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Zhu Y, Balaji A, Han M, Andronov L, Roy AR, Wei Z, Chen C, Miles L, Cai S, Gu Z, Tse A, Yu BC, Uenaka T, Lin X, Spakowitz AJ, Moerner WE, Qi LS. High-resolution dynamic imaging of chromatin DNA communication using Oligo-LiveFISH. Cell 2025:S0092-8674(25)00350-2. [PMID: 40239646 DOI: 10.1016/j.cell.2025.03.032] [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: 09/05/2024] [Revised: 02/10/2025] [Accepted: 03/17/2025] [Indexed: 04/18/2025]
Abstract
Three-dimensional (3D) genome dynamics are crucial for cellular functions and disease. However, real-time, live-cell DNA visualization remains challenging, as existing methods are often confined to repetitive regions, suffer from low resolution, or require complex genome engineering. Here, we present Oligo-LiveFISH, a high-resolution, reagent-based platform for dynamically tracking non-repetitive genomic loci in diverse cell types, including primary cells. Oligo-LiveFISH utilizes fluorescent guide RNA (gRNA) oligo pools generated by computational design, in vitro transcription, and chemical labeling, delivered as ribonucleoproteins. Utilizing machine learning, we characterized the impact of gRNA design and chromatin features on imaging efficiency. Multi-color Oligo-LiveFISH achieved 20-nm spatial resolution and 50-ms temporal resolution in 3D, capturing real-time enhancer and promoter dynamics. Our measurements and dynamic modeling revealed two distinct modes of chromatin communication, and active transcription slows enhancer-promoter dynamics at endogenous genes like FOS. Oligo-LiveFISH offers a versatile platform for studying 3D genome dynamics and their links to cellular processes and disease.
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Affiliation(s)
- Yanyu Zhu
- Department of Bioengineering, Stanford University, Stanford, CA 94305, USA
| | - Ashwin Balaji
- Department of Chemistry, Stanford University, Stanford, CA 94305, USA; Biophysics PhD Program, Stanford University, Stanford, CA 94305, USA
| | - Mengting Han
- Department of Bioengineering, Stanford University, Stanford, CA 94305, USA
| | - Leonid Andronov
- Department of Chemistry, Stanford University, Stanford, CA 94305, USA
| | - Anish R Roy
- Department of Chemistry, Stanford University, Stanford, CA 94305, USA
| | - Zheng Wei
- Computational Biology Program, Public Health Sciences Division and Translational Data Science IRC, Fred Hutchinson Cancer Center, Seattle, WA 98109, USA
| | - Crystal Chen
- Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA
| | - Leanne Miles
- Department of Bioengineering, Stanford University, Stanford, CA 94305, USA
| | - Sa Cai
- Department of Materials Science and Engineering, Stanford University, Stanford, CA 94305, USA
| | - Zhengxi Gu
- Department of Bioengineering, Stanford University, Stanford, CA 94305, USA
| | - Ariana Tse
- Department of Materials Science and Engineering, Stanford University, Stanford, CA 94305, USA
| | - Betty Chentzu Yu
- Computational Biology Program, Public Health Sciences Division and Translational Data Science IRC, Fred Hutchinson Cancer Center, Seattle, WA 98109, USA
| | - Takeshi Uenaka
- Institute for Stem Cell Biology & Regenerative Medicine and Department of Pathology, Stanford University School of Medicine, Stanford, CA 94305, USA
| | - Xueqiu Lin
- Computational Biology Program, Public Health Sciences Division and Translational Data Science IRC, Fred Hutchinson Cancer Center, Seattle, WA 98109, USA
| | - Andrew J Spakowitz
- Department of Chemistry, Stanford University, Stanford, CA 94305, USA; Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA
| | - W E Moerner
- Department of Chemistry, Stanford University, Stanford, CA 94305, USA; Sarafan ChEM-H, Stanford University, Stanford, CA 94305, USA.
| | - Lei S Qi
- Department of Bioengineering, Stanford University, Stanford, CA 94305, USA; Sarafan ChEM-H, Stanford University, Stanford, CA 94305, USA; Chan Zuckerberg Biohub, San Francisco, CA 94080, USA.
