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Reaction-Diffusion kinetics of Protein DNA Interactions
Uppsala University, Disciplinary Domain of Science and Technology, Biology, Department of Cell and Molecular Biology, Computational and Systems Biology.ORCID iD: 0000-0002-6084-0197
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Transcription factors need to rapidly find one specific binding site among millions of nonspecific sites on the chromosomal DNA. In this thesis I use various aspects of reaction-diffusion theory to investigate the interaction between proteins and DNA and to explain the searching, finding and binding to specific operator sites. Using molecular dynamics methods we calculate the free energy profile for the model protein LacI as it leaves a nonspecific stretch of DNA and as it slides along DNA. Based on the free energy profiles we estimate the microscopic dissociation rate constant, kdmicro ~1.45×104s-1, and the 1D diffusion coefficient, D1 ~ 0.05-0.29 μm2s-1 (2-40μs to slide 1 basepair (bp)). At a non-atomistic level of detail we estimate the number of microscopic rebindings before a macroscopic dissociation occurs which leads to the  macroscopic residence time, τDmacro ~ 48±12ms resulting in a in vitro sliding length estimate of 135-345bp.

When we fit the DNA interaction parameters for in vivo conditions to recent single molecule in vivo experiments we conclude that neither hopping nor intersegment transfer contribute to the target search for the LacI dimer, that it appears to bind the specific Osym operator site as soon as it slides into it, and that the sliding length is around 40bp in the cell. The estimated in vivo D1 ~ 0.025 μm2s-1 is higher than expected from estimates of D1 based on viscosity and the atomistic simulations. Surprisingly, we were also forced to conclude that the nonspecific association for the LacI dimer appeared reaction limited which is in conflict with the free energy profile. This inconsistency is resolved by allowing for steric effects. Using reaction-diffusion theory and simulations we show that an apparent reaction limited association can be diffusion limited if geometry and steric effects are taken into account. Furthermore, the simulations show that a protein binds ~2 times faster to a DNA molecule with a helical reactive patch than to a stripe patch running along the length of the DNA. This facilitated binding has a direct impact on the search time especially in the presence of other DNA binding proteins.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2015. , 56 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1299
Keyword [en]
umbrella sampling, molecular dynamics, RDME, PDE, sliding, intersegment transfer, hopping, sterics, intersegment transfer
National Category
Biophysics Bioinformatics and Systems Biology
Research subject
Biology with specialization in Molecular Biotechnology
Identifiers
URN: urn:nbn:se:uu:diva-263527ISBN: 978-91-554-9360-8 (print)OAI: oai:DiVA.org:uu-263527DiVA: diva2:858613
Public defence
2015-11-06, C8:301, Husargatan 3, Uppsala, 13:00 (English)
Opponent
Supervisors
Available from: 2015-10-16 Created: 2015-10-02 Last updated: 2016-09-09
List of papers
1. What matters for lac repressor search in vivo-sliding, hopping, intersegment transfer, crowding on DNA or recognition?
Open this publication in new window or tab >>What matters for lac repressor search in vivo-sliding, hopping, intersegment transfer, crowding on DNA or recognition?
2015 (English)In: Nucleic Acids Research, ISSN 0305-1048, E-ISSN 1362-4962, Vol. 43, no 7, 3454-3464 p.Article in journal (Refereed) Published
Abstract [en]

We have investigated which aspects of transcription factor DNA interactions are most important to account for the recent in vivo search time measurements for the dimeric lac repressor. We find the best agreement for a sliding model where non-specific binding to DNA is improbable at first contact and the sliding LacI protein binds at high probability when reaching the specific O-sym operator. We also find that the contribution of hopping to the overall search speed is negligible although physically unavoidable. The parameters that give the best fit reveal sliding distances, including hopping, close to what has been proposed in the past, i.e. similar to 40 bp, but with an unexpectedly high 1D diffusion constant on non-specific DNA sequences. Including a mechanism of inter-segment transfer between distant DNA segments does not bring down the 1D diffusion to the expected fraction of the in vitro value. This suggests a mechanism where transcription factors can slide less hindered in vivo than what is given by a simple viscosity scaling argument or that a modification of the model is needed. For example, the estimated diffusion rate constant would be consistent with the expectation if parts of the chromosome, away from the operator site, were inaccessible for searching.

National Category
Biochemistry and Molecular Biology
Identifiers
urn:nbn:se:uu:diva-256544 (URN)10.1093/nar/gkv207 (DOI)000354722500012 ()25779051 (PubMedID)
Available from: 2015-06-25 Created: 2015-06-24 Last updated: 2017-12-04Bibliographically approved
2. Lost in presumption: stochastic reactions in spatial models
Open this publication in new window or tab >>Lost in presumption: stochastic reactions in spatial models
2012 (English)In: Nature Methods, ISSN 1548-7091, E-ISSN 1548-7105, Vol. 9, no 12, 1163-1166 p.Article in journal (Refereed) Published
Abstract [en]

Physical modeling is increasingly important for generating insights into intracellular processes. We describe situations in which combined spatial and stochastic aspects of chemical reactions are needed to capture the relevant dynamics of biochemical systems.

National Category
Biochemistry and Molecular Biology
Identifiers
urn:nbn:se:uu:diva-191793 (URN)10.1038/nmeth.2253 (DOI)000312093500016 ()
Available from: 2013-01-14 Created: 2013-01-14 Last updated: 2017-12-06
3. Transcription-factor binding and sliding on DNA studied using micro- and macroscopic models
Open this publication in new window or tab >>Transcription-factor binding and sliding on DNA studied using micro- and macroscopic models
Show others...
2013 (English)In: Proceedings of the National Academy of Sciences of the United States of America, ISSN 0027-8424, E-ISSN 1091-6490, Vol. 110, no 49, 19796-19801 p.Article in journal (Refereed) Published
Abstract [en]

Transcription factors search for specific operator sequences by alternating rounds of 3D diffusion with rounds of 1D diffusion (sliding) along the DNA. The details of such sliding have largely been beyond direct experimental observation. For this purpose we devised an analytical formulation of umbrella sampling along a helical coordinate, and from extensive and fully atomistic simulations we quantified the free-energy landscapes that underlie the sliding dynamics and dissociation kinetics for the LacI dimer. The resulting potential of mean force distributions show a fine structure with an amplitude of 1 k(B)T for sliding and 12 kBT for dissociation. Based on the free-energy calculations the repressor slides in close contact with DