Persistence as an optimal hedging strategy

Abstract

<jats:title>Abstract</jats:title><jats:p>Bacteria invest in a slow-growing subpopulation, called <jats:italic>persisters</jats:italic>, to ensure survival in the face of uncertainty. This hedging strategy, which we term <jats:italic>cellular hedging</jats:italic>, is remarkably similar to financial hedging where diversifying an investment portfolio protects against economic uncertainty. We provide a new theoretical foundation for understanding cellular hedging by unifying the study of biological population dynamics and the mathematics of financial risk management. Our approach explicitly incorporates environmental volatility as a stochastic process, and we study the persister strategy that maximises the expected per-capita growth rate by formulating a stochastic optimal control problem. We demonstrate that persistence is only advantageous in the presence of environmental volatility. Analytical and simulation results probe the optimal persister strategy, revealing results that are consistent with experimental observations and suggest new opportunities for experimental investigation. Overall, we provide a new way of conceptualising and modelling cellular decision making by unifying previously disparate theory from mathematical biology and finance.</jats:p>

[Retracted] A Study of the Spatial Effects of Financial Support and Economic Growth under Optimal Control of Nonlinear Generalized Complex Systems

“…At the early stage of the development of generalized systems, the fundamental theory of generalized systems was discussed more systematically, thus marking a new stage of development in the research on the fundamental theory of generalized systems. In the following years, the research work on generalized systems received increased attention from experts and scholars in different fields of control and achieved an impressive and vigorous development [17]. A generalized system is a powerful tool for portraying and describing real systems, and the generalized system model is proposed with a profound background of practical applications and exists in many fields of social production.…”

Identifiability analysis for stochastic differential equation models in systems biology

“…Other external effects, such as seasonal effects, are often incorporated into epidemic models [157,158]. In other systems, extrinsic noise describing, for example, the environment, forms a core part of the process and is described by an SDE independent of the population size [45]. Grey-box models use a diffusion term to characterise uncertain physiological effects [58] that could obscure inference, rather than contain information.…”

“…Stochasticity is fundamental to many processes [2,[39][40][41][42][43][44][45]. For example, diabetic patients rely on the rapid interpretation of highly volatile blood glucose measurements to determine insulin input (figure 1f ) [46,47].…”

“…Stochastic differential equation (SDE) models of the Itô form are widely applied in systems biology to describe stochastic phenomena [50][51][52][53]. SDE models can describe intrinsic noise in, for example, gene expression [2,9,23] or a bio-chemical reaction network [54]; extrinsic noise describing volatility in the environment [45,50,55,56]; and model approximations and unknown effects in so-called grey-box models [57,58]. Explicitly modelling this variability in biological systems can often capture more information about a process than a deterministic model is able to [59][60][61][62].…”

Identifying cell-to-cell variability in internalisation using flow cytometry

“…Single-cell in vitro analysis of internalisation and similar dynamical processes reveals significant cell-to-cell variability in otherwise isogenic cell populations [6][7][8][9][10][11][12]. Such heterogeneity is ubiquitous to biology and essential to life, allowing for robust decision making, development, and adaptation of cell populations to environmental uncertainty [13][14][15][16][17]. From a clinical perspective, heterogeneity in drug uptake and response is considered a leading contributor to treatment inefficiencies and resistance [18,19].…”