1
|
Soubrier C, Foxall E, Ciandrini L, Dao Duc K. Optimal control of ribosome population for gene expression under periodic nutrient intake. J R Soc Interface 2024; 21:20230652. [PMID: 38442858 PMCID: PMC10914516 DOI: 10.1098/rsif.2023.0652] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2023] [Accepted: 02/05/2024] [Indexed: 03/07/2024] Open
Abstract
Translation of proteins is a fundamental part of gene expression that is mediated by ribosomes. As ribosomes significantly contribute to both cellular mass and energy consumption, achieving efficient management of the ribosome population is also crucial to metabolism and growth. Inspired by biological evidence for nutrient-dependent mechanisms that control both ribosome-active degradation and genesis, we introduce a dynamical model of protein production, that includes the dynamics of resources and control over the ribosome population. Under the hypothesis that active degradation and biogenesis are optimal for maximizing and maintaining protein production, we aim to qualitatively reproduce empirical observations of the ribosome population dynamics. Upon formulating the associated optimization problem, we first analytically study the stability and global behaviour of solutions under constant resource input, and characterize the extent of oscillations and convergence rate to a global equilibrium. We further use these results to simplify and solve the problem under a quasi-static approximation. Using biophysical parameter values, we find that optimal control solutions lead to both control mechanisms and the ribosome population switching between periods of feeding and fasting, suggesting that the intense regulation of ribosome population observed in experiments allows to maximize and maintain protein production. Finally, we find some range for the control values over which such a regime can be observed, depending on the intensity of fasting.
Collapse
Affiliation(s)
- Clément Soubrier
- Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z4
| | - Eric Foxall
- Department of Mathematics, University of British Columbia Okanagan, Kelowna, British Columbia, Canada V1V 1V7
| | - Luca Ciandrini
- Centre de Biochimie Structurale (CBS), INSERM U154, CNRS UMR5048, University of Montpellier, Montpellier, France
- Institut Universitaire de France (IUF), Paris, France
| | - Khanh Dao Duc
- Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z4
| |
Collapse
|
2
|
Bersani A, Davico G, Viceconti M. Modeling Human Suboptimal Control: A Review. J Appl Biomech 2023; 39:294-303. [PMID: 37586711 DOI: 10.1123/jab.2023-0015] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2023] [Revised: 07/03/2023] [Accepted: 07/03/2023] [Indexed: 08/18/2023]
Abstract
This review paper provides an overview of the approaches to model neuromuscular control, focusing on methods to identify nonoptimal control strategies typical of populations with neuromuscular disorders or children. Where possible, the authors tightened the description of the methods to the mechanisms behind the underlying biomechanical and physiological rationale. They start by describing the first and most simplified approach, the reductionist approach, which splits the role of the nervous and musculoskeletal systems. Static optimization and dynamic optimization methods and electromyography-based approaches are summarized to highlight their limitations and understand (the need for) their developments over time. Then, the authors look at the more recent stochastic approach, introduced to explore the space of plausible neural solutions, thus implementing the uncontrolled manifold theory, according to which the central nervous system only controls specific motions and tasks to limit energy consumption while allowing for some degree of adaptability to perturbations. Finally, they explore the literature covering the explicit modeling of the coupling between the nervous system (acting as controller) and the musculoskeletal system (the actuator), which may be employed to overcome the split characterizing the reductionist approach.
