We present an approach to project time-series gene expression data on sequential layers of a multilayer network, thus creating a **temporal multilayer network** (tMLN), and implemented it within the Cytoscape app TimeNexus.
**It easily creates, manages and visualizes temporal multilayer networks by combining node and edge tables carrying the information on interacting nodes, as well as the gene expression related to each node over time.**
See the third section below for the definitions.
### How to build multilayer networks
TimeNexus builds a mutilayer network by converting tables into a collection of Cytoscape networks, each network becoming one layer in the multilayer network. The conversion requires 2 types of tables: **a node table** containing attributes for each of the layer-nodes and **an intra-layer edge table** connecting the layer-nodes (Figure 2: 1. data import). Optionally, **an inter-layer edge table** can be provided to define particular connection between layers.
The node table includes the node names (gene names) and whether a layer-node is a query or not. The query attribute is important as it is used by the subnetwork extracting apps to identify the layer-nodes that will contribute to the extracted subnetwork. A node weight can be defined, but it won't be exploited by the PathLinker app.
The intra-layer edge table contains the information to build the edges within each layer, while the inter-layer edge table links each two consecutive layers by defining an edge from one layer-node to its counterpart or another layer-node in the next layer. Other attributes can be defined, such as edge weight or direction.
In general, TimeNexus can build any type of multilayer networks which follow one main constraint: the layers must be ordered, such as the layer N is connected to the layer N+1.
### How to extract multilayer subnetworks
To extract active subnetworks from the temporal multilayer network and enable further explorations, our approach exploits the apps **PathLinker** and **AnatApp**, which manage conventional static networks. PathLinker app must be installed within Cytoscape, while to use AnatApp algorithms, it only requires an internet connection. TimeNexus creates and forwards regular Cytoscape objects in the form of static versions of the temporal multilayer network to these extracting apps in three different ways: either the entire collapsed set of layers, over two consecutive layers at a time, or on single layers at a time.
The user should refer to the document of these apps to set their parameters and adapt the structure of the multilayer network to their needs (e.g.. AnatApp cannot support two edges between a node, while PathLinker can; AnatApp uses both node and edge weights, while PathLinker only uses the edge weights).
### What are temporal multilayer networks
We project temporal gene expression data from a time-series on a multilayer network structure in the Cytoscape app TimeNexus, whereby we assign the expression data from each time point to the layer representing this time point. We refer to this network model as a temporal multilayer network (tMLN). We define the tMLN such as each layer has the same semantics (the same types of nodes and edges) and an identical network structure. We refer to a node on an individual layer as a **layer-node**, as opposed to a node of a single-layer static network. Edges connecting nodes within one layer are termed **intra-layer edges**; those connecting the same entity between two different layers are called **inter-layer edges**. For follow-up analysis of the tMLN, we furthermore need to define **query nodes**: a query is a layer-node that shows significant differential expression in that specific layer and thus, at the associated time-point.
TimeNexus tMLNs are 3D-like objects, if one considers that a simple network has a 2D structure. As Cytoscape cannot manage multilayer networks, TimeNexus "projects" the 3D tMLN onto two 2D simple networks: the **‘Flattened network’** and the **‘Aggregated network’**. These two networks are complementary, but the Flattened network serves for most applications, e.g. visualizing the tMLN and processing it by static-network tools.
Thereby, in Cytoscape, a TimeNexus tMLN is represented by a network collection, which includes the aforementioned networks as well as a static network for each layer, representing the snapshot of gene expression at a given. In the Flattened network, the layer-nodes become independent entities and the intra- and inter-layer edges become indistinguishable. The Aggregated network collapses all layers such as layer-nodes and intra-layer edges are unified in a single node and edge, respectively, and all temporal information is lost.