Boolean network model predicts cell cycle sequence of fission yeast

Abstract

A Boolean network model of the cell-cycle regulatory network of fission yeast (Schizosaccharomyces Pombe) is constructed solely on the basis of the known biochemical interaction topology. Simulating the model in the computer faithfully reproduces the known activity sequence of regulatory proteins along the cell cycle of the living cell. Contrary to existing differential equation models, no parameters enter the model except the structure of the regulatory circuitry. The dynamical properties of the model indicate that the biological dynamical sequence is robustly implemented in the regulatory network, with the biological stationary state G1 corresponding to the dominant attractor in state space, and with the biological regulatory sequence being a strongly attractive trajectory. Comparing the fission yeast cell-cycle model to a similar model of the corresponding network in S. cerevisiae, a remarkable difference in circuitry, as well as dynamics is observed. While the latter operates in a strongly damped mode, driven by external excitation, the S. pombe network represents an auto-excited system with external damping.

Figure 1. Network model.

Network model of the fission yeast cell-cycle regulation. Nodes denote threshold functions (1), representing the switching behavior of regulatory proteins. Thresholds for the specific nodes are chosen as described in the text. Arrows represent interactions between proteins as defined in the interaction matrix a_ij of the model (with a_ij = +1 for green/solid arrows and a_ij = −1 for red/dashed arrows).

Figure 2. Network state space.

State space of the 1024 possible network states (green circles) and their dynamical trajectories, all converging towards fixed point attractors. Each circle corresponds to one specific network state with each of the ten proteins being in one specific activation state (active/inactive). The largest attractor tree corresponds to all network states flowing to the G1 fixed point (blue node). Arrows between the network states indicate the direction of the dynamical flow from one network state to its subsequent state. The fission yeast cell-cycle sequence is shown with blue arrows.

Figure 3. Budding yeast model.

Budding yeast cell cycle network model for comparison with our model of fission yeast. This network relies on transcriptional regulation more than the fission yeast network. Note that some homologues corresponding to the latter do not have to be included here. Note also the difference in circuitry.