[Paper Review] Asymptotic Cellular Growth Rate as the Effective Information Utilization Rate

Rami Pugatch, Naama Barkai+1 more|arXiv (Cornell University)|Aug 2, 2013

Gene Regulatory Network Analysis4 citations

TL;DR

This paper introduces a framework that decomposes the asymptotic growth rate (AGR) of cell populations in fluctuating environments into three components: a baseline game-theoretic growth rate, relative information between actual and worst-case environment distributions, and an information utilization rate. The key contribution is quantifying how effectively cells use environmental information for growth, showing that optimal utilization maximizes AGR via channel capacity, while suboptimal strategies incur information dissipation losses.

ABSTRACT

We study the average asymptotic growth rate of cells in randomly fluctuating environments, with multiple viable phenotypes per environment. We show that any information processing strategy has an asymptotic growth rate, which is the sum of: (i) the maximal growth rate at the worst possible distribution of environments, (ii) relative information between the actual distribution of environments to the worst one, and (iii) information utilization rate, which is the information rate of the sensory devices minus the "information dissipation rate", the amount of information not utilized by the cell for growth. In non-stationary environments, we find that the optimal phenotypic switching times equally partition the information dissipation rate between consecutive switching intervals.

Motivation & Objective

• To understand how cells in fluctuating environments can optimally utilize environmental information to maximize long-term growth.
• To quantify the trade-off between information acquisition and its effective use in phenotypic decision-making.
• To derive a decomposition of the asymptotic growth rate (AGR) that isolates the role of information utilization efficiency.
• To identify conditions under which feedback in phenotypic switching becomes detrimental due to temporal correlations.
• To establish optimal switching strategies in non-stationary environments that minimize information dissipation over time intervals.

Proposed method

• Formalizes the AGR as a function of environment distribution, phenotype choice, and sensory information using a Markovian framework.
• Introduces two extreme strategies: a min-max (game-theoretic) baseline (Λ_game) and an optimal information utilization upper bound (Λ_opt).
• Derives a decomposition: Λ = D(p||p*) + U + Λ_game, where D is relative entropy, U is the information utilization rate, and Λ_opt = D(p||p*) + I + Λ_game.
• Uses relative entropy D(p||p*) to quantify the advantage of actual environment distribution over the worst-case distribution.
• Defines the information utilization rate U = I - Σ p^s_j D(p(⋅|S=j) || p′(⋅|S=j)), where I is the channel capacity and the second term is the information dissipation rate.
• Applies optimization under constraints to derive optimal phenotypic switching times in non-stationary environments, showing that equal distribution of information loss across intervals is optimal.

Experimental results

Research questions

• RQ1 How can the asymptotic growth rate of a cell population be decomposed into components related to information use and environmental uncertainty?
• RQ2 What is the maximum possible growth rate gain from using environmental information, and how is it bounded by channel capacity?
• RQ3 How does information dissipation affect growth when cells cannot fully utilize sensory input?
• RQ4 What is the optimal strategy for phenotypic switching in non-stationary environments with limited sensing and response speed?
• RQ5 Under what conditions does feedback in phenotypic switching become detrimental to growth?

Key findings

• The asymptotic growth rate (AGR) is decomposed into three components: a baseline game-theoretic growth rate (Λ_game), relative information D(p||p*) between actual and worst-case environment distributions, and an information utilization rate U.
• The information utilization rate U is bounded by the difference between the channel capacity I and the information dissipation rate, which quantifies unused or misused information.
• In non-stationary environments, optimal phenotypic switching times equally distribute the information dissipation rate across intervals, minimizing cumulative loss.
• The optimal switching strategy corresponds to a time-average of the instantaneous optimal response, ensuring robustness to environmental drift.
• The optimal trajectory in strategy space is a geodesic in a Riemannian metric defined by the Fisher information, indicating a geometric optimality principle.
• Feedback in phenotypic switching can reduce growth if environmental correlations decay faster than the feedback delay, explaining the prevalence of feed-forward networks in cellular systems.