Source-linked AI summary
Boolean network model predicts cell cycle sequence of fission yeast
Maria I. Davidich, Stefan Bornholdt
TL;DR
The paper addresses whether Boolean networks can predict cell-cycle dynamics without the biochemical parameters required by differential-equation models. It constructs a fission-yeast model from known regulatory circuitry alone and finds that the biological sequence is reproduced, with G1 as the dominant attractor and the trajectory robust to perturbation.
Problem
Detailed dynamical models of cellular control require biochemical parameters, motivating tests of whether state sequences can be predicted from network structure alone.
Method
The authors construct a discrete Boolean model of the fission-yeast cell-cycle network using binary protein states and known activating or inhibiting circuitry.
Results
The model exactly reproduces the biological cell-cycle expression sequence, while the G1 state attracts 77% of all network states.
Takeaways & Limitations
The biological sequence is robustly implemented in the regulatory network, with G1 as the dominant attractor and perturbations along the trajectory returning to G1 in 90 of 100 cases.
Abstract
from arXiv · showhide
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 sequence of regulatory activity patterns 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.
Introduction
The paper asks whether discrete Boolean network models can generalize across organisms while avoiding the biochemical parameters required by detailed dynamical models. It proposes testing this approach on the fission yeast cell-cycle network.
- Predicting dynamics in complex molecular networks remains a central systems-biology challenge.
- Detailed differential-equation models capture time evolution but require many biochemical parameters that are difficult to obtain.
- For questions about cellular progression, the sequence of control-circuit states may matter more than the exact time course.
- Binary-state discrete dynamical models can simplify molecular-network modeling by targeting state sequences rather than accurate timing.
- The study tests whether Boolean-network construction generalizes by modeling the well-characterized but distinct fission-yeast cell cycle.
- The model is based only on the known biochemical circuitry, omitting kinetic constants and other parameters used in existing models.
The fission yeast cell cycle network
The fission yeast cell cycle is organized into four stages, regulated by a biochemical network centered on the Cdc2/Cdc13 complex. The study compiles this network into an activating and inhibiting interaction graph for simulation.
- The cell division cycle proceeds through G1, S, G2, and M stages.G1 supports growth and commitment, S replicates DNA, G2 is a gap phase, and M separates chromosomes and divides the cell.
- Cdc2/Cdc13 is the major regulatory complex, with Tyr-15 marking its concentration and phosphorylation controlling its activity.The complex is inactive during G2 and becomes active during the G2–M transition.
- The authors compile the key regulators into an interaction graph with activating and inhibiting links.This graph, based on the known network, provides the starting point for the discrete dynamical simulation.
A discrete dynamical model of the cell cycle network
The model represents proteins as binary nodes and updates them in parallel from the signs of their regulatory interactions. It deliberately removes interaction strengths, biochemical timescales, and most parameter values while retaining selected activation rules and biological initial conditions.
- Each protein node receives a binary state indicating whether the protein is present or absent.
- Nodes update synchronously in discrete time according to the net signed input from activating and inhibiting interactions.
- Activating links have aij = 1, inhibiting links have aij = −1, and absent links have aij = 0.
- The simplification removes distinctions in interaction strength, biochemical timescales, kinetic constants, and related parameter values.
- Slp1 requires a highly active Cdc2/Cdc13 complex, creating a barrier to mitotic entry.
- Self-degradation is represented by inhibitory self-links for nodes lacking negative regulation from other nodes.
- Functionally equivalent proteins are merged into single nodes because this does not change the modeled dynamics.
- The simulation starts with all nodes inactive except Start, Ste9, Rum1, and Wee1/Mik1.
Simulation of the fission yeast cell cycle
The model reproduces the biological fission-yeast cell-cycle sequence and returns to G1, while state-space analysis shows a dominant, perturbation-resistant attractor.
- Sequence reproduction: The simulated activation-state sequence exactly matches the biological progression from START through S, G2, and M before returning to G1.The sequence is presented as the temporal evolution of the network’s protein states.
- Attractor structure: 77% of the 1024 possible initial states flow to the fixed point corresponding to biological G1.The G1 state is therefore the network’s dominant attractor.
- State-space analysis: The state-space analysis includes all 1024 network states and their trajectories toward fixed-point attractors, with the biological sequence marked separately.Each state represents one active/inactive configuration of ten proteins.
- Robustness: A single-node state reversal during the biological sequence returns the system to G1 in 90 out of 100 cases.This indicates increased probability of remaining within the biological fixed point’s attractor basin after perturbation.
- Network architecture: The biological network’s largest attractor averages 77% of states, compared with about 38% for matched random networks.The random-network comparison used 1000 networks with the same specified structural features and thresholds.
Comparison with S. cerevisiae
Although the two yeast networks share broad cell-cycle logic, they differ substantially in biochemical circuitry and global dynamics. S. cerevisiae is externally driven and strongly damped, whereas S. pombe is auto-excited with additional damping, yet both have similar attractor structure.
- Circuitry: Closely related genes can have substantially different functions in the two yeasts, producing distinct biochemical control circuitry.For example, Cdc25 is essential for the fission-yeast G2–M transition, whereas its budding-yeast homologue Mih1 is insignificant.
- Global dynamics: Both yeast cell cycles retain surprisingly similar overall dynamics despite considerable differences in signaling-network machinery.
- Global dynamics: S. cerevisiae operates as a strongly damped system driven by external excitation, whereas S. pombe is auto-excited with additional damping.In S. pombe, external signals counteract internal damping and trigger activity spreading through the network.
- Global dynamics: Despite differing network mechanics, both organisms show few attractors and one dominant global attractor corresponding to the stationary G1 state.The dominant attractor contains 86% of initial states in one model and 77% in the other.
- Circuitry: S. cerevisiae relies more on transcriptional regulation, while S. pombe relies mainly on post-translational regulation.
Discussion
The Boolean model reproduces fission-yeast cell-cycle behavior using only network connectivity, omitting kinetic parameters required by the ODE model. Its dominant attractor and robust trajectory support built-in dynamical robustness.
- The Boolean network reproduces the biological sequence of cell-cycle expression patterns solely from the fission-yeast regulatory network’s connectivity graph.The model neglects biochemical kinetic parameters while matching the activation sequence.
- The model has a dominant attractor with a basin attracting most possible states, and its dynamics remain robust against perturbations of the biological expression pattern.
- 47 kinetic constants required by the ODE approach can be omitted while preserving the biological activation pattern.The Boolean model replaces continuous parameter values with interaction signs.
- The model’s immediate reproduction of the biological sequence without parameter tuning supports the hypothesis that the network operates in a parameter-insensitive, dynamically robust way.The authors connect this built-in robustness to possible functional robustness in organisms.