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2
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Cromer L, Tiscareno-Andrade M, Lefranc S, Chambon A, Hurel A, Brogniez M, Guérin J, Le Masson I, Adam G, Charif D, Andrey P, Grelon M. Rapid meiotic prophase chromosome movements in Arabidopsis thaliana are linked to essential reorganization at the nuclear envelope. Nat Commun 2024; 15:5964. [PMID: 39013853 PMCID: PMC11252379 DOI: 10.1038/s41467-024-50169-4] [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: 11/21/2023] [Accepted: 07/02/2024] [Indexed: 07/18/2024] Open
Abstract
Meiotic rapid prophase chromosome movements (RPMs) require connections between the chromosomes and the cytoskeleton, involving SUN (Sad1/UNC-84)-domain-containing proteins at the inner nuclear envelope (NE). RPMs remain significantly understudied in plants, with respect to their importance in the regulation of meiosis. Here, we demonstrate that Arabidopsis thaliana meiotic centromeres undergo rapid (up to 500 nm/s) and uncoordinated movements during the zygotene and pachytene stages. These centromere movements are not affected by altered chromosome organization and recombination but are abolished in the double mutant sun1 sun2. We also document the changes in chromosome dynamics and nucleus organization during the transition from leptotene to zygotene, including telomere attachment to SUN-enriched NE domains, bouquet formation, and nucleolus displacement, all of which were defective in sun1 sun2. These results establish A. thaliana as a model species for studying the functional implications of meiotic RPMs and demonstrate the mechanistic conservation of telomere-led RPMs in plants.
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Affiliation(s)
- Laurence Cromer
- Université Paris-Saclay, INRAE, AgroParisTech, Institute Jean-Pierre Bourgin for Plant Sciences (IJPB), 78000, Versailles, France
| | - Mariana Tiscareno-Andrade
- Université Paris-Saclay, INRAE, AgroParisTech, Institute Jean-Pierre Bourgin for Plant Sciences (IJPB), 78000, Versailles, France
| | - Sandrine Lefranc
- Université Paris-Saclay, INRAE, AgroParisTech, Institute Jean-Pierre Bourgin for Plant Sciences (IJPB), 78000, Versailles, France
| | - Aurélie Chambon
- Université Paris-Saclay, INRAE, AgroParisTech, Institute Jean-Pierre Bourgin for Plant Sciences (IJPB), 78000, Versailles, France
| | - Aurélie Hurel
- Université Paris-Saclay, INRAE, AgroParisTech, Institute Jean-Pierre Bourgin for Plant Sciences (IJPB), 78000, Versailles, France
| | - Manon Brogniez
- Université Paris-Saclay, INRAE, AgroParisTech, Institute Jean-Pierre Bourgin for Plant Sciences (IJPB), 78000, Versailles, France
| | - Julie Guérin
- Université Paris-Saclay, INRAE, AgroParisTech, Institute Jean-Pierre Bourgin for Plant Sciences (IJPB), 78000, Versailles, France
| | - Ivan Le Masson
- Université Paris-Saclay, AgroParisTech, INRAE, UMR Agronomie, 91120, Palaiseau, France
| | - Gabriele Adam
- Université Paris-Saclay, CNRS, INRAE, Institute of Plant Sciences Paris-Saclay (IPS2), 91190, Gif sur Yvette, France
- Université Evry, Institute of Plant Sciences Paris-Saclay (IPS2), 91190, Gif sur Yvette, France
- Université Paris Cité, CNRS, INRAE, Institute of Plant Sciences Paris-Saclay (IPS2), 91190, Gif sur Yvette, France
| | - Delphine Charif
- Université Paris-Saclay, INRAE, AgroParisTech, Institute Jean-Pierre Bourgin for Plant Sciences (IJPB), 78000, Versailles, France
| | - Philippe Andrey
- Université Paris-Saclay, INRAE, AgroParisTech, Institute Jean-Pierre Bourgin for Plant Sciences (IJPB), 78000, Versailles, France
| | - Mathilde Grelon
- Université Paris-Saclay, INRAE, AgroParisTech, Institute Jean-Pierre Bourgin for Plant Sciences (IJPB), 78000, Versailles, France.
