Networking the nucleus

Abstract

The nuclei of differentiating cells exhibit several fundamental principles of self-organization. They are composed of many dynamical units connected physically and functionally to each other--a complex network--and the different parts of the system are mutually adapted and produce a characteristic end state. A unique cell-specific signature emerges over time from complex interactions among constituent elements that delineate coordinate gene expression and chromosome topology. Each element itself consists of many interacting components, all dynamical in nature. Self-organizing systems can be simplified while retaining complex information using approaches that examine the relationship between elements, such as spatial relationships and transcriptional information. These relationships can be represented using well-defined networks. We hypothesize that during the process of differentiation, networks within the cell nucleus rewire according to simple rules, from which a higher level of order emerges. Studying the interaction within and among networks provides a useful framework for investigating the complex organization and dynamic function of the nucleus.

Figure 1

Reprogramming: a network view. Network diagrams (A–C) are representations of collective information from chromosomal topology (D) and transcriptome (E) networks, that is the biological network, where nodes are genes or chromosomes. Thus, we define the network in (A) as a nuclear circuit, composed of the networks in (D, E) (rectangular outline). (A) A biological network representing the specific network signature of the MEF, where some genes are connected, and some are not. The connectivity is weighted, that is the strength of the connection depends on the gene pair, shown by edge thickness. For example, connectivity between genes 2 and 5 is weaker than between 2 and 3. MyoD (the red node) is part of the network but in this case has no connection with other genes as it not expressed. (B) Activated MyoD establishes connections with the rest of the genes and initiates rewiring, accompanied by an increase in MyoD binding affinity. (C) The differentiated system has unique network architecture; new edges appear, resulting in a new network. Note that between (B) and (C) other network structures exist but we have only shown a few points during the process. (D, E) (Within-network organization): the MEF network initially exists in a unique pattern before induction of MyoD. After MyoD induction, the chromosomal network begins to rewire, increasing its connectivity and indicating changes in spatial architecture. The transcriptome network lags behind but gradually increases connectivity, and reaches a network state similar to the chromosomal network (higher communication). (F) Schematic representation of the question: is form a precondition for, or does form follow, function? The fibroblast and myoblast differ in nuclear architecture. In both cell types, actively transcribed genes (red circles) will be localized in active regions of chromatin (blue circles) and show a network of physical adjacencies (edges) within other regions of active chromatin. If form follows function, then muscle gene expression will precede or coincide with localization of a gene to an active region and rearrangement of nuclear adjacencies; whereas if function follows form, then repositioning of genes to active regions and rearrangement of nuclear adjacencies will precede gene transcription.

Figure 2

A quantitative view of how spatial arrangement of chromosomes may influence gene expression, and may precede nuclear reprogramming. (A) The blue networks on the left represent chromosomal spatial arrangement over six time points during reprogramming or differentiation, and the yellow networks represent gene expression. (B) Each connection (edge) between nodes within the networks in (A) at the first time point is assigned a value of one, and absence of an edge is assigned a value of zero in the unweighted adjacency matrices shown. This can be easily extended to the weighted case, where an edge can be assigned numerical values according to the strength of the connection. Equations for the computation of algebraic connectivity between adjacency matrices are given and are plotted in (C) for the six time points. In this case, the network organization is initially similar, but the chromosomal network precedes the expression network in organization. After the fifth time point, the two networks, possibly by an iterative communication process, converge on a unique steady state. This concept is also illustrated in Figure 3, where the initial networks at time point 1 exist within steady state 1, and the final networks at time point 6 exist within steady state 2.

Figure 3

Schematic illustration for the mechanics of self-organization and differentiation. Right: a nuclear circuit demonstrating organization during cellular differentiation. Local interactions (gene coregulation) lead to chromosomal associations that emerge cooperatively in cell-specific organization of the nucleus, which in turn feeds back to strengthen the local associations, and the self-organized system fine-tunes over time. Left: the initial state of this system is at the center of steady state 1. A perturbation, such as activation of a specific signaling pathway or shown here as induction of the transcription factor MyoD, may drive the state of the system towards the boundary of the basin of attraction of stable state 1 (locally stable state). A basin of attraction is a set of initial conditions that ultimately lead to behavior that approaches a specific state (the attractor). In other words, the system approaches cell-specific organization. When it transitions to stable state 2 (globally stable state), stability is lost and the system regains its stability only in the new steady state. In the case of MyoD, induction in MEF cells leads to a state transition into the myogenic lineage. The system is considered to be robust if its functions are still intact, regardless of whether it is in stable state 1 or 2. In an extreme case, the system may continue to transition between multiple stable state points to cope with ongoing perturbations.