Faithful modeling of transient expression and its application to elucidating negative feedback regulation

Abstract

Modeling and analysis of genetic regulatory networks is essential both for better understanding their dynamic behavior and for elucidating and refining open issues. We hereby present a discrete computational model that effectively describes the transient and sequential expression of a network of genes in a representative developmental pathway. Our model system is a transcriptional cascade that includes positive and negative feedback loops directing the initiation and progression through meiosis in budding yeast. The computational model allows qualitative analysis of the transcription of early meiosis-specific genes, specifically, Ime2 and their master activator, Ime1. The simulations demonstrate a robust transcriptional behavior with respect to the initial levels of Ime1 and Ime2. The computational results were verified experimentally by deleting various genes and by changing initial conditions. The model has a strong predictive aspect, and it provides insights into how to distinguish among and reason about alternative hypotheses concerning the mode by which negative regulation through Ime1 and Ime2 is accomplished. Some predictions were validated experimentally, for instance, showing that the decline in the transcription of IME1 depends on Rpd3, which is recruited by Ime1 to its promoter. Finally, this general model promotes the analysis of systems that are devoid of consistent quantitative data, as is often the case, and it can be easily adapted to other developmental pathways.

Fig. 1.

Working hypothesis network describing the relationship between the expression of IME1 and IME2. Names of RNA molecules are in all capitals. In protein names, only the first letter is capitalized. Solid black arrows represent activation, and solid black lines with a knob represent repression. Solid gray lines with a knob reflect degradation. The dotted gray arrows (going from a node to an edge) represent gating by conjunction (AND). The node S represents the signal that induces entry into meiosis, in our case, nitrogen depletion in the presence of acetate as the sole carbon source.

Fig. 2.

The model faithfully describes the meiotic pattern of expression of IME1 and IME2. (A) Simulation of the network presented in Fig. 1 when N = 9. The initial state of IME1 RNA was 1, that of Ume6/Rpd3 was 9, and the rest were 0. (B) Wild-type diploid cells (Y422) were shifted to meiotic conditions (SPM), and RNA was isolated at the indicated hours. The level of IME1 and IME2 RNA was measured by quantitative PCR. Filled squares, IME1 RNA; open squares, Ime1; filled triangles, IME2 RNA; open triangles, Ime2.

Fig. 3.

Rpd3 is recruited by Ime1 to its promoter, serving as a negative regulator. (A) Simulation of the network upon deletion of the outgoing edge from X. The initial state of IME1 RNA was 1, that of Ume6/Rpd3 was 9, and the other nodes were in state 0. (B) Wild-type diploid cells (Y1635-1) and their isogenic rpd3Δ/rpd3Δ cells were shifted to meiotic conditions (SPM), and RNA was isolated at the indicated hours. The level of IME1 and IME2 RNA was measured by quantitative PCR. Filled squares, IME1 wild type; filled triangles, IME2 wild type; open squares, IME1 rpd3Δ (XΔ); open triangles, IME2 rpd3Δ (XΔ). (C and D) Samples for ChIP analysis were taken from cells incubated in SPM for the indicated times or from synthetic dextrose (SD)-grown cells. The PCRs amplified either the IME1 gene (C and D) or the IME2 gene (D). The diploid strains used were Y422 (wild type), Y449 (ime1Δ), and Y1326–1 (ume6Δ), carrying on 2 μ vectors the following chimeric genes: IME2 (YEp1791), RPD3–13xmyc (YEp2546), and pADH1-gal4(dbd)-ime1(id) (YEp2780). Antibodies directed against myc and Gal4(dbd) were used for IP. WCE, whole-cell extract.

Fig. 4.

Karnaugh-like maps. Shown is the functional dependence between initial states and the type of behavior of the trajectory, for four hypothetical networks. (A) Null hypothesis network as illustrated in Fig. 1. (B) Deletion of edge from Ime2 to the edge from Ime1 to X. (C) Addition of negative edge from Ime2 to IME1; Ime2 affects IME1 directly. (D) Addition of a positive edge from Ime2 to X; Ime2 affects X directly. Each cell in the tables represents a specific initial vector. The rows of the tables are indexed by the initial states of IME1 RNA and proteins, respectively, and the columns are indexed by the similar states of IME2. The numbers in the cells state the length of the trajectory of the corresponding initial vector. The cells are marked by different colors representing the following four types of trajectories' behavior (see SI Fig. 6): normal transient expression (green); restrained expression with weak transience (yellow); short trajectories, expression not induced (purple); and IME1 expression is weak but transient, whereas IME2 is not expressed or expressed before Ime1 (turquoise).