Autocatalytic feedback in centrosome growth drives centrosome size inequality.

(A) Schematic showing the dynamics of centrosomes during the cell cycle. In the G1 phase there is a single centrosome with mother (M) and daughter (D) centrioles at the core, surrounded by the pericentriolic material (PCM). The two new centriole pairs with old mother (oM) and new mother (nM) separate into two centrosomes in the G2/M phase after centriole duplication. The spatially separated centrosomes then grow via a process called centrosome maturation(red arrow), prior cell division. (B) Schematic of the autocatalytic growth model for centrosomes, where the assembly rate increases with increasing centrosome size. (C) Autocatalytic growth of centrosomes captures the sigmoidal size dynamics for single and a pair of centrosomes, but unable to ensure size equality of a centrosome pair. See Table 1 for a list of parameter values.

Lack of robust size control in autocatalytic growth.

(A) The relative difference in centrosome size, |δV |/⟨V⟩, as a function of the growth rate constants and , with an initial size difference of 0.1 μm3. The light gray and dashed black lines represent the lines |δV| / ⟨V⟩ = 0.2 and ⟨δV⟩ / ⟨V⟩ = 1.0. (B,C) Size dynamics of a pair centrosomes for (B) weakly cooperative and (C) strongly cooperative growth regimes. (D) Dynamics of centrosome size for a single centrosome and a pair of centrosomes simulated using the non-cooperative growth model. Inset: Schematic of centrosome growth via centriole-localized assembly and disassembly distributed throughout the PCM. The |δV| /⟨V⟩ values in (A) represent average over 1000 ensembles. The values of and are in the units of ×600 μM−1 s−1. See Table 1 for a list of parameter values.

Catalytic growth in a shared enzyme pool leads to robust size control of a centrosome pair.

(A) Schematic of centrosome growth via catalytic activity of an enzyme that is activated by PCM proteins at a rate proportional to PCM size. (B) Reactions describing centrosome growth via catalytic activity of enzyme E. The centrosome (Sn) can activate the enzyme in a state E*, which in turn creates an activated subunit that binds the PCM. (C) Size dynamics of a centrosome pair (blue, red curves) growing via catalytic assembly and the dynamics of the activated enzyme ([E*]) in time (blue curve). (D) The ensemble average of relative absolute size difference |δV|/⟨V⟩ is insensitive to change in relative initial size difference δV0/V0. Inset: Probability distribution of δV for two different values of initial size difference (δV0/V0 = 0.1 and δV0/V0 = 0.4). (E) Centrosome growth curves obtained from the catalytic growth model (lines) fitted to experimental growth curves (points) measured at different stages of C. elegans development. (F) Degree of sigmoidal growth, measured by Hill coefficient α, as a function of the growth rate constant k+ and the total enzyme concentration [E]. (G) Model of shared catalysis considering a constant concentration of inactive enzyme (E) throughout the growth period. Inset: Schematic of the reactions showing the steady state cycle between S1, and Sn. (H) Centrosome pair growth in the presence of unlimited inactive enzyme pool exhibits size equality as well as cooperative growth dynamics. Inset: Dynamics of S1 and concentrations. See Table. 1 for a list of parameter values.

Centrosome size scaling with cell size.

(A) Scaling of centrosome size with cell size obtained from the catalytic growth model (line) fitted to experimental data (points) in C. elegans embryo (8). (B) Centrosome size does not scale with cell size when the assembly rates are much lower compared to disassembly rate (i.e., k*, k+ ≲ k−Vc). (C) Dynamics of the cytoplasmic fraction of subunits (S1 and combined) reveal significantly higher pool depletion in the size scaling regimes. The two curves correspond to the growth curves shown in panels A (blue) and B (black). The dashed lines are theoretical results obtained from the deterministic model. (D) An analytically obtained phase diagram of centrosome size scaling as functions of enzyme-dependent and enzyme-independent assembly rate constants. The color indicates the strength of size scaling (measured by dV/dVc). The dashed gray line indicates the contour dV/dVc = 0.1. Here the slope values are shown in δv units. Insets: Characteristic size scaling behaviours. See Table 1 for a list of parameter values.

Control of centrosome size asymmetry via differential growth.

(A) Schematic illustrating asymmetric size regulation via differential growth in the (top) catalytic growth model and (bottom) autocatalytic growth model. (B,C) Ten representative trajectories showing the dynamics of centrosome size difference (V1 − V2) for (B) catalytic growth model (δk+/k+ = 0.2), and (C) autocatalytic growth model The two centrosomes are initially of the same size. (D) Efficiency growth-rate-dependent control of centrosome size asymmetry (ε = N +/Ntot) as a function of (normalized) initial size difference (δV0/V0) and (normalized) growth rate difference (δk+/k+), in the catalytic growth model. (E) Efficiency of growth-rate-dependent control of centrosome size asymmetry as a function of (normalized) initial size difference (δV0/V0) and (normalized) growth rate difference , in the autocatalytic growth model. See Table 1 for a list of model parameters.

Parameter values

Two component growth model across organisms

Multi-component model for centrosome growth.

(A) Schematic of centrosome growth model driven by two scaffold components a and b, and enzyme E. a can bind the existing PCM independent of b or the enzyme E. The enzyme is activated by a in the scaffold, then released in the cytoplasm as E*. The other scaffold former b binds to PCM in a-dependent manner in an intermediate form bi which can undergo rapid disassembly. The intermediate form bi can get incorporated in the b-scaffold by the active enzyme E* via forming an activated subunit form E*bi. The red arrows indicate the size dependent positive feedback and the green arrow indicates the catalytic activity of the enzyme. (B) Centrosome size (V1, V2) dynamics for growth with localized enzyme. (C) Centrosome size (V1, V2) dynamics for growth with shared enzyme pool (black and red curve) and the pulse-like dynamics of activated enzyme concentration ([E*], blue curve). (D) Radial spread of the two scaffold former components a and b corresponding to the centrosome growth shown in panel-C. See Table 1 for a list of parameter values.