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Dynamic biological networks model changes in the network topology over time. However, often the topologies of these networks are not available at specific time points. Existing algorithms for studying dynamic networks often ignore this problem and focus only on the time points at which experimental data is available. In this paper, we develop a novel alignment based network construction algorithm, ANCA , that constructs the dynamic networks at the missing time points by exploiting the information from a reference dynamic network. Our experiments on synthetic and real networks demonstrate that ANCA predicts the missing target networks accurately, and scales to large-scale biological networks in practical time. Our analysis of an E. coli protein-protein interaction network shows that ANCA successfully identifies key temporal changes in the biological networks. Our analysis also suggests that by focusing on the topological differences in the network, our method can be used to find important genes and temporal functional changes in the biological networks.

Biological networks provide great potential to understand how cells function. Motifs in biological networks, frequent topological patterns, represent key structures through which biological networks operate. Studying motifs answers important biological questions. Finding motifs in biological networks remains to be a computationally challenging task as the sizes of the motif and the underlying network grow. Several algorithms exist in the literature to solve this problem. This chapter discusses the biological significance of network motifs, motivation behind solving the motif detection problem and the key challenges of this problem. We discuss different formulations of motif detection problem based on several orthogonal perspectives that change the problem definition as well as solution significantly. The first perspective considers the number of input networks involved (i.e., one or more than one networks). The second perspective focuses on the labeling (i.e., labeled or unlabeled) of the nodes and edges of the input network. The third one considers different frequency definitions of counting motif instances (i.e., F1, F2, and F3) in a network. The fourth perspective describes whether the underlying network is directed or undirected. The last one considers motif detection under different types of network models (i.e., deterministic, probabilistic, or dynamic model). As a case study for each formulation, we briefly discuss important existing methods from the literature. Finally, we conclude with future research directions.

Biological networks describe the interactions among molecules. Unlike static biological networks at a single time point, temporal networks capture how the network topology evolves over time in response to external stimuli or internal variations. We say that two temporal networks have co-evolving subnetworks if the topologies of these subnetworks remain similar to each other as the networks evolve over time. Existing methods for identifying co-evolving patterns make the strong and unrealistic assumption that the two network topologies evolve at the same rate. In this paper, we consider the generalized problem, where each network may evolve at different rates and the rates of evolution may change over time. Moreover, the two networks may have network topologies available for different number of time points. Existing methods fail to solve this problem as they rely on the strong prior assumption. We develop an efficient algorithm, Tempo++, for identifying co-evolving subnetworks within two given temporal networks. Unlike existing methods, Tempo++ does not assume that the networks have same and uniform evolutionary rates. We experimentally demonstrate that Tempo++ scales efficiently and accurately on both synthetic and real datasets. Our results on E. coli time resolved response to five different environmental stress conditions demonstrate that Tempo++ identifies genes specific to those conditions that conforms to well-known studies in the literature. Statistical significance of alignments found by Tempo++ outperforms existing strategies. Moreover, Tempo++ correctly identifies co-evolving networks with similar stress response compared to networks with different stress response.

Biological networks provide great potential to understand how cells function. Motifs are topological patterns which are repeated frequently in a specific network. Network motifs are key structures through which biological networks operate. However, counting independent (i.e., non-overlapping) instances of a specific motif remains to be a computationally hard problem. Motif counting problem becomes computationally even harder for biological networks as biological interactions are uncertain events. The main challenge behind this problem is that different embeddings of a given motif in a network can share edges. Such edges can create complex computational dependencies between different instances of the given motif when considering uncertainty of those edges. In this paper, we develop a novel algorithm for counting independent instances of a specific motif topology in probabilistic biological networks. We present a novel mathematical model to capture the dependency between each embedding and all the other embeddings, which it overlaps with. We prove the correctness of this model. We evaluate our model on real and synthetic networks with different probability, and topology models as well as reasonable range of network sizes. Our results demonstrate that our method counts non-overlapping embeddings in practical time for a broad range of networks.

Background Identifying motifs in biological networks is essential in uncovering key functions served by these networks. Finding non-overlapping motif instances is however a computationally challenging task. The fact that biological interactions are uncertain events further complicates the problem, as it makes the existence of an embedding of a given motif an uncertain event as well. Results In this paper, we develop a novel method, ProMotE (Probabilistic Motif Embedding), to count non-overlapping embeddings of a given motif in probabilistic networks. We utilize a polynomial model to capture the uncertainty. We develop three strategies to scale our algorithm to large networks. Conclusions Our experiments demonstrate that our method scales to large networks in practical time with high accuracy where existing methods fail. Moreover, our experiments on cancer and degenerative disease networks show that our method helps in uncovering key functional characteristics of biological networks.

MotivationBiological networks describes the mechanisms which govern cellular functions. Temporal networks show how these networks evolve over time. Studying the temporal progression of network topologies is of utmost importance since it uncovers how a network evolves and how it resists to external stimuli and internal variations. Two temporal networks have co-evolving subnetworks if the topologies of these subnetworks remain similar to each other as the network topology evolves over a period of time. In this paper, we consider the problem of identifying co-evolving pair of temporal networks, which aim to capture the evolution of molecules and their interactions over time. Although this problem shares some characteristics of the well-known network alignment problems, it differs from existing network alignment formulations as it seeks a mapping of the two network topologies that is invariant to temporal evolution of the given networks. This is a computationally challenging problem as it requires capturing not only similar topologies between two networks but also their similar evolution patterns.ResultsWe present an efficient algorithm,Tempo, for solving identifying coevolving subnetworks with two given temporal networks. We formally prove the correctness of our method. We experimentally demonstrate that Tempo scales efficiently with the size of network as well as the number of time points, and generates statistically significant alignments—even when evolution rates of given networks are high. Our results on a human aging dataset demonstrate that Tempo identifies novel genes contributing to the progression of Alzheimer’s, Huntington’s and Type II diabetes, while existing methods fail to do so.AvailabilitySoftware is available online (https://www.cise.ufi.edu/∼relhesha/temporal.zip).Contactrelhesha@ufi.eduSupplementary informationSupplementary data are available atBioinformaticsonline.

Biological networks provide great potential to understand how cells function. Network motifs, frequent topological patterns, are key structures through which biological networks operate. Counting independent (i.e. non-overlapping) copies of a given motif however remains to be a computationally hard problem. Motif counting problem becomes computationally even harder for biological networks as biological interactions are uncertain events. The central challenge behind this problem is that different embeddings of a given motif in a network can share edges. Such edges can create complex computational dependencies between different instances of the given motif. In this paper, we develop a novel algorithm for counting independent copies of a given motif topology in probabilistic biological networks. We propose a novel mathematical model to capture the dependency between each embedding and all the other embeddings, which it overlaps with. We prove the correctness of this model. Our experiments on real and synthetic networks demonstrate that our method counts non-overlapping embeddings in practical time for a broad range of networks with different probability, and topology models as well as reasonable range of network sizes.