Maximum entropy and population heterogeneity in continuous cell cultures

Abstract

Continuous cultures of mammalian cells are complex systems displaying hallmark phenomena of nonlinear dynamics, such as multi-stability, hysteresis, as well as sharp transitions between different metabolic states. In this context mathematical models may suggest control strategies to steer the system towards desired states. Although even clonal populations are known to exhibit cell-to-cell variability, most of the currently studied models assume that the population is homogeneous. To overcome this limitation, we use the maximum entropy principle to model the phenotypic distribution of cells in a chemostat as a function of the dilution rate. We consider the coupling between cell metabolism and extracellular variables describing the state of the bioreactor and take into account the impact of toxic byproduct accumulation on cell viability. We present a formal solution for the stationary state of the chemostat and show how to apply it in two examples. First, a simplified model of cell metabolism where the exact solution is tractable, and then a genome-scale metabolic network of the Chinese hamster ovary (CHO) cell line. Along the way we discuss several consequences of heterogeneity, such as: qualitative changes in the dynamical landscape of the system, increasing concentrations of byproducts that vanish in the homogeneous case, and larger population sizes.

Inferring metabolic fluxes in nutrient-limited continuous cultures: A Maximum Entropy Approach with minimum information

“…However, in the literature, it is not usual to find formulations that do make the explicit distinction between both spaces. 2019). We respect the original form of the constraints over for the observable growth rate, but we also add a similar constraint over the uptake of the limiting nutrient.…”

Dynamic metabolic resource allocation based on the maximum entropy principle

“…Combining a metabolic performance index J red that is linear in the u k with the constraint (7) would result in an optimal control law that allocates the entire fraction of resource exclusively to the EFM with highest return-on-investment [13,14]. Such a control is the socalled FBA or Bang-Bang policy, which for a variety of evolutionary reasons does not appear to be the most robust nor economically efficient resource allocation strategy in the face of environmental fluctuations [7,18,19,20,21,25,26]. This motivates the revised concept [7,11] that regulatory decisions for the control variables u k should be made based on the projected system response over a (short) time interval of length ∆t.…”

“…These behavioural theories are based on using the principle of maximum entropy [24] to formulate an optimality problem, because from an information-theoretic standpoint the distribution that best represents the current state of knowledge is the one with largest entropy. The maximum entropy principle has recently been applied to static metabolic modelling in various scenarios, including: extensions of FBA to include population heterogeneity [25,26], experimental decomposition of fluxes using elementary mode analysis [27,28], and to put forward the suggestion that organisms evolve toward a state of maximum physical entropy [29,30]. Hitherto, there has been no attempt to incorporate the maximum entropy principle into dynamic models of metabolism with resource allocation.…”

Modified Maximum Entropy Method and Estimating the AIF via DCE-MRI Data Analysis

“…Entropy maximization or related concepts has been frequently utilized in the past ten years to analyze large biological datasets in various fields. These fields range from determining macromolecular interactions and structures [ 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 ] to inferring signaling [ 21 , 22 , 23 , 24 , 25 ] and regulatory networks [ 26 , 27 , 28 ] and the coding organization in neural populations [ 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 ] based on DNA sequence analyzes (the detection of specific binding sites, for instance) [ 42 , 43 , 44 , 45 , 46 ]. MEM is a powerful vehicle to reconstruct images based on various datasets.…”