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Efficient allocation of energy resources to key physiological functions allows living organisms to grow and thrive in diverse environments and adapt to a wide range of perturbations. To quantitatively understand how unicellular organisms utilize their energy resources in response to changes in growth environment, we introduce a theory of dynamic energy allocation that describes cellular growth dynamics by partitioning metabolizable energy into key physiological functions: growth, division, cell shape regulation, energy storage and loss through dissipation. By optimizing the energy flux for growth, we develop the equations governing the time evolution of cell morphology and growth rate in diverse environments. The resulting model accurately captures experimentally observed dependencies of bacterial cell size on growth rate, superlinear scaling of metabolic rate with cell size and predicts nutrient-dependent trade-offs between energy expended for growth, division and shape maintenance. By calibrating model parameters with experimental data for the model organismEscherichia coli, our model describes bacterial growth control in dynamic conditions, particularly during nutrient shifts and osmotic shocks. Integrating both the mechanical properties of the cell and underlying biochemical regulation, our model predicts the driving factors behind a wide range of observed morphological and growth phenomena with minimal added complexity.
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Rich Dynamics of a General Producer–Grazer Interaction Model under Shared Multiple Resource Limitations
Organism growth is often determined by multiple resources interdependently. However, growth models based on the Droop cell quota framework have historically been built using threshold formulations, which means they intrinsically involve single-resource limitations. In addition, it is a daunting task to study the global dynamics of these models mathematically, since they employ minimum functions that are non-smooth (not differentiable). To provide an approach to encompass interactions of multiple resources, we propose a multiple-resource limitation growth function based on the Droop cell quota concept and incorporate it into an existing producer–grazer model. The formulation of the producer’s growth rate is based on cell growth process time-tracking, while the grazer’s growth rate is constructed based on optimal limiting nutrient allocation in cell transcription and translation phases. We show that the proposed model captures a wide range of experimental observations, such as the paradox of enrichment, the paradox of energy enrichment, and the paradox of nutrient enrichment. Together, our proposed formulation and the existing threshold formulation provide bounds on the expected growth of an organism. Moreover, the proposed model is mathematically more tractable, since it does not use the minimum functions as in other stoichiometric models.
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- Award ID(s):
- 1930728
- PAR ID:
- 10468216
- Publisher / Repository:
- MDPI
- Date Published:
- Journal Name:
- Applied Sciences
- Edition / Version:
- 1
- Volume:
- 13
- Issue:
- 7
- ISSN:
- 2076-3417
- Page Range / eLocation ID:
- 4150
- Subject(s) / Keyword(s):
- multiple resource limitation Liebig’s law of the minimum colimitation producer–grazer predator–prey dynamics growth law ecological stoichiometry
- Format(s):
- Medium: X Size: 2.6MB Other: pdf
- Size(s):
- 2.6MB
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/app13074150