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Olaya I, Burgess SM, Rog O. Formation and resolution of meiotic chromosome entanglements and interlocks. J Cell Sci 2024; 137:jcs262004. [PMID: 38985540 PMCID: PMC11267460 DOI: 10.1242/jcs.262004] [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] [Indexed: 07/12/2024] Open
Abstract
Interactions between parental chromosomes during the formation of gametes can lead to entanglements, entrapments and interlocks between unrelated chromosomes. If unresolved, these topological constraints can lead to misregulation of exchanges between chromosomes and to chromosome mis-segregation. Interestingly, these configurations are largely resolved by the time parental chromosomes are aligned during pachytene. In this Review, we highlight the inevitability of topologically complex configurations and discuss possible mechanisms to resolve them. We focus on the dynamic nature of a conserved chromosomal interface - the synaptonemal complex - and the chromosome movements that accompany meiosis as potential mechanisms to resolve topological constraints. We highlight the advantages of the nematode Caenorhabditis elegans for understanding biophysical features of the chromosome axis and synaptonemal complex that could contribute to mechanisms underlying interlock resolution. In addition, we highlight advantages of using the zebrafish, Danio rerio, as a model to understand how entanglements and interlocks are avoided and resolved.
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Affiliation(s)
- Iván Olaya
- Department of Molecular and Cellular Biology, University of California Davis, Davis, CA 95616, USA
- Integrative Genetics and Genomics Graduate Group, University of California Davis, Davis, CA 95616, USA
| | - Sean M. Burgess
- Department of Molecular and Cellular Biology, University of California Davis, Davis, CA 95616, USA
| | - Ofer Rog
- School of Biological Sciences and Center for Cell and Genome Sciences, University of Utah, Salt Lake City, UT 84112, USA
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Marshall WF, Fung JC. Modeling homologous chromosome recognition via nonspecific interactions. Proc Natl Acad Sci U S A 2024; 121:e2317373121. [PMID: 38722810 PMCID: PMC11098084 DOI: 10.1073/pnas.2317373121] [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: 10/06/2023] [Accepted: 03/18/2024] [Indexed: 05/18/2024] Open
Abstract
In many organisms, most notably Drosophila, homologous chromosomes associate in somatic cells, a phenomenon known as somatic pairing, which takes place without double strand breaks or strand invasion, thus requiring some other mechanism for homologs to recognize each other. Several studies have suggested a "specific button" model, in which a series of distinct regions in the genome, known as buttons, can associate with each other, mediated by different proteins that bind to these different regions. Here, we use computational modeling to evaluate an alternative "button barcode" model, in which there is only one type of recognition site or adhesion button, present in many copies in the genome, each of which can associate with any of the others with equal affinity. In this model, buttons are nonuniformly distributed, such that alignment of a chromosome with its correct homolog, compared with a nonhomolog, is energetically favored; since to achieve nonhomologous alignment, chromosomes would be required to mechanically deform in order to bring their buttons into mutual register. By simulating randomly generated nonuniform button distributions, many highly effective button barcodes can be easily found, some of which achieve virtually perfect pairing fidelity. This model is consistent with existing literature on the effect of translocations of different sizes on homolog pairing. We conclude that a button barcode model can attain highly specific homolog recognition, comparable to that seen in actual cells undergoing somatic homolog pairing, without the need for specific interactions. This model may have implications for how meiotic pairing is achieved.
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Affiliation(s)
- Wallace F. Marshall
- Department of Biochemistry and Biophysics, University of California, San Francisco, CA94158
| | - Jennifer C. Fung
- Department of Obstetrics, Gynecology and Reproductive Sciences, University of California, San Francisco, CA94158
- Center for Reproductive Sciences, University of California, San Francisco, CA94158
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5
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Chriss A, Börner GV, Ryan SD. Agent-based modeling of nuclear chromosome ensembles identifies determinants of homolog pairing during meiosis. PLoS Comput Biol 2024; 20:e1011416. [PMID: 38739641 PMCID: PMC11115365 DOI: 10.1371/journal.pcbi.1011416] [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: 08/08/2023] [Revised: 05/23/2024] [Accepted: 04/10/2024] [Indexed: 05/16/2024] Open
Abstract
During meiosis, pairing of homologous chromosomes (homologs) ensures the formation of haploid gametes from diploid precursor cells, a prerequisite for sexual reproduction. Pairing during meiotic prophase I facilitates crossover recombination and homolog segregation during the ensuing reductional cell division. Mechanisms that ensure stable homolog alignment in the presence of an excess of non-homologous chromosomes have remained elusive, but rapid chromosome movements appear to play a role in the process. Apart from homolog attraction, provided by early intermediates of homologous recombination, dissociation of non-homologous associations also appears to contribute to homolog pairing, as suggested by the detection of stable non-homologous chromosome associations in pairing-defective mutants. Here, we have developed an agent-based model for homolog pairing derived from the dynamics of a naturally occurring chromosome ensemble. The model simulates unidirectional chromosome movements, as well as collision dynamics determined by attractive and repulsive forces arising from close-range physical interactions. Chromosome number and size as well as movement velocity and repulsive forces are identified as key factors in the kinetics and efficiency of homologous pairing in addition to homolog attraction. Dissociation of interactions between non-homologous chromosomes may contribute to pairing by crowding homologs into a limited nuclear area thus creating preconditions for close-range homolog attraction. Incorporating natural chromosome lengths, the model accurately recapitulates efficiency and kinetics of homolog pairing observed for wild-type and mutant meiosis in budding yeast, and can be adapted to nuclear dimensions and chromosome sets of other organisms.
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Affiliation(s)
- Ariana Chriss
- Department of Mathematics and Statistics, Cleveland State University, Cleveland, Ohio, United States of America
- Department of Biological, Geological, and Environmental Sciences, Cleveland State University, Cleveland, Ohio, United States of America
| | - G. Valentin Börner
- Department of Biological, Geological, and Environmental Sciences, Cleveland State University, Cleveland, Ohio, United States of America
- Center for Gene Regulation in Health and Disease, Cleveland State University, Cleveland, Ohio, United States of America
| | - Shawn D. Ryan
- Department of Mathematics and Statistics, Cleveland State University, Cleveland, Ohio, United States of America
- Center for Applied Data Analysis and Modeling, Cleveland State University, Cleveland, Ohio, United States of America
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6
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Chriss A, Börner GV, Ryan SD. Agent-based modeling of nuclear chromosome ensemble identifies determinants of homolog pairing during meiosis. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2023.08.09.552574. [PMID: 38260664 PMCID: PMC10802385 DOI: 10.1101/2023.08.09.552574] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/24/2024]
Abstract
During meiosis, pairing of homologous chromosomes (homologs) ensures the formation of haploid gametes from diploid precursor cells, a prerequisite for sexual reproduction. Pairing during meiotic prophase I facilitates crossover recombination and homolog segregation during the ensuing reductional cell division. Mechanisms that ensure stable homolog alignment in the presence of an excess of non-homologous chromosomes have remained elusive, but rapid chromosome movements during prophase I appear to play a role in the process. Apart from homolog attraction, provided by early intermediates of homologous recombination, dissociation of non-homologous associations also appears to contribute to homolog pairing, as suggested by the detection of stable non-homologous chromosome associations in pairing-defective mutants. Here, we have developed an agent-based model for homolog pairing derived from the dynamics of a naturally occurring chromosome ensemble. The model simulates unidirectional chromosome movements, as well as collision dynamics determined by attractive and repulsive forces arising from close-range physical interactions. In addition to homolog attraction, chromosome number and size as well as movement velocity and repulsive forces are identified as key factors in the kinetics and efficiency of homologous pairing. Dissociation of interactions between non-homologous chromosomes may contribute to pairing by crowding homologs into a limited nuclear area thus creating preconditions for close-range homolog attraction. Predictions from the model are readily compared to experimental data from budding yeast, parameters can be adjusted to other cellular systems and predictions from the model can be tested via experimental manipulation of the relevant chromosomal features.
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Affiliation(s)
- Ariana Chriss
- Department of Mathematics and Statistics, Cleveland State University, Cleveland, OH 44115
- Department of Biological, Geological, and Environmental Sciences, Cleveland State University, Cleveland, OH 44115
| | - G. Valentin Börner
- Department of Biological, Geological, and Environmental Sciences, Cleveland State University, Cleveland, OH 44115
- Center for Gene Regulation in Health and Disease, Cleveland State University, Cleveland, OH 44115
| | - Shawn D. Ryan
- Department of Mathematics and Statistics, Cleveland State University, Cleveland, OH 44115
- Center for Applied Data Analysis and Modeling, Cleveland State University, Cleveland, OH 44115
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7
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Dutta S, Ghosh A, Boettiger AN, Spakowitz AJ. Leveraging polymer modeling to reconstruct chromatin connectivity from live images. Biophys J 2023; 122:3532-3540. [PMID: 37542372 PMCID: PMC10502477 DOI: 10.1016/j.bpj.2023.08.001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2023] [Revised: 06/19/2023] [Accepted: 08/01/2023] [Indexed: 08/06/2023] Open
Abstract
Chromosomal dynamics plays a central role in a number of critical biological processes, such as transcriptional regulation, genetic recombination, and DNA replication. However, visualization of chromatin is generally limited to live imaging of a few fluorescently labeled chromosomal loci or high-resolution reconstruction of multiple loci from a single time frame. To aid in mapping the underlying chromosomal structure based on parsimonious experimental measurements, we present an exact analytical expression for the evolution of the polymer configuration based on a flexible-polymer model, and we propose an algorithm that tracks the polymer configuration from live images of chromatin marked with several fluorescent marks. Our theory identifies the resolution of microscopy needed to achieve high-accuracy tracking for a given spacing of markers, establishing the statistical confidence in the assignment of genome identity to the visualized marks. We then leverage experimental data of locus-tracking measurements to demonstrate the validity of our modeling approach and to establish a basis for the design of experiments with a desired resolution. Altogether, this work provides a computational approach founded on polymer physics that vastly improves the interpretation of in vivo measurements of biopolymer dynamics.
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Affiliation(s)
- Sayantan Dutta
- Department of Chemical Engineering, Stanford University, Stanford, California
| | - Ashesh Ghosh
- Department of Chemical Engineering, Stanford University, Stanford, California
| | | | - Andrew J Spakowitz
- Department of Chemical Engineering, Stanford University, Stanford, California; Department of Materials Science and Engineering, Stanford University, Stanford, California; Program in Biophysics, Stanford University, Stanford, California.
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Marshall WF, Fung JC. Homologous chromosome recognition via nonspecific interactions. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.06.09.544427. [PMID: 37333079 PMCID: PMC10274854 DOI: 10.1101/2023.06.09.544427] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/20/2023]
Abstract
In many organisms, most notably Drosophila, homologous chromosomes in somatic cells associate with each other, a phenomenon known as somatic homolog pairing. Unlike in meiosis, where homology is read out at the level of DNA sequence complementarity, somatic homolog pairing takes place without double strand breaks or strand invasion, thus requiring some other mechanism for homologs to recognize each other. Several studies have suggested a "specific button" model, in which a series of distinct regions in the genome, known as buttons, can associate with each other, presumably mediated by different proteins that bind to these different regions. Here we consider an alternative model, which we term the "button barcode" model, in which there is only one type of recognition site or adhesion button, present in many copies in the genome, each of which can associate with any of the others with equal affinity. An important component of this model is that the buttons are non-uniformly distributed, such that alignment of a chromosome with its correct homolog, compared with a non-homolog, is energetically favored; since to achieve nonhomologous alignment, chromosomes would be required to mechanically deform in order to bring their buttons into mutual register. We investigated several types of barcodes and examined their effect on pairing fidelity. We found that high fidelity homolog recognition can be achieved by arranging chromosome pairing buttons according to an actual industrial barcode used for warehouse sorting. By simulating randomly generated non-uniform button distributions, many highly effective button barcodes can be easily found, some of which achieve virtually perfect pairing fidelity. This model is consistent with existing literature on the effect of translocations of different sizes on homolog pairing. We conclude that a button barcode model can attain highly specific homolog recognition, comparable to that seen in actual cells undergoing somatic homolog pairing, without the need for specific interactions. This model may have implications for how meiotic pairing is achieved.
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9
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Mazur AK, Gladyshev E. C-DNA may facilitate homologous DNA pairing. Trends Genet 2023:S0168-9525(23)00023-9. [PMID: 36804168 DOI: 10.1016/j.tig.2023.01.008] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2022] [Revised: 01/23/2023] [Accepted: 01/30/2023] [Indexed: 02/17/2023]
Abstract
Recombination-independent homologous pairing represents a prominent yet largely enigmatic feature of chromosome biology. As suggested by studies in the fungus Neurospora crassa, this process may be based on the direct pairing of homologous DNA molecules. Theoretical search for the DNA structures consistent with those genetic results has led to an all-atom model in which the B-DNA conformation of the paired double helices is strongly shifted toward C-DNA. Coincidentally, C-DNA also features a very shallow major groove that could permit initial homologous contacts without atom-atom clashes. The hereby conjectured role of C-DNA in homologous pairing should encourage the efforts to discover its biological functions and may also clarify the mechanism of recombination-independent recognition of DNA homology.
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Affiliation(s)
- Alexey K Mazur
- CNRS, Université Paris Cité, UPR 9080, Laboratoire de Biochimie Théorique, 13 rue Pierre et Marie Curie, Paris, France; Institut Pasteur, Université Paris Cité, Group Fungal Epigenomics, Paris, France.
| | - Eugene Gladyshev
- Institut Pasteur, Université Paris Cité, Group Fungal Epigenomics, Paris, France.
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10
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Ghosh A, Spakowitz AJ. Active and thermal fluctuations in multi-scale polymer structure and dynamics. SOFT MATTER 2022; 18:6629-6637. [PMID: 36000419 DOI: 10.1039/d2sm00593j] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
The presence of athermal noise or biological fluctuations control and maintain crucial life-processes. In this work, we present an exact analytical treatment of the dynamic behavior of a flexible polymer chain that is subjected to both thermal and active forces. Our model for active forces incorporates temporal correlation associated with the characteristic time scale and processivity of enzymatic function (driven by ATP hydrolysis), leading to an active-force time scale that competes with relaxation processes within the polymer chain. We analyze the structure and dynamics of an active-Brownian polymer using our exact results for the dynamic structure factor and the looping time for the chain ends. The spectrum of relaxation times within a polymer chain implies two different behaviors at small and large length scales. Small length-scale relaxation is faster than the active-force time scale, and the dynamic and structural behavior at these scales are oblivious to active forces and, are thus governed by the true thermal temperature. Large length-scale behavior is governed by relaxation times that are much longer than the active-force time scale, resulting in an effective active-Brownian temperature that dramatically alters structural and dynamic behavior. These complex multi-scale effects imply a time-dependent temperature that governs living and non-equilibrium systems, serving as a unifying concept for interpreting and predicting their physical behavior.
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Affiliation(s)
- Ashesh Ghosh
- Department of Chemical Engineering, Stanford University, Stanford, California, USA.
| | - Andrew J Spakowitz
- Department of Chemical Engineering, Stanford University, Stanford, California, USA.
- Biophysics Program, Stanford University, Stanford, California, USA
- Department of Materials Science & Engineering, Stanford University, Stanford, California, USA
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