Cellular Griffiths-like phase

Abstract

Protein compartmentalization in the frame of a liquid-liquid phase separation is a key mechanism to optimize spatiotemporal control of biological systems. Such a compartmentalization process reduces the intrinsic noise in protein concentration due to stochasticity in gene expression. Employing Flory-Huggins solution theory, Avramov/Casalini's model, and the Grüneisen parameter, we unprecedentedly propose a cellular Griffiths-like phase (CGLP), which can impact its functionality and self-organization. The here-proposed CGLP is key ranging from the understanding of primary organisms' evolution to the treatment of diseases. Our findings pave the way for an alternative Biophysics approach to investigate coacervation processes.

Keywords: Cell criticality; Flory-Huggins solution theory; Griffiths phase; Grüneisen parameter; Primary organisms; Protein compartmentalization.

Graphical abstract

Figure 1

a) Schematic representation of the temperature T versus protein concentration ϕ_p phase diagram depicting the single and the two phases regions separated by the binodal line, which is governed by a critical point (orange color). The spinodal line is also depicted (blue line). In the two-phases region, protein droplets emerge within the cell. A cell containing various protein droplets (green circles) embedded in a solvent (blue color) is schematically depicted zoomed in within the two-phases region. The blue and green color gradient background represents the increasing of proteins inside the cell. b) Schematic representation of the T versus U/W∝℘⁻¹ phase diagram of the molecular system κ-(BEDT-TTF)₂Cu₂(CN)₃, where U is the on-site Coulomb repulsion, W the bandwidth, and ℘ pressure, showing the coexistence region between Fermi-liquid F.L. (metal) and Mott insulator. The finite-T critical end point is depicted (orange color). The blue and green background gradient represents the metallic and Mott insulating phases, respectively. In the coexistence region, insulating puddles (green) embedded in a metallic matrix (blue background) with their corresponding volumes, namely, v_M and v_I, are depicted. The interaction parameter δε is indicated. Panel b) is adapted from Ref. .

Figure 2

a) Density plot of the temperature T versus protein concentration ϕ_pversus effective Grüneisen parameter γ depicting both the solvent rich, protein rich, and the two phases region governed by a critical point (orange color). The red dashed line depicts the Ginzburg criteria for the FHS theory considering N = 2000. b) Logarithm of the protein diffusion time τ versus ϕ_p (green solid line) for T = 350 K, where the cellular Griffiths-like and both solvent and protein rich phases are depicted. c) Density plot of T versus ϕ_pversus the coefficient of variation CV² (noise strength). The white solid line is the binodal line. d) Brownian displacement λ_x in the x direction versus time t for T = 350 K . Upon crossing the binodal line and ϕ_p = 0.5, λ_x→ 0. The cyan dotted line represents a typical ${\lambda }_x\propto \sqrt{t}$ behavior. e) Schematic representation of the cellular Griffiths-like phase (CGLP). In the single-phase region, the proteins (green spheres) diffuse in the solvent matrix with a characteristic diffusion time τ₀. As ϕ_p is increased and the vicinity of the binodal line is achieved, there is a phase separation and protein droplets emerge and start to grow, so that k_in > k_out. The diffusion time τ → ∞ and the CGLP is achieved. Also, at ϕ_p = 0.5 the CGLP sets in, where k_in, k_out → 0 and τ → ∞. More details in the main text.