Noise resistance in the spindle assembly checkpoint

Abstract

Genetically identical cells vary in the amount of expressed proteins even when growing under the same conditions. It is not yet clear how cellular information processing copes with such stochastic fluctuations in protein levels. Here we examine the capacity of the spindle assembly checkpoint to buffer temporal fluctuations in the expression of Cdc20, a critical checkpoint target whose activity is inhibited to prevent premature cell cycle progression. Using mathematical modeling, we demonstrate that the checkpoint can buffer significant fluctuations in Cdc20 production rate. Critical to this buffering capacity is the use of sequestering-based mechanism for inhibiting Cdc20, as apposed to inhibition by enhancing protein degradation. We propose that the design of biological networks is limited by the need to overcome noise in gene expression.

Figure 1

‘The spindle assembly checkpoint'. (A) A scheme of the checkpoint: as long as even a single kinetochore is not properly attached to the mitotic spindles, anaphase does not commence. The ‘stop-anaphase' signal is generated at the unattached kinetochores. Once all kinetochores are attached, anaphase initiation is rapid. (B) Two models for Cdc20 inhibition: Cdc20 can be inhibited either by enhanced degradation or by sequestering. Cdc20 and the inactive and active complexes are denoted as ‘c', ‘m' and ‘m*' respectively. The models were solved and analyzed with respect to their ability to tightly inhibit Cdc20 (quantified by the ‘amplification' ratio), and to activate rapidly the system once the last kinetochore is attached (reactivation). Both models were found to fulfill the requirements for a broad range of parameters (right most panel). Solid lines represent the borders for a solution where the amplification (ρ) is 100 and the reactivation time (τ) is 200 s. Dashed lines represent an increase or decrease of these restraints by a factor of 2. Parameter used: m_total=10 and k_ass.=k_deg.^on=10 M s⁻¹.

Figure 2

Noise resistance. (A) A typical response to noise: The two models were exposed to the identical noisy input shown, and their dynamics was followed. We note that the sequestering-based model is much more resistant to noise than the degradation-based model. A frequency–response analysis of this system was also performed, which confirmed these results (see Supplementary information). Parameters used: Degradation model: k_prod.=1 M s⁻¹, k_deg.^on=0.1 M s⁻¹ and k_deg.^on=1 s⁻¹. Sequestering model: k_prod.=0.01 M s⁻¹, k_deg.=0.01 s⁻¹, k_ass.∼0.01 M s⁻¹ and k_diss.∼0.1 M s⁻¹. Both models: m_tot.=10, k_m=1 s⁻¹and k_−m=100 s⁻¹. (B) In order to compare the two models, we defined a noise resistance threshold corresponding to the time, ‘t_limit', it takes for either model to reach a fraction of 1−e⁻¹ of the difference between its initial and final value. The larger t_limit, the longer time it takes for the system to reach its final steady-state value. t_limit is thus a measure of how long perturbations the system can handle. In the figure, we see how the critical time varies with the amplification and reactivation time. The fact that the sequestering-based model is able to buffer longer perturbations is clearly seen. Worth noting is also that the vertical location of the sequestering curve depends on the free parameter k_deg., the current value was thus chosen as an example rather than as an absolute value. Parameter used: degradation model — k_prod.=1 M s⁻¹, k_deg.^on=0.1 M s⁻¹ and k_deg.^on=1 s⁻¹; storage model — k_prod.=0.01 M s⁻¹, k_deg.=0.05 s⁻¹ and k_ass.∼0.1 M s⁻¹; both models—m_tot.=10, k_m=1 s⁻¹and k_−m=100 s⁻¹.