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Dynamic resource allocation in eukaryotic Resource Balance Analysis

Saeed Sadeghi Arjmand

TL;DR

The work addresses dynamic resource allocation in eukaryotic cells within the Resource Balance Analysis (RBA) framework by formulating a time-dependent optimal-control problem that accounts for macromolecular turnover and organelle compartmentalization. It shows that turnover preserves the convex, linear structure of RBA, extends RBA to multi-compartment eukaryotic cells, and derives Pontryagin-based conditions that predict bang-bang allocation between metabolic enzymes and translational machinery. The results connect dynamic allocation strategies with classical steady-state RBA, viewing steady-state growth as the envelope of an underlying dynamic optimization, and demonstrate tractability at genome scale via linear programming and convex analysis. This dynamic foundation clarifies how cells might switch allocation regimes during growth and environmental change while preserving the key RBA insights on growth–composition trade-offs. Overall, the paper provides a unified, dynamically grounded framework that links eukaryotic organelle organization, turnover, and resource distribution to growth optimization.

Abstract

Resource Balance Analysis (RBA) is a framework for predicting steady-state cellular growth under resource constraints. However, classical RBA formulations are static and do not capture the dynamic regulation of biosynthetic resources or macromolecular turnover, which is particularly important in eukaryotic cells. In this work, we propose a dynamic extension of eukaryotic RBA based on an optimal control formulation. Cellular growth is modeled as the result of a time-dependent allocation of translational capacity between metabolic enzymes and macromolecular machinery, aimed at maximizing biomass accumulation over a finite time horizon. Using Pontryagin's Maximum Principle, we characterize optimal allocation strategies and show that steady-state RBA solutions arise as limiting regimes of the dynamic problem.

Dynamic resource allocation in eukaryotic Resource Balance Analysis

TL;DR

The work addresses dynamic resource allocation in eukaryotic cells within the Resource Balance Analysis (RBA) framework by formulating a time-dependent optimal-control problem that accounts for macromolecular turnover and organelle compartmentalization. It shows that turnover preserves the convex, linear structure of RBA, extends RBA to multi-compartment eukaryotic cells, and derives Pontryagin-based conditions that predict bang-bang allocation between metabolic enzymes and translational machinery. The results connect dynamic allocation strategies with classical steady-state RBA, viewing steady-state growth as the envelope of an underlying dynamic optimization, and demonstrate tractability at genome scale via linear programming and convex analysis. This dynamic foundation clarifies how cells might switch allocation regimes during growth and environmental change while preserving the key RBA insights on growth–composition trade-offs. Overall, the paper provides a unified, dynamically grounded framework that links eukaryotic organelle organization, turnover, and resource distribution to growth optimization.

Abstract

Resource Balance Analysis (RBA) is a framework for predicting steady-state cellular growth under resource constraints. However, classical RBA formulations are static and do not capture the dynamic regulation of biosynthetic resources or macromolecular turnover, which is particularly important in eukaryotic cells. In this work, we propose a dynamic extension of eukaryotic RBA based on an optimal control formulation. Cellular growth is modeled as the result of a time-dependent allocation of translational capacity between metabolic enzymes and macromolecular machinery, aimed at maximizing biomass accumulation over a finite time horizon. Using Pontryagin's Maximum Principle, we characterize optimal allocation strategies and show that steady-state RBA solutions arise as limiting regimes of the dynamic problem.
Paper Structure (8 sections, 4 theorems, 47 equations, 1 figure)

This paper contains 8 sections, 4 theorems, 47 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Notations
  3. Preliminary results on modeling RBA for prokaryotic cells
  4. RBA for eukaryotic cells
  5. Modeling organelles
  6. Formulation of the RBA problem for eukaryotic cells
  7. Optimal resource allocation
  8. Pontryagin’s Maximum Principle for dynamic resource allocation

Key Result

Proposition 3.3

If the RBA problem $\mathcal{P}_p(\mu)$ is feasible for some $\mu \ge 0$, then $\mathcal{P}_p(\mu')$ is feasible for any $\mu' \in [0,\mu]$.

Figures (1)

  • Figure 4.1: The eukaryotic cell with interaction of two compartments.

Theorems & Definitions (13)

  • Remark 3.1: Degeneracy and non-uniqueness of optimal solutions
  • Remark 3.2
  • Proposition 3.3: Monotonicity of feasibility
  • proof
  • Corollary 3.4: Existence of a maximal growth rate
  • proof
  • Remark 3.5
  • Proposition 3.6: Convexity preservation of RBA under macromolecular turnover
  • proof
  • Proposition 3.7: Existence of a maximal growth rate
  • ...and 3 more