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Many carbon‐fixing organisms have evolved CO₂concentrating mechanisms (CCMs) to enhance the delivery of CO₂to RuBisCO, while minimizing reactions with the competitive inhibitor, molecular O₂. These distinct types of CCMs have been extensively studied using genetics, biochemistry, cell imaging, mass spectrometry, and metabolic flux analysis. Highlighted in this paper, the cyanobacterial CCM features a bacterial microcompartment (BMC) called ‘carboxysome’ in which RuBisCO is co‐encapsulated with the enzyme carbonic anhydrase (CA) within a semi‐permeable protein shell. The cyanobacterial CCM is capable of increasing CO₂around RuBisCO, leading to one of the most efficient processes known for fixing ambient CO₂. The carboxysome life cycle is dynamic and creates a unique subcellular environment that promotes activity of the Calvin–Benson (CB) cycle. The carboxysome may function within a larger cellular metabolon, physical association of functionally coupled proteins, to enhance metabolite channelling and carbon flux. In light of CCMs, synthetic biology approaches have been used to improve enzyme complex for CO₂fixations. Research on CCM‐associated metabolons has also inspired biologists to engineer multi‐step pathways by providing anchoring points for enzyme cascades to channel intermediate metabolites towards valuable products.

 

This paper presents an online algorithm for identification of partial differential equations (PDEs) based on the weak-form sparse identification of nonlinear dynamics algorithm (WSINDy). The algorithm is online in a sense that if performs the identification task by processing solution snapshots that arrive sequentially. The core of the method combines a weak-form discretization of candidate PDEs with an online proximal gradient descent approach to the sparse regression problem. In particular, we do not regularize the ℓ0-pseudo-norm, instead finding that directly applying its proximal operator (which corresponds to a hard thresholding) leads to efficient online system identification from noisy data. We demonstrate the success of the method on the Kuramoto-Sivashinsky equation, the nonlinear wave equation with time-varying wavespeed, and the linear wave equation, in one, two, and three spatial dimensions, respectively. In particular, our examples show that the method is capable of identifying and tracking systems with coefficients that vary abruptly in time, and offers a streaming alternative to problems in higher dimensions. 

Interacting particle system (IPS) models have proven to be highly successful for describing the spatial movement of organisms. However, it is challenging to infer the interaction rules directly from data. In the field of equation discovery, the weak-form sparse identification of nonlinear dynamics (WSINDy) methodology has been shown to be computationally efficient for identifying the governing equations of complex systems from noisy data. Motivated by the success of IPS models to describe the spatial movement of organisms, we develop WSINDy for the second-order IPS to learn equations for communities of cells. Our approach learns the directional interaction rules for each individual cell that in aggregate govern the dynamics of a heterogeneous population of migrating cells. To sort a cell according to the active classes present in its model, we also develop a novel ad hoc classification scheme (which accounts for the fact that some cells do not have enough evidence to accurately infer a model). Aggregated models are then constructed hierarchically to simultaneously identify different species of cells present in the population and determine best-fit models for each species. We demonstrate the efficiency and proficiency of the method on several test scenarios, motivated by common cell migration experiments.