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Song YM, Campbell S, Shiau L, Kim JK, Ott W. Noisy Delay Denoises Biochemical Oscillators. PHYSICAL REVIEW LETTERS 2024; 132:078402. [PMID: 38427894 DOI: 10.1103/physrevlett.132.078402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2023] [Accepted: 11/17/2023] [Indexed: 03/03/2024]
Abstract
Genetic oscillations are generated by delayed transcriptional negative feedback loops, wherein repressor proteins inhibit their own synthesis after a temporal production delay. This delay is distributed because it arises from a sequence of noisy processes, including transcription, translocation, translation, and folding. Because the delay determines repression timing and, therefore, oscillation period, it has been commonly believed that delay noise weakens oscillatory dynamics. Here, we demonstrate that noisy delay can surprisingly denoise genetic oscillators. Specifically, moderate delay noise improves the signal-to-noise ratio and sharpens oscillation peaks, all without impacting period and amplitude. We show that this denoising phenomenon occurs in a variety of well-studied genetic oscillators, and we use queueing theory to uncover the universal mechanisms that produce it.
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Affiliation(s)
- Yun Min Song
- Department of Mathematical Sciences, KAIST, Daejeon 34141, Republic of Korea
- Biomedical Mathematics Group, Pioneer Research Center for Mathematical and Computational Sciences, Institute for Basic Science, Daejeon 34126, Republic of Korea
| | - Sean Campbell
- Department of Mathematics, University of Houston, Houston, Texas 77204, USA
| | - LieJune Shiau
- Department of Mathematics and Statistics, University of Houston Clear Lake, Houston, Texas 77058, USA
| | - Jae Kyoung Kim
- Department of Mathematical Sciences, KAIST, Daejeon 34141, Republic of Korea
- Biomedical Mathematics Group, Pioneer Research Center for Mathematical and Computational Sciences, Institute for Basic Science, Daejeon 34126, Republic of Korea
| | - William Ott
- Department of Mathematics, University of Houston, Houston, Texas 77204, USA
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Jo H, Hong H, Hwang HJ, Chang W, Kim JK. Density physics-informed neural networks reveal sources of cell heterogeneity in signal transduction. PATTERNS (NEW YORK, N.Y.) 2024; 5:100899. [PMID: 38370126 PMCID: PMC10873160 DOI: 10.1016/j.patter.2023.100899] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/08/2023] [Revised: 11/05/2023] [Accepted: 11/24/2023] [Indexed: 02/20/2024]
Abstract
The transduction time between signal initiation and final response provides valuable information on the underlying signaling pathway, including its speed and precision. Furthermore, multi-modality in a transduction-time distribution indicates that the response is regulated by multiple pathways with different transduction speeds. Here, we developed a method called density physics-informed neural networks (Density-PINNs) to infer the transduction-time distribution from measurable final stress response time traces. We applied Density-PINNs to single-cell gene expression data from sixteen promoters regulated by unknown pathways in response to antibiotic stresses. We found that promoters with slower signaling initiation and transduction exhibit larger cell-to-cell heterogeneity in response intensity. However, this heterogeneity was greatly reduced when the response was regulated by slow and fast pathways together. This suggests a strategy for identifying effective signaling pathways for consistent cellular responses to disease treatments. Density-PINNs can also be applied to understand other time delay systems, including infectious diseases.
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Affiliation(s)
- Hyeontae Jo
- Biomedical Mathematics Group, Pioneer Research Center for Mathematical and Computational Sciences, Institute for Basic Science, Daejeon 34126, Republic of Korea
| | - Hyukpyo Hong
- Biomedical Mathematics Group, Pioneer Research Center for Mathematical and Computational Sciences, Institute for Basic Science, Daejeon 34126, Republic of Korea
- Department of Mathematical Sciences, KAIST, Daejeon 34141, Republic of Korea
| | - Hyung Ju Hwang
- Department of Mathematics, Pohang University of Science and Technology, Pohang 37673, Republic of Korea
| | - Won Chang
- Division of Statistics and Data Science, University of Cincinnati, Cincinnati, OH 45221, USA
| | - Jae Kyoung Kim
- Biomedical Mathematics Group, Pioneer Research Center for Mathematical and Computational Sciences, Institute for Basic Science, Daejeon 34126, Republic of Korea
- Department of Mathematical Sciences, KAIST, Daejeon 34141, Republic of Korea
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Grima R, Esmenjaud PM. Quantifying and correcting bias in transcriptional parameter inference from single-cell data. Biophys J 2024; 123:4-30. [PMID: 37885177 PMCID: PMC10808030 DOI: 10.1016/j.bpj.2023.10.021] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2023] [Revised: 09/12/2023] [Accepted: 10/19/2023] [Indexed: 10/28/2023] Open
Abstract
The snapshot distribution of mRNA counts per cell can be measured using single-molecule fluorescence in situ hybridization or single-cell RNA sequencing. These distributions are often fit to the steady-state distribution of the two-state telegraph model to estimate the three transcriptional parameters for a gene of interest: mRNA synthesis rate, the switching on rate (the on state being the active transcriptional state), and the switching off rate. This model assumes no extrinsic noise, i.e., parameters do not vary between cells, and thus estimated parameters are to be understood as approximating the average values in a population. The accuracy of this approximation is currently unclear. Here, we develop a theory that explains the size and sign of estimation bias when inferring parameters from single-cell data using the standard telegraph model. We find specific bias signatures depending on the source of extrinsic noise (which parameter is most variable across cells) and the mode of transcriptional activity. If gene expression is not bursty then the population averages of all three parameters are overestimated if extrinsic noise is in the synthesis rate; underestimation occurs if extrinsic noise is in the switching on rate; both underestimation and overestimation can occur if extrinsic noise is in the switching off rate. We find that some estimated parameters tend to infinity as the size of extrinsic noise approaches a critical threshold. In contrast when gene expression is bursty, we find that in all cases the mean burst size (ratio of the synthesis rate to the switching off rate) is overestimated while the mean burst frequency (the switching on rate) is underestimated. We estimate the size of extrinsic noise from the covariance matrix of sequencing data and use this together with our theory to correct published estimates of transcriptional parameters for mammalian genes.
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Affiliation(s)
- Ramon Grima
- School of Biological Sciences, University of Edinburgh, Edinburgh, United Kingdom.
| | - Pierre-Marie Esmenjaud
- Biology Department, Ecole Polytechnique, Institut Polytechnique de Paris, Palaiseau, France
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Hong H, Cortez MJ, Cheng YY, Kim HJ, Choi B, Josić K, Kim JK. Inferring delays in partially observed gene regulation processes. Bioinformatics 2023; 39:btad670. [PMID: 37935426 PMCID: PMC10660296 DOI: 10.1093/bioinformatics/btad670] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2022] [Revised: 10/25/2023] [Accepted: 11/02/2023] [Indexed: 11/09/2023] Open
Abstract
MOTIVATION Cell function is regulated by gene regulatory networks (GRNs) defined by protein-mediated interaction between constituent genes. Despite advances in experimental techniques, we can still measure only a fraction of the processes that govern GRN dynamics. To infer the properties of GRNs using partial observation, unobserved sequential processes can be replaced with distributed time delays, yielding non-Markovian models. Inference methods based on the resulting model suffer from the curse of dimensionality. RESULTS We develop a simulation-based Bayesian MCMC method employing an approximate likelihood for the efficient and accurate inference of GRN parameters when only some of their products are observed. We illustrate our approach using a two-step activation model: an activation signal leads to the accumulation of an unobserved regulatory protein, which triggers the expression of observed fluorescent proteins. With prior information about observed fluorescent protein synthesis, our method successfully infers the dynamics of the unobserved regulatory protein. We can estimate the delay and kinetic parameters characterizing target regulation including transcription, translation, and target searching of an unobserved protein from experimental measurements of the products of its target gene. Our method is scalable and can be used to analyze non-Markovian models with hidden components. AVAILABILITY AND IMPLEMENTATION Our code is implemented in R and is freely available with a simple example data at https://github.com/Mathbiomed/SimMCMC.
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Affiliation(s)
- Hyukpyo Hong
- Department of Mathematical Sciences, KAIST, Daejeon 34141, Korea
- Biomedical Mathematics Group, Pioneer Research Center for Mathematical and Computational Sciences, Institute for Basic Science, Daejeon 34126, Korea
| | - Mark Jayson Cortez
- Institute of Mathematical Sciences and Physics, University of the Philippines Los Baños, Laguna 4031, Philippines
| | - Yu-Yu Cheng
- Department of Biochemistry, University of Wisconsin–Madison, Madison, WI 53706, United States
| | - Hang Joon Kim
- Division of Statistics and Data Science, University of Cincinnati, Cincinnati, OH 45221, United States
| | - Boseung Choi
- Biomedical Mathematics Group, Pioneer Research Center for Mathematical and Computational Sciences, Institute for Basic Science, Daejeon 34126, Korea
- Division of Big Data Science, Korea University Sejong Campus, Sejong 30019, Korea
- College of Public Health, The Ohio State University, Columbus, OH 43210, United States
| | - Krešimir Josić
- Department of Mathematics, University of Houston, Houston, TX 77204, United States
- Department of Biology and Biochemistry, University of Houston, Houston, TX 77204, United States
| | - Jae Kyoung Kim
- Department of Mathematical Sciences, KAIST, Daejeon 34141, Korea
- Biomedical Mathematics Group, Pioneer Research Center for Mathematical and Computational Sciences, Institute for Basic Science, Daejeon 34126, Korea
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Fu X, Zhou X, Gu D, Cao Z, Grima R. DelaySSAToolkit.jl: stochastic simulation of reaction systems with time delays in Julia. Bioinformatics 2022; 38:4243-4245. [PMID: 35799359 DOI: 10.1093/bioinformatics/btac472] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2022] [Revised: 06/02/2022] [Accepted: 07/06/2022] [Indexed: 12/24/2022] Open
Abstract
SUMMARY DelaySSAToolkit.jl is a Julia package for modelling reaction systems with non-Markovian dynamics, specifically those with time delays. These delays implicitly capture multiple intermediate reaction steps and hence serve as an effective model reduction technique for complex systems in biology, chemistry, ecology and genetics. The package implements a variety of exact formulations of the delay stochastic simulation algorithm. AVAILABILITY AND IMPLEMENTATION The source code and documentation of DelaySSAToolkit.jl are available at https://github.com/palmtree2013/DelaySSAToolkit.jl.
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Affiliation(s)
- Xiaoming Fu
- MOE Key Laboratory of Smart Manufacturing in Energy Chemical Process, East China University of Science and Technology, Shanghai, China.,School of Biological Sciences, The University of Edinburgh, Edinburgh, UK
| | - Xinyi Zhou
- MOE Key Laboratory of Smart Manufacturing in Energy Chemical Process, East China University of Science and Technology, Shanghai, China
| | - Dongyang Gu
- MOE Key Laboratory of Smart Manufacturing in Energy Chemical Process, East China University of Science and Technology, Shanghai, China
| | - Zhixing Cao
- MOE Key Laboratory of Smart Manufacturing in Energy Chemical Process, East China University of Science and Technology, Shanghai, China
| | - Ramon Grima
- School of Biological Sciences, The University of Edinburgh, Edinburgh, UK
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Kim DW, Hong H, Kim JK. Systematic inference identifies a major source of heterogeneity in cell signaling dynamics: The rate-limiting step number. SCIENCE ADVANCES 2022; 8:eabl4598. [PMID: 35302852 PMCID: PMC8932658 DOI: 10.1126/sciadv.abl4598] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/14/2021] [Accepted: 01/26/2022] [Indexed: 06/14/2023]
Abstract
Identifying the sources of cell-to-cell variability in signaling dynamics is essential to understand drug response variability and develop effective therapeutics. However, it is challenging because not all signaling intermediate reactions can be experimentally measured simultaneously. This can be overcome by replacing them with a single random time delay, but the resulting process is non-Markovian, making it difficult to infer cell-to-cell heterogeneity in reaction rates and time delays. To address this, we developed an efficient and scalable moment-based Bayesian inference method (MBI) with a user-friendly computational package that infers cell-to-cell heterogeneity in the non-Markovian signaling process. We applied MBI to single-cell expression profiles from promoters responding to antibiotics and discovered a major source of cell-to-cell variability in antibiotic stress response: the number of rate-limiting steps in signaling cascades. This knowledge can help identify effective therapies that destroy all pathogenic or cancer cells, and the approach can be applied to precision medicine.
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Affiliation(s)
- Dae Wook Kim
- Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea
- Biomedical Mathematics Group, Institute for Basic Science, Daejeon 34126, Republic of Korea
| | - Hyukpyo Hong
- Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea
- Biomedical Mathematics Group, Institute for Basic Science, Daejeon 34126, Republic of Korea
| | - Jae Kyoung Kim
- Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea
- Biomedical Mathematics Group, Institute for Basic Science, Daejeon 34126, Republic of Korea
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