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Heltberg M, von Borries M, Bendix PM, Oddershede LB, Jensen MH. Temperature Controls Onset and Period of NF- κB Oscillations and can Lead to Chaotic Dynamics. Front Cell Dev Biol 2022; 10:910738. [PMID: 35794861 PMCID: PMC9251302 DOI: 10.3389/fcell.2022.910738] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2022] [Accepted: 05/18/2022] [Indexed: 12/01/2022] Open
Abstract
The transcription factor NF-κB plays a vital role in the control of the immune system, and following stimulation with TNF-α its nuclear concentration shows oscillatory behaviour. How environmental factors, in particular temperature, can control the oscillations and thereby affect gene stimulation is still remains to be resolved question. In this work, we reveal that the period of the oscillations decreases with increasing temperature. We investigate this using a mathematical model, and by applying results from statistical physics, we introduce temperature dependency to all rates, resulting in a remarkable correspondence between model and experiments. Our model predicts how temperature affects downstream protein production and find a crossover, where high affinity genes upregulates at high temperatures. Finally, we show how or that oscillatory temperatures can entrain NF-κB oscillations and lead to chaotic dynamics presenting a simple path to chaotic conditions in cellular biology.
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Affiliation(s)
| | | | | | | | - Mogens H. Jensen
- Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
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On chaotic dynamics in transcription factors and the associated effects in differential gene regulation. Nat Commun 2019; 10:71. [PMID: 30622249 PMCID: PMC6325146 DOI: 10.1038/s41467-018-07932-1] [Citation(s) in RCA: 36] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2018] [Accepted: 11/23/2018] [Indexed: 12/13/2022] Open
Abstract
The control of proteins by a transcription factor with periodically varying concentration exhibits intriguing dynamical behaviour. Even though it is accepted that transcription factors vary their dynamics in response to different situations, insight into how this affects downstream genes is lacking. Here, we investigate how oscillations and chaotic dynamics in the transcription factor NF-κB can affect downstream protein production. We describe how it is possible to control the effective dynamics of the transcription factor by stimulating it with an oscillating ligand. We find that chaotic dynamics modulates gene expression and up-regulates certain families of low-affinity genes, even in the presence of extrinsic and intrinsic noise. Furthermore, this leads to an increase in the production of protein complexes and the efficiency of their assembly. Finally, we show how chaotic dynamics creates a heterogeneous population of cell states, and describe how this can be beneficial in multi-toxic environments. It is becoming clear that the dynamics of transcription factors may be important for gene regulation. Here, the authors study the implications of oscillatory and chaotic dynamics of NF-κB and demonstrate that it allows a degree of control of gene expression and can generate phenotypic heterogeneity.
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Stochastic sensitivity analysis and kernel inference via distributional data. Biophys J 2015; 107:1247-1255. [PMID: 25185560 DOI: 10.1016/j.bpj.2014.07.025] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2014] [Revised: 07/08/2014] [Accepted: 07/15/2014] [Indexed: 12/18/2022] Open
Abstract
Cellular processes are noisy due to the stochastic nature of biochemical reactions. As such, it is impossible to predict the exact quantity of a molecule or other attributes at the single-cell level. However, the distribution of a molecule over a population is often deterministic and is governed by the underlying regulatory networks relevant to the cellular functionality of interest. Recent studies have started to exploit this property to infer network states. To facilitate the analysis of distributional data in a general experimental setting, we introduce a computational framework to efficiently characterize the sensitivity of distributional output to changes in external stimuli. Further, we establish a probability-divergence-based kernel regression model to accurately infer signal level based on distribution measurements. Our methodology is applicable to any biological system subject to stochastic dynamics and can be used to elucidate how population-based information processing may contribute to organism-level functionality. It also lays the foundation for engineering synthetic biological systems that exploit population decoding to more robustly perform various biocomputation tasks, such as disease diagnostics and environmental-pollutant sensing.
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Mélykúti B, Hespanha JP, Khammash M. Equilibrium distributions of simple biochemical reaction systems for time-scale separation in stochastic reaction networks. J R Soc Interface 2015; 11:20140054. [PMID: 24920118 PMCID: PMC4208355 DOI: 10.1098/rsif.2014.0054] [Citation(s) in RCA: 40] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
Abstract
Many biochemical reaction networks are inherently multiscale in time and in the counts of participating molecular species. A standard technique to treat different time scales in the stochastic kinetics framework is averaging or quasi-steady-state analysis: it is assumed that the fast dynamics reaches its equilibrium (stationary) distribution on a time scale where the slowly varying molecular counts are unlikely to have changed. We derive analytic equilibrium distributions for various simple biochemical systems, such as enzymatic reactions and gene regulation models. These can be directly inserted into simulations of the slow time-scale dynamics. They also provide insight into the stimulus–response of these systems. An important model for which we derive the analytic equilibrium distribution is the binding of dimer transcription factors (TFs) that first have to form from monomers. This gene regulation mechanism is compared to the cases of the binding of simple monomer TFs to one gene or to multiple copies of a gene, and to the cases of the cooperative binding of two or multiple TFs to a gene. The results apply equally to ligands binding to enzyme molecules.
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Affiliation(s)
- Bence Mélykúti
- Department of Mathematical Stochastics, University of Freiburg, Eckerstraße 1, 79104 Freiburg, Germany Centre for Biological Systems Analysis (ZBSA), University of Freiburg, Habsburgerstraße 49, 79104 Freiburg, Germany
| | - João P Hespanha
- Electrical and Computer Engineering, University of California, Harold Frank Hall, Santa Barbara, CA 93106-9560, USA
| | - Mustafa Khammash
- Department of Biosystems Science and Engineering, ETH Zürich, Mattenstrasse 26, 4058 Basel, Switzerland
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Iyer-Biswas S, Crooks GE, Scherer NF, Dinner AR. Universality in stochastic exponential growth. PHYSICAL REVIEW LETTERS 2014; 113:028101. [PMID: 25062238 DOI: 10.1103/physrevlett.113.028101] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2013] [Indexed: 06/03/2023]
Abstract
Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.
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Affiliation(s)
- Srividya Iyer-Biswas
- James Franck Institute and Institute for Biophysical Dynamics, University of Chicago, Chicago, Illinois 60637, USA
| | - Gavin E Crooks
- Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Norbert F Scherer
- James Franck Institute and Institute for Biophysical Dynamics, University of Chicago, Chicago, Illinois 60637, USA
| | - Aaron R Dinner
- James Franck Institute and Institute for Biophysical Dynamics, University of Chicago, Chicago, Illinois 60637, USA
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Lin Y, Li Y, Crosson S, Dinner AR, Scherer NF. Phase resetting reveals network dynamics underlying a bacterial cell cycle. PLoS Comput Biol 2012; 8:e1002778. [PMID: 23209388 PMCID: PMC3510036 DOI: 10.1371/journal.pcbi.1002778] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2012] [Accepted: 09/17/2012] [Indexed: 01/08/2023] Open
Abstract
Genomic and proteomic methods yield networks of biological regulatory interactions but do not provide direct insight into how those interactions are organized into functional modules, or how information flows from one module to another. In this work we introduce an approach that provides this complementary information and apply it to the bacterium Caulobacter crescentus, a paradigm for cell-cycle control. Operationally, we use an inducible promoter to express the essential transcriptional regulatory gene ctrA in a periodic, pulsed fashion. This chemical perturbation causes the population of cells to divide synchronously, and we use the resulting advance or delay of the division times of single cells to construct a phase resetting curve. We find that delay is strongly favored over advance. This finding is surprising since it does not follow from the temporal expression profile of CtrA and, in turn, simulations of existing network models. We propose a phenomenological model that suggests that the cell-cycle network comprises two distinct functional modules that oscillate autonomously and couple in a highly asymmetric fashion. These features collectively provide a new mechanism for tight temporal control of the cell cycle in C. crescentus. We discuss how the procedure can serve as the basis for a general approach for probing network dynamics, which we term chemical perturbation spectroscopy (CPS). During the cell cycle, the cell progresses through a series of stages that are associated with various cell cycle events such as replication of genetic materials. Genetic and molecular dissections have revealed that the cell cycle is regulated by a network of interacting molecules that produces oscillatory dynamics. The major cell cycle regulators have been identified previously in different species and the activity of these regulators oscillates. However, the question of how cell cycle regulators coordinate different cell cycle events during the cell cycle remains controversial. Here, we investigate this question in a model bacterial system for cell cycle, Caulobacter crescentus. We perturb the expression of the master cell cycle regulator ctrA in a pulsatile fashion and quantify the response of the cell cycle to such perturbations. The measured response is contradictory to the existing mechanism of Caulobacter cell cycle control, which views the cell cycle progression as a sequential activation/inhibition process. We propose a new model that involves coupling of multiple oscillators and show the quantitative agreement between this new model and our measurements. We expect this procedure to be generalized and applied to a broad range of systems to obtain information that complements that obtained from other methods.
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Affiliation(s)
- Yihan Lin
- Department of Chemistry, University of Chicago, Chicago, Illinois, United States of America
- Institute for Biophysical Dynamics, University of Chicago, Chicago, Illinois, United States of America
| | - Ying Li
- Institute for Biophysical Dynamics, University of Chicago, Chicago, Illinois, United States of America
- Department of Physics, University of Chicago, Chicago, Illinois, United States of America
| | - Sean Crosson
- Department of Biochemistry and Molecular Biology, University of Chicago, Chicago, Illinois, United States of America
| | - Aaron R. Dinner
- Department of Chemistry, University of Chicago, Chicago, Illinois, United States of America
- Institute for Biophysical Dynamics, University of Chicago, Chicago, Illinois, United States of America
- * E-mail: (ARD); (NFS)
| | - Norbert F. Scherer
- Department of Chemistry, University of Chicago, Chicago, Illinois, United States of America
- Institute for Biophysical Dynamics, University of Chicago, Chicago, Illinois, United States of America
- * E-mail: (ARD); (NFS)
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The slow-scale linear noise approximation: an accurate, reduced stochastic description of biochemical networks under timescale separation conditions. BMC SYSTEMS BIOLOGY 2012; 6:39. [PMID: 22583770 PMCID: PMC3532178 DOI: 10.1186/1752-0509-6-39] [Citation(s) in RCA: 101] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/28/2011] [Accepted: 03/13/2012] [Indexed: 11/10/2022]
Abstract
BACKGROUND It is well known that the deterministic dynamics of biochemical reaction networks can be more easily studied if timescale separation conditions are invoked (the quasi-steady-state assumption). In this case the deterministic dynamics of a large network of elementary reactions are well described by the dynamics of a smaller network of effective reactions. Each of the latter represents a group of elementary reactions in the large network and has associated with it an effective macroscopic rate law. A popular method to achieve model reduction in the presence of intrinsic noise consists of using the effective macroscopic rate laws to heuristically deduce effective probabilities for the effective reactions which then enables simulation via the stochastic simulation algorithm (SSA). The validity of this heuristic SSA method is a priori doubtful because the reaction probabilities for the SSA have only been rigorously derived from microscopic physics arguments for elementary reactions. RESULTS We here obtain, by rigorous means and in closed-form, a reduced linear Langevin equation description of the stochastic dynamics of monostable biochemical networks in conditions characterized by small intrinsic noise and timescale separation. The slow-scale linear noise approximation (ssLNA), as the new method is called, is used to calculate the intrinsic noise statistics of enzyme and gene networks. The results agree very well with SSA simulations of the non-reduced network of elementary reactions. In contrast the conventional heuristic SSA is shown to overestimate the size of noise for Michaelis-Menten kinetics, considerably under-estimate the size of noise for Hill-type kinetics and in some cases even miss the prediction of noise-induced oscillations. CONCLUSIONS A new general method, the ssLNA, is derived and shown to correctly describe the statistics of intrinsic noise about the macroscopic concentrations under timescale separation conditions. The ssLNA provides a simple and accurate means of performing stochastic model reduction and hence it is expected to be of widespread utility in studying the dynamics of large noisy reaction networks, as is common in computational and systems biology.
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