[Paper Review] Cell development obeys maximum Fisher information

B. Roy Frieden, Robert A. Gatenby|arXiv (Cornell University)|Apr 29, 2014

RNA and protein synthesis mechanisms14 references3 citations

TL;DR

This paper proposes that eukaryotic cell development optimizes intracellular messenger protein flux to maximize Fisher information about nuclear pore complex (NPC) position, modeling the cell as a spherical system with a 10 µm cell membrane and 6 µm nuclear membrane. The model predicts optimal protein trafficking pathways, including 1–4 protein pathways, 4 nm EGFR size, and a flux of ~10^16 proteins/m²s, with maximum information transfer enabling life-like non-equilibrium dynamics.

ABSTRACT

Eukaryotic cell development has been optimized by natural selection to obey maximal intracellular flux of messenger proteins. This, in turn, implies maximum Fisher information on angular position about a target nuclear pore complex (NPR). The cell is simply modeled as spherical, with cell membrane (CM) diameter 10 micron and concentric nuclear membrane (NM) diameter 6 micron. The NM contains about 3000 nuclear pore complexes (NPCs). Development requires messenger ligands to travel from the CM-NPC-DNA target binding sites. Ligands acquire negative charge by phosphorylation, passing through the cytoplasm over Newtonian trajectories toward positively charged NPCs (utilizing positive nuclear localization sequences). The CM-NPC channel obeys maximized mean protein flux F and Fisher information I at the NPC, with first-order delta I = 0 and approximate 2nd-order delta I = 0 stability to environmental perturbations. Many of its predictions are confirmed, including the dominance of protein pathways of from 1-4 proteins, a 4nm size for the EGFR protein and the approximate flux value F =10^16 proteins/m2-s. After entering the nucleus, each protein ultimately delivers its ligand information to a DNA target site with maximum probability, i.e. maximum Kullback-Liebler entropy HKL. In a smoothness limit HKL approaches IDNA/2, so that the total CM-NPC-DNA channel obeys maximum Fisher I. Thus maximum information approaches non-equilibrium, one condition for life.

Motivation & Objective

• To investigate whether cell development follows a principle of maximum Fisher information in intracellular protein transport.
• To model the cell as a spherical system with defined membrane diameters and nuclear pore complexes to analyze protein flux and information transfer.
• To determine if maximum Fisher information at the nuclear pore complex (NPC) explains observed protein pathway lengths, sizes, and flux rates.
• To link maximum information transfer to non-equilibrium dynamics, a hallmark of life.

Proposed method

• Model the cell as a spherical system with a 10 µm cell membrane and 6 µm nuclear membrane, containing ~3000 NPCs.
• Apply Fisher information theory to quantify information about angular position of the NPC from messenger protein trajectories.
• Use Newtonian mechanics to model protein motion from cell membrane to NPC, assuming phosphorylation confers negative charge and nuclear localization sequences guide toward positively charged NPCs.
• Optimize for maximum mean protein flux F and maximum Fisher information I at the NPC, with first- and second-order stability (δI = 0).
• Apply the Kullback-Liebler entropy (HKL) to DNA target binding, showing HKL ≈ IDNA/2 in the smoothness limit, implying maximum total information transfer.
• Use variational principles to derive optimal protein pathways and flux values under constraints of environmental perturbations.

Experimental results

Research questions

• RQ1 Does maximum Fisher information in protein trafficking explain observed protein pathway lengths in eukaryotic cells?
• RQ2 Can the size of key signaling proteins like EGFR be predicted from maximum Fisher information constraints?
• RQ3 Is the experimentally observed protein flux of ~10^16 proteins/m²s consistent with maximum information transfer at the NPC?
• RQ4 Does maximum information transfer in the CM-NPC-DNA channel correspond to non-equilibrium dynamics necessary for life?

Key findings

• The model predicts that optimal protein trafficking occurs via pathways of 1 to 4 proteins, consistent with biological observations.
• The estimated size of the EGFR protein is approximately 4 nm, matching experimental measurements.
• The predicted mean protein flux at the NPC is approximately 10^16 proteins/m²s, aligning with empirical data.
• Maximum Fisher information at the NPC is achieved when both first- and second-order variations in information (δI = 0) are minimized, indicating robustness to perturbations.
• The total CM-NPC-DNA channel achieves maximum Fisher information, implying maximum information transfer, which supports non-equilibrium dynamics characteristic of living systems.