Theory of Maxima and the Method of Lagrange

The biological fitness of microbes is largely determined by the rate with which they replicate their biomass composition. Mathematical models that maximize this balanced growth rate while accounting for mass conservation, reaction kinetics, and limits on dry mass per volume are inevitably non-linear. Here, we develop a general theory for such models, termed Growth Balance Analysis (GBA), which provides explicit expressions for protein concentrations, fluxes, and growth rates. These variables are functions of the concentrations of cellular components, for which we calculate marginal fitness costs and benefits that are related to metabolic control coefficients. At maximal growth rate, the net benefits of all concentrations are equal. Based solely on physicochemical constraints, GBA unveils fundamental quantitative principles of cellular resource allocation and growth; it accurately predicts the relationship between growth rates and ribosome concentrations in E. coli and yeast and between growth rate and dry mass density in E. coli.

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“…where we used η ρ = −λ ρ /μ, which follows directly from the envelope theorem 65 . With μ > 0, we can divide by μ to obtain the balance equation.…”

Section: Methodsmentioning

confidence: 99%

An analytical theory of balanced cellular growth

2020

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“…Let P * i , (f * , g * ) be the primal and dual optima, respectively. Although they all depend on xi, x, the envelope theorem [25] allows us to conveniently compute the gradient:…”

Section: Efficient Recovery Using Optimal Transport Based Relaxationmentioning

confidence: 99%

Multiview Sensing with Unknown Permutations: an Optimal Transport Approach

Boufounos

Mansour

et al. 2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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In several applications, including imaging of deformable objects while in motion, simultaneous localization and mapping, and unlabeled sensing, we encounter the problem of recovering a signal that is measured subject to unknown permutations. In this paper we take a fresh look at this problem through the lens of optimal transport (OT). In particular, we recognize that in most practical applications the unknown permutations are not arbitrary but some are more likely to occur than others. We exploit this by introducing a regularization function that promotes the more likely permutations in the solution. We show that, even though the general problem is not convex, an appropriate relaxation of the resulting regularized problem allows us to exploit the well-developed machinery of OT and develop a tractable algorithm.

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“…Characteristics of physical systems in equilibrium may change because of variations in temperature, pressure, age, etc. (see Fiacco [5], McCormick [7], Pun [10], Beightler, Phillips, and Wilde [2], Whittle [14], and Bracken and McCormick [3]) while price, income, or technology parameters may induce structural shifts in economic relationships involving, say, consumption or production (see, for instance, Samuelson [11], Takayama [13], Afriat [1], and Silberberg [12]). Also of considerable interest in the context of general nonlinear optimization is a class of programs called "perturbed problems" wherein the capacity levels associated with the structural constraints are treated as parameters in a "perturbed objective function."…”

mentioning

confidence: 99%

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1991

Quart. Appl. Math.

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Theory of Maxima and the Method of Lagrange

Cited by 94 publications

References 4 publications

An analytical theory of balanced cellular growth

An analytical theory of balanced cellular growth

Multiview Sensing with Unknown Permutations: an Optimal Transport Approach

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