaction rates and stoichiometries in order to compensate for unavoidable non-idealities in the molecular implementation, such as imperfectly synthesized molecules and spurious "leak" pathways that compete with desired pathways.

We successfully implement three distinct autocatalytic reactions, which we then combine into a de novo chemical oscillator. Unlike biological networks, which use sophisticated evolved molecules (like proteins) to realize such behavior, our test tube realization is the first to demonstrate that Watson-Crick base pairing interactions alone suffice for oscillatory dynamics. Since our design pipeline is general and applicable to any CRN, our experimental demonstration of a de novo chemical oscillator could enable the systematic construction of CRNs with other dynamic behaviors.

Algorithms for Self-Healing Networks

Many modern networks are \emph{reconfigurable}, in the sense that the topology of the network can be changed by the nodes in the network. For example, peer-to-peer, wireless and ad-hoc networks are reconfigurable. More generally, many social networks, such as a company's organizational chart; infrastructure networks, such as an airline's transportation network; and biological networks, such as the human brain, are also reconfigurable. Modern reconfigurable networks have a complexity unprecedented in the history of engineering, resembling more a dynamic and evolving living animal rather than a structure of steel designed from a blueprint. Unfortunately, our mathematical and algorithmic tools have not yet developed enough to handle this complexity and fully exploit the flexibility of these networks. We believe that it is no longer possible to build networks that are scalable and never have node failures. Instead, these networks should be able to admit small, and maybe, periodic failures and still recover like skin heals from a cut. This process, where the network can recover itself by maintaining key invariants in response to attack by a powerful adversary is what we call \emph{self-healing}. Here, we present several fast and provably good distributed algorithms for self-healing in reconfigurable dynamic networks. Each of these algorithms have different properties, a different set of gaurantees and limitations. We also discuss future directions and theoretical questions we would like to answer. %in the final dissertation that this document is proposed to lead to.

Inter-plant communication through mycorrhizal networks mediates complex adaptive behaviour in plant communities

Adaptive behaviour of plants, including rapid changes in physiology, gene regulation and defence response, can be altered when linked to neighbouring plants by a mycorrhizal network (MN). Mechanisms underlying the behavioural changes include mycorrhizal fungal colonization by the MN or interplant communication via transfer of nutrients, defence signals or allelochemicals. We focus this review on our new findings in ectomycorrhizal ecosystems, and also review recent advances in arbuscular mycorrhizal systems. We have found that the behavioural changes in ectomycorrhizal plants depend on environmental cues, the identity of the plant neighbour and the characteristics of the MN. The hierarchical integration of this phenomenon with other biological networks at broader scales in forest ecosystems, and the consequences we have observed when it is interrupted, indicate that underground ‘tree talk’ is a foundational process in the complex adaptive nature of forest ecosystems.

Resilience of protein-protein interaction networks as determined by their large-scale topological features

The relationship between the structure and function of biological networks constitutes a fundamental issue in systems biology. Particularly, the structure of protein-protein interaction networks is related to important biological functions. In this work, we investigated how such a resilience is determined by the large scale features of the respective networks. Four species are taken into account, namely yeast Saccharomyces cerevisiae, worm Caenorhabditis elegans, fly Drosophila melanogaster and Homo sapiens. We adopted two entropy-related measurements (degree entropy and dynamic entropy) in order to quantify the overall degree of robustness of these networks. We verified that while they exhibit similar structural variations under random node removal, they differ significantly when subjected to intentional attacks (hub removal). As a matter of fact, more complex species tended to exhibit more robust networks. More specifically, we quantified how six important measurements of the networks topology (namely clustering coefficient, average degree of neighbors, average shortest path length, diameter, assortativity coefficient, and slope of the power law degree distribution) correlated with the two entropy measurements. Our results revealed that the fraction of hubs and the average neighbor degree contribute significantly for the resilience of networks. In addition, the topological analysis of the removed hubs indicated that the presence of alternative paths between the proteins connected to hubs tend to reinforce resilience. The performed analysis helps to understand how resilience is underlain in networks and can be applied to the development of protein network models.

Dynamics of Spatial Game Theory Networks with Novel Modifications

Introduction: Advances in biotechnology have shed light on many biological processes. In biological networks, nodes are used to represent the function of individual entities within a system and have historically been studied in isolation. Network structure adds edges that enable communication between nodes. An emerging fieldis to combine node function and network structure to yield network function. One of the most complex networks known in biology is the neural network within the brain. Modeling neural function will require an understanding of networks, dynamics, andneurophysiology. It is with this work that modeling techniques will be developed to work at this complex intersection. Methods: Spatial game theory was developed by Nowak in the context of modeling evolutionary dynamics, or the way in which species evolve over time. Spatial game theory offers a two dimensional view of analyzingthe state of neighbors and updating based on the surroundings. Our work builds upon this foundation by studying evolutionary game theory networks with respect to neural networks. This novel concept is that neurons may adopt a particular strategy that will allow propagation of information. The strategy may therefore act as the mechanism for gating. Furthermore, the strategy of a neuron, as in a real brain, isimpacted by the strategy of its neighbors. The techniques of spatial game theory already established by Nowak are repeated to explain two basic cases and validate the implementation of code. Two novel modifications are introduced in Chapters 3 and 4 that build on this network and may reflect neural networks. Results: The introduction of two novel modifications, mutation and rewiring, in large parametricstudies resulted in dynamics that had an intermediate amount of nodes firing at any given time. Further, even small mutation rates result in different dynamics more representative of the ideal state hypothesized. Conclusions: In both modificationsto Nowak's model, the results demonstrate the network does not become locked into a particular global state of passing all information or blocking all information. It is hypothesized that normal brain function occurs within this intermediate range and that a number of diseases are the result of moving outside of this range.

Accelerating, hyperaccelerating, and decelerating networks

Many growing networks possess accelerating statistics where the number of links added with each new node is an increasing function of network size so the total number of links increases faster than linearly with network size. In particular, biological networks can display a quadratic growth in regulator number with genome size even while remaining sparsely connected. These features are mutually incompatible in standard treatments of network theory which typically require that every new network node possesses at least one connection. To model sparsely connected networks, we generalize existing approaches and add each new node with a probabilistic number of links to generate either accelerating, hyperaccelerating, or even decelerating network statistics in different regimes. Under preferential attachment for example, slowly accelerating networks display stationary scale-free statistics relatively independent of network size while more rapidly accelerating networks display a transition from scale-free to exponential statistics with network growth. Such transitions explain, for instance, the evolutionary record of single-celled organisms which display strict size and complexity limits.

Neural networks: A principled perspective

Introductory accounts of artificial neural networks often rely for motivation on analogies with models of information processing in biological networks. One limitation of such an approach is that it offers little guidance on how to find optimal algorithms, or how to verify the correct performance of neural network systems. A central goal of this paper is to draw attention to a quite different viewpoint in which neural networks are seen as algorithms for statistical pattern recognition based on a principled, i.e. theoretically well-founded, framework. We illustrate the concept of a principled viewpoint by considering a specific issue concerned with the interpretation of the outputs of a trained network. Finally, we discuss the relevance of such an approach to the issue of the validation and verification of neural network systems.

Neural networks: A principled perspective

Introductory accounts of artificial neural networks often rely for motivation on analogies with models of information processing in biological networks. One limitation of such an approach is that it offers little guidance on how to find optimal algorithms, or how to verify the correct performance of neural network systems. A central goal of this paper is to draw attention to a quite different viewpoint in which neural networks are seen as algorithms for statistical pattern recognition based on a principled, i.e. theoretically well-founded, framework. We illustrate the concept of a principled viewpoint by considering a specific issue concerned with the interpretation of the outputs of a trained network. Finally, we discuss the relevance of such an approach to the issue of the validation and verification of neural network systems.

Probabilistic Inductive Querying Using ProbLog

We study how probabilistic reasoning and inductive querying can be combined within ProbLog, a recent probabilistic extension of Prolog. ProbLog can be regarded as a database system that supports both probabilistic and inductive reasoning through a variety of querying mechanisms. After a short introduction to ProbLog, we provide a survey of the different types of inductive queries that ProbLog supports, and show how it can be applied to the mining of large biological networks.