Design principles of regulatory networks: searching for the molecular algorithms of the cell

Abstract

A challenge in biology is to understand how complex molecular networks in the cell execute sophisticated regulatory functions. Here we explore the idea that there are common and general principles that link network structures to biological functions, principles that constrain the design solutions that evolution can converge upon for accomplishing a given cellular task. We describe approaches for classifying networks based on abstract architectures and functions, rather than on the specific molecular components of the networks. For any common regulatory task, can we define the space of all possible molecular solutions? Such inverse approaches might ultimately allow the assembly of a design table of core molecular algorithms that could serve as a guide for building synthetic networks and modulating disease networks.

Figure 1. Underlying Design Principles

(A) Mechanical devices often show core design principles intimately linked to their function. For example, chairs, despite many differences in detail and in origin, usually share common features that are linked to the physical requirements of supporting a seated human being. (B) Molecular machines also often shown common features, as illustrated by the common organization of diverse DNA polymerases. (Panel is adapted from Steitz, 1999.) (C) Ways in which complex cellular circuits might be abstracted into simpler core networks. A complex network could potentially be composed of several subnetwork modules, each with a simpler core function. (D) Three interlinked ways to explore the existence of design rules and constraints: physical/biochemical constraints should prescribe the range of possible network solutions to a functional problem; common functional network solutions are expected to be enriched in natural evolutionary examples; synthetic molecular networks should also obey design rules.

Figure 2. Enriched Network Motifs

(A) The most common motifs in the bacterial transcription factor network are positive and negative feedback loops. (B) Feedforward loops (FFL) are a common three-node motif. The top and bottom nodes (X and Z) are linked by both a direct regulatory path and an indirect one (via node Y). There are eight major subclasses of FFLs, characterized by the signs of their regulatory links. Coherent FFLs have indirect and direct links with the same overall sign. Incoherent FFLs have indirect and direct links with the opposite overall signs. (C) A type I coherent feedforward loop with an AND gate terminal node can show the behavior of a persistence detector—it will only respond to a longer pulse of input. (D) Table showing examples of simple functional behaviors and network architectures that are often associated with them (reviewed in Alon, 2007; Sneppen et al., 2010; Tyson and Novák, 2010).

Figure 3. Theoretically Mapping Network Structure Function

(A) Ideal goal of exploring how distinct functions (X and Y) map to regions of possible network space. Two functions might correspond to completely distinct or partially overlapping classes of network architectures. (B) Mapping the complexity of network space for one function. In this case there are two major regions of network space that can show robust performance (fitness) of function X. (C) Adaptation maps to two general network solutions. Adaptation is observed in many sensory systems, and is defined as when the system output responds transiently to a change in input, but then restores itself at the original steady-state output level in order to allow for response to further changes in input. Searching the space of all three-node enzymatic networks (16,000 possible architectures) for robust solutions for adaptation revealed only two major solution classes: negative feedback loop with buffering node (NFBLB) and incoherent feedforward loop with proportioner node (IFFLP). The architectures require specific parameter ranges for links that control the key regulatory node B (Ma et al., 2009).

Figure 4. Using Synthetic Biology to Empirically Map Network Space

(A) Improvements in transcriptional oscillator design. The original repressilator design, a minimal three-ring negative feedback loop made of three repressors, functioned but did not show consistent periods or amplitudes (Elowitz and Leibler, 2000). (B) Many iterative improvements have been made in oscillator design, as exemplified by a two-repressor negative feedback loop coupled with positive and negative self-feedback loops, which yields a robust, tunable oscillator (Stricker et al., 2008). (C and D) Exploration of multicellular patterning using synthetic circuits. Cell-cell communication circuits in bacteria have been used to generate fields of many cells that show developmental-like, static as well as expanding patterns such as ring/stripe formation (Basu et al., 2005; Liu et al., 2011). (E) Probing circuits that can yield intracellular spatial self-organization. Parallel computational and synthetic studies were performed to construct circuits that can robustly generate self-organized cell polarization. The most robust network involves a combination of less functional minimal motifs, and was used to build a circuit that generated artificial phosphoinositide (3,4,5) tris-phosphate (PIP3) poles in yeast (Chau et al., 2012).

Figure 5. Concept of a Design Table for Biological Regulatory Networks

The periodic table abstracts the complex electronic structure of a particular atom and organizes it according to atomic number and valence. These features are in turn the functionally most important features relevant to understanding how the atom forms bonds to generate higher-order chemical structures. Analogously, a hypothetical design table of core regulatory network motifs might encompass and abstract the general/common solutions to core biological functions (which result from the constraints on molecular systems). This organization and classification might prove useful in understanding how evolution or engineering can build higher-order networks that show particular complex behaviors.