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Abstract Spreading and mixing are complementary processes that promote reaction of two reactive aqueous solutes present in contiguous plumes in groundwater. Spreading reconfigures the plume geometry, elongating the interface between the plumes, while mixing increases the volume of aquifer occupied by each plume, bringing the solute molecules together to react. Since reaction only occurs where the two solute plumes are in contact with each other, local mechanisms that drive flow and transport near the interface between the plumes control the amount of reaction. This work uses local characteristics of the plumes and the flow field near the plume interface to analyze the relative contributions of pore‐scale mixing and mechanical dispersion to instantaneous, irreversible, bimolecular reaction in a homogeneous aquifer with active spreading caused by radial flow from a well. Two solutes are introduced in sequence at the well, creating concentric circular plumes. We allow for incomplete mixing of the solutes in the pore space, by modeling the pore space as a segregated compartment and a mixed compartment with first‐order mass transfer between the two compartments. We develop semi‐analytical expressions for concentrations of the solutes in both compartments. We found that the relative contribution of mechanical dispersion to reaction increases over time and also increases due to increases in the Peclet number, in the relative source concentration of the chasing solute, and in the mass transfer rate from the segregated compartment to the mixed compartment of the pore space.
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Compartmental exchange regulates steady states and stochastic switching of a phosphorylation network
The phosphoregulation of proteins with multiple phosphorylation sites is governed by biochemical reaction networks that can exhibit multistable behavior. However, the behavior of such networks is typically studied in a single reaction volume, while cells are spatially organized into compartments that can exchange proteins. In this work, we use stochastic simulations to study the impact of compartmentalization on a two-site phosphorylation network. We characterize steady states and fluctuation-driven transitions between them as a function of the rate of protein exchange between two compartments. Surprisingly, the average time spent in a state before stochastically switching to another depends nonmonotonically on the protein exchange rate, with the most frequent switching occurring at intermediate exchange rates. At sufficiently small exchange rates, the state of the system and mean switching time are controlled largely by fluctuations in the balance of enzymes in each compartment. This leads to negatively correlated states in the compartments. For large exchange rates, the two compartments behave as a single effective compartment. However, when the compartmental volumes are unequal, the behavior differs from a single compartment with the same total volume. These results demonstrate that exchange of proteins between distinct compartments can regulate the emergent behavior of a common signaling motif.
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- Award ID(s):
- 1753017
- PAR ID:
- 10546236
- Publisher / Repository:
- Cell Press
- Date Published:
- Journal Name:
- Biophysical Journal
- Volume:
- 123
- Issue:
- 5
- ISSN:
- 0006-3495
- Page Range / eLocation ID:
- 598 to 609
- Format(s):
- Medium: X
- 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/10.1016/j.bpj.2024.01.039
