Emergent Simplicities in Stochastic Intergenerational Homeostasis

Abstract

We reconceptualize homeostasis from an inherently stochastic, intergenerational perspective. Here we use our SChemostat technology to directly record high-precision multigenerational trains of sizes of statistically identical non-interacting individual cells of Caulobacter crescentus in precisely controlled environmental conditions. We first show that individual cells indeed maintain stochastic intergenerational homeostasis of their characteristic sizes, then extract organizational principles in the form of an intergenerational scaling law and other "emergent simplicities", which facilitate a principled route to dimensional reduction of the problem. We use these emergent simplicities to formulate the precise theoretical framework for stochastic homeostasis, which not only captures the exact kinematics of stochastic intergenerational cell size homeostasis (providing spectacular theory-data matches with no fitting parameters), but also determines the necessary and sufficient condition for stochastic intergenerational homeostasis. Compellingly, our reanalysis of existing data published by other groups using different single-cell technologies demonstrates that this intergenerational framework is applicable to other microorganisms (Escherichia coli and Bacillus subtilis) in a variety of growth conditions. Finally, we establish that in balanced growth conditions stochastic intergenerational cell size homeostasis is achieved through elastic adaptation, thus precluding the possibility that cell size can act as a repository of intergenerational memory.

Intergenerational scaling law determines the precision kinematics of stochastic individual-cell-size homeostasis

“…4) data, taken from [10]. Moreover, compelling data-theory matches were also obtained for the C. crescentus data as detailed in [1]. Thus we have comprehensively validated the framework we propose here.…”

“…These datasets focus on the same ensemble of statistically identical non-interacting cells over the course of tens of generations, imaged in precisely controlled time invariant growth conditions. In [1], we reported direct evidence of stochastic cell size homeostasis using these data, demonstrating that the intergenerational dynamics are Markovian and that stochastic homeostasis follows an intergenerational scaling law for cell size (see Fig. 2).…”

“…This heuristic falls short when the fully stochastic picture is considered. In contrast, in this work we have shown that the necessary and sufficient condition for homeostasis, when considering the data-informed [1] inherently stochastic formulation of the problem, is | a | ≤ 1 /s max , where s max > 1 is the upper limit of the support of the mean-rescaled distribution Π, introduced in Eq. (3).…”

“…In this work we take advantage of recently reported “emergent simplicities” in the stochastic intergenerational size homeostasis of individual cells of Caulobacter crescentus [1]. These datasets were obtained using the SChemostat technology, in which the original “mother” cell is retained after each division, and the newborn “daughter” cell leaves the experimental arena; this facilitates high-precision characterization of all cells being imaged [9, 11].…”

“…What rules ensure intergenerational stochastic homeostasis of individual cell sizes? Valuable clues have emerged from high-precision longterm tracking of individual statistically-identical Caulobacter crescentus cells as reported in [1]: Intergenerational cell size homeostasis is an inherently stochastic phenomenon, follows Markovian or memory-free dynamics, and cells obey an intergenerational scaling law, which governs the stochastic map characterizing generational sequences of characteristic cell sizes. These observed emergent simplicities serve as essential building blocks of the first-principles-based theoretical framework we develop here.…”