The correlation between cell and nucleus size is explained by an eukaryotic cell growth model

Abstract

In eukaryotes, the cell volume is observed to be strongly correlated with the nuclear volume. The slope of this correlation depends on the cell type, growth condition, and the physical environment of the cell. We develop a computational model of cell growth and proteome increase, incorporating the kinetics of amino acid import, protein/ribosome synthesis and degradation, and active transport of proteins between the cytoplasm and the nucleoplasm. We also include a simple model of ribosome biogenesis and assembly. Results show that the cell volume is tightly correlated with the nuclear volume, and the cytoplasm-nucleoplasm transport rates strongly influence the cell growth rate as well as the cell/nucleus volume ratio (C/N ratio). Ribosome assembly and the ratio of ribosomal proteins to mature ribosomes also influence the cell volume and the cell growth rate. We find that in order to regulate the cell growth rate and the cell/nucleus volume ratio, the cell must optimally control groups of kinetic and transport parameters together, which could explain the quantitative roles of canonical growth pathways. Finally, although not explicitly demonstrated in this work, we point out that it is possible to construct a detailed proteome distribution using our model and RNAseq data, provided that a quantitative cell division mechanism is known.

Fig 1

(a) Nuclear volume vs. cell volume for several cell lines grown on 500Pa polyacrylamide (PAA) substrates coated with collagen I. Each point is a single cell. The nuclear volume is proportional to the cell volume. (b) Slope of nuclear volume vs. cell volume for cell lines from several different types of human tissue. Brain (T98G, U-87), breast (MCF10A0JSB, HTERT-HME1, MDA-MB-231, MCF7, HCC1937a, T-47D), colorectal (SW480, SW620, HT-29, HCT116), lung (NCI-H2087, NL20, NCI-H2126), ovary (SK-OV-3, NIH: OVCAR-3, Coav3), pancreas (Panc-1, HTERT-HPNE, Capan-1), prostate (DU145, 22RV1, LnCaP Clone FG, PC-3, RWPE-1), skin (WM266–4, A375, MeWo, SK-MEL-2). (c) A model of eukaryotic cell growth with mass transport. During cell growth, amino acids are imported into the cytoplasm and assembled into non-ribosomal proteins and ribosomal proteins by mature ribosome particles. The ribosomal proteins are transported into the nucleoplasm to combine with ribosomal RNA to mature into ribosome particles, which are then transported back out to the cytoplasm. Non-ribosomal proteins are also actively transported in and out of the nucleoplasm. Proteins and ribosomes are also actively degraded. These processes can be captured by a simple set of mass flux equations.

Fig 2. The cell volume is proportional to the impermeable macromolecular number (proteins, buffers, and ribosomes) because the concentration of small charged molecules such as amino acids and ATP are likely regulated together with concentration of ions.

For example, amino acids can be imported into the cytoplasm together with Na⁺ in a voltage independent manner, or imported individually in a voltage dependent manner. The transmembrane voltage ϕ_m also depends on ion concentration (Na⁺, K⁺, Cl⁻, etc). Models of cell ionic homeostasis predict that the cell water content is directly proportional to cell macromolecular number.

Fig 3. Model results for cell and nuclear volumes of Saccharomyces cerevisiae (yeast) and HeLa (mammalian) over several cell cycles.

Here the cell divides when the cell volume doubles. (a) The cell volume (V_Cell = V_C + V_N) and nuclear volume (V_N) for a repeatedly dividing cell. (b) The number of cell components (amino acids, proteins, ribosomal proteins and ribosomes) for successive rounds of cell division. (c) The cell volume grows exponentially if amino acid is rich, and ${\overline{t}}_1\propto P_C$. The computed growth trajectory is approximately linear if amino acid is poor and ${\overline{t}}_1$ is a constant. In the quiescent case, the cell volume becomes stationary. (d) In all cases, the C/N ratio (V_Cell/V_N) reaches a constant. In the quiescent case, the cell growth rate is zero, and the C/N ratio is small. (e)-(h) Corresponding results for mammalian cell. Parameters used are listed in Tables 1 and 2.

Fig 4. Effects of synthesis and transport parameters on the cell growth rate and the C/N ratio.

(a)-(c) Effects of amino acid import (t₁), ribosomal protein transport (t₂), ribosome transport (t₃) and non-ribosomal protein transport (t₄ and t₅) on growth rate. Notably, the growth rate is non-monotonically influenced by t₂, and there’s a sharp change in growth rate around t₄ = t₅. (d)-(e) Effects of non-ribosomal and ribosomal protein synthesis (s₁ and s₂) and ribosome synthesis (s₃) on growth rate. There is an optimal s₁/s₂ for the maximum growth rate. (f)-(j) Effects of transport and synthesis on the C/N ratio. protein synthesis coefficients s₁ and s₂ have a non-monotonic influence on C/N ratio. (k)-(t) Corresponding results for mammalian cells. Interestingly, compared to yeast cell case, s₁ and s₂ have different effects on C/N ratio due to different ribosome synthesis coefficient s₃. Realistic values are marked as “X”. All parameters except for the scanned parameters are listed in Table 2.

Fig 5. Effects of protein degradation and ribosome disassembly on cell growth and the C/N ratio.

(a)-(b) effects of degradation on growth rate and C/N ratio. (c)-(d) Non-monotonic influences of disassembly on growth rate in different ribosomal protein synthesis levels. (e)-(h) Corresponding results for mammalian cells. All parameters except scanned parameters are listed in Table 2.

Fig 6

Non-monotonic effects of ribosomal protein to ribosome ratio (RP/R) on growth rate when tuning (a) disassembly coefficient d₃, (b) ribosome synthesis coefficient s₃ and (c) ribosomal protein synthesis coefficient t₂. (d)-(f) Corresponding results for mammalian cells. All parameters are listed in Table 2.

Fig 7

(a)-(f) Gradients of the cell growth rate and the C/N ratio with respect to the normalized model parameters for exponential, linear growth conditions, respectively. For the quiescent case, gradients of the steady state cell volume with respect to parameters are shown. Amino acid and non-ribosomal protein transport (t₁, t₄, t₅) are most important parameters in exponential and linear growth conditions. For the quiescent case, ribosomal protein transport (t₂) and ribosome synthesis (s₃) play most important roles. (g)-(l) Corresponding results for mammalian cell. All parameters are listed in Table 2.

Fig 8. Computed proteome distributions (yeast parameters) in exponential growth and linear growth.

Mammalian cell models show a similar behavior. (a) equal synthesis of P₁ and P₂ without gene regulation. The two proteins are naturally correlated because of growth through cell cycle. (b) unequal synthesis without correlation. (c) one protein enhances the synthesis of the other. (d) one protein suppresses the synthesis of the other. The distribution is not linearly correlated for synthesis enhancement and suppression cases. (e)-(h) Corresponding results for linear growth. All parameters except synthesis parameters are listed in Table 2. In the linear growth case, transport coefficient is set to be: $\overline{t_1}=2850h^{-1}$.