Collapse
Affiliation(s)
- Alex Bersani
- Medical Technology Lab, IRCCS Istituto Ortopedico Rizzoli, Bologna,Italy
- Department of Industrial Engineering, Alma Mater Studiorum, University of Bologna, Bologna,Italy
| | - Giorgio Davico
- Medical Technology Lab, IRCCS Istituto Ortopedico Rizzoli, Bologna,Italy
- Department of Industrial Engineering, Alma Mater Studiorum, University of Bologna, Bologna,Italy
| | - Marco Viceconti
- Medical Technology Lab, IRCCS Istituto Ortopedico Rizzoli, Bologna,Italy
- Department of Industrial Engineering, Alma Mater Studiorum, University of Bologna, Bologna,Italy
| |
Collapse
|
3
|
Saldaña F, Steindorf V, Srivastav AK, Stollenwerk N, Aguiar M. Optimal vaccine allocation for the control of sexually transmitted infections. J Math Biol 2023; 86:75. [PMID: 37058156 PMCID: PMC10103681 DOI: 10.1007/s00285-023-01910-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2022] [Revised: 03/10/2023] [Accepted: 03/31/2023] [Indexed: 04/15/2023]
Abstract
The burden of sexually transmitted infections (STIs) poses a challenge due to its large negative impact on sexual and reproductive health worldwide. Besides simple prevention measures and available treatment efforts, prophylactic vaccination is a powerful tool for controlling some viral STIs and their associated diseases. Here, we investigate how prophylactic vaccines are best distributed to prevent and control STIs. We consider sex-specific differences in susceptibility to infection, as well as disease severity outcomes. Different vaccination strategies are compared assuming distinct budget constraints that mimic a scarce vaccine stockpile. Vaccination strategies are obtained as solutions to an optimal control problem subject to a two-sex Kermack-McKendrick-type model, where the control variables are the daily vaccination rates for females and males. One important aspect of our approach relies on conceptualizing a limited but specific vaccine stockpile via an isoperimetric constraint. We solve the optimal control problem via Pontryagin's Maximum Principle and obtain a numerical approximation for the solution using a modified version of the forward-backward sweep method that handles the isoperimetric budget constraint in our formulation. The results suggest that for a limited vaccine supply ([Formula: see text]-[Formula: see text] vaccination coverage), one-sex vaccination, prioritizing females, appears to be more beneficial than the inclusion of both sexes into the vaccination program. Whereas, if the vaccine supply is relatively large (enough to reach at least [Formula: see text] coverage), vaccinating both sexes, with a slightly higher rate for females, is optimal and provides an effective and faster approach to reducing the prevalence of the infection.
Collapse
Affiliation(s)
- Fernando Saldaña
- BCAM- Basque Center for Applied Mathematics, Basque Country, Spain.
| | | | | | - Nico Stollenwerk
- BCAM- Basque Center for Applied Mathematics, Basque Country, Spain
- Dipartimento di Matematica, Universita̧ degli Studi di Trento, Povo, Italy
| | - Maíra Aguiar
- BCAM- Basque Center for Applied Mathematics, Basque Country, Spain
- Dipartimento di Matematica, Universita̧ degli Studi di Trento, Povo, Italy
- Ikerbasque, Basque Foundation for Science, Basque Country, Spain
| |
Collapse
|
4
|
Tottori T, Kobayashi TJ. Forward-Backward Sweep Method for the System of HJB-FP Equations in Memory-Limited Partially Observable Stochastic Control. ENTROPY (BASEL, SWITZERLAND) 2023; 25:e25020208. [PMID: 36832575 PMCID: PMC9955073 DOI: 10.3390/e25020208] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/05/2022] [Revised: 01/09/2023] [Accepted: 01/16/2023] [Indexed: 06/01/2023]
Abstract
Memory-limited partially observable stochastic control (ML-POSC) is the stochastic optimal control problem under incomplete information and memory limitation. To obtain the optimal control function of ML-POSC, a system of the forward Fokker-Planck (FP) equation and the backward Hamilton-Jacobi-Bellman (HJB) equation needs to be solved. In this work, we first show that the system of HJB-FP equations can be interpreted via Pontryagin's minimum principle on the probability density function space. Based on this interpretation, we then propose the forward-backward sweep method (FBSM) for ML-POSC. FBSM is one of the most basic algorithms for Pontryagin's minimum principle, which alternately computes the forward FP equation and the backward HJB equation in ML-POSC. Although the convergence of FBSM is generally not guaranteed in deterministic control and mean-field stochastic control, it is guaranteed in ML-POSC because the coupling of the HJB-FP equations is limited to the optimal control function in ML-POSC.
Collapse
Affiliation(s)
- Takehiro Tottori
- Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8654, Japan
| | - Tetsuya J. Kobayashi
- Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8654, Japan
- Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan
- Department of Electrical Engineering and Information Systems, Graduate School of Engineering, The University of Tokyo, Tokyo 113-8654, Japan
- Universal Biology Institute, The University of Tokyo, Tokyo 113-8654, Japan
| |
Collapse
|
5
|
Mononen T, Kuosmanen T, Cairns J, Mustonen V. Understanding cellular growth strategies via optimal control. J R Soc Interface 2023; 20:20220744. [PMID: 36596459 PMCID: PMC9810423 DOI: 10.1098/rsif.2022.0744] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Abstract
Evolutionary prediction and control are increasingly interesting research topics that are expanding to new areas of application. Unravelling and anticipating successful adaptations to different selection pressures becomes crucial when steering rapidly evolving cancer or microbial populations towards a chosen target. Here we introduce and apply a rich theoretical framework of optimal control to understand adaptive use of traits, which in turn allows eco-evolutionarily informed population control. Using adaptive metabolism and microbial experimental evolution as a case study, we show how demographic stochasticity alone can lead to lag time evolution, which appears as an emergent property in our model. We further show that the cycle length used in serial transfer experiments has practical importance as it may cause unintentional selection for specific growth strategies and lag times. Finally, we show how frequency-dependent selection can be incorporated to the state-dependent optimal control framework allowing the modelling of complex eco-evolutionary dynamics. Our study demonstrates the utility of optimal control theory in elucidating organismal adaptations and the intrinsic decision making of cellular communities with high adaptive potential.
Collapse
Affiliation(s)
- Tommi Mononen
- Department of Computer Science, Organismal and Evolutionary Biology Research Programme, University of Helsinki, Helsinki 00014, Finland
| | - Teemu Kuosmanen
- Department of Computer Science, Organismal and Evolutionary Biology Research Programme, University of Helsinki, Helsinki 00014, Finland
| | - Johannes Cairns
- Department of Computer Science, Organismal and Evolutionary Biology Research Programme, University of Helsinki, Helsinki 00014, Finland
| | - Ville Mustonen
- Department of Computer Science, Organismal and Evolutionary Biology Research Programme, University of Helsinki, Helsinki 00014, Finland,Institute of Biotechnology, University of Helsinki, Helsinki 00014, Finland
| |
Collapse
|
6
|
Zhong A, DeWeese MR. Limited-control optimal protocols arbitrarily far from equilibrium. Phys Rev E 2022; 106:044135. [PMID: 36397571 DOI: 10.1103/physreve.106.044135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2022] [Accepted: 09/16/2022] [Indexed: 06/16/2023]
Abstract
Recent studies have explored finite-time dissipation-minimizing protocols for stochastic thermodynamic systems driven arbitrarily far from equilibrium, when granted full external control to drive the system. However, in both simulation and experimental contexts, systems often may only be controlled with a limited set of degrees of freedom. Here, going beyond slow- and fast-driving approximations employed in previous studies, we obtain exact finite-time optimal protocols for this limited-control setting. By working with deterministic Fokker-Planck probability density time evolution, we can frame the work-minimizing protocol problem in the standard form of an optimal control theory problem. We demonstrate that finding the exact optimal protocol is equivalent to solving a system of Hamiltonian partial differential equations, which in many cases admit efficiently calculable numerical solutions. Within this framework, we reproduce analytical results for the optimal control of harmonic potentials and numerically devise optimal protocols for two anharmonic examples: varying the stiffness of a quartic potential and linearly biasing a double-well potential. We confirm that these optimal protocols outperform other protocols produced through previous methods, in some cases by a substantial amount. We find that for the linearly biased double-well problem, the mean position under the optimal protocol travels at a near-constant velocity. Surprisingly, for a certain timescale and barrier height regime, the optimal protocol is also nonmonotonic in time.
Collapse
Affiliation(s)
- Adrianne Zhong
- Department of Physics, University of California, Berkeley, Berkeley, California 94720, USA
| | - Michael R DeWeese
- Department of Physics, University of California, Berkeley, Berkeley, California 94720, USA and Redwood Center For Theoretical Neuroscience and Helen Wills Neuroscience Institute, University of California, Berkeley, Berkeley, California 94720, USA
| |
Collapse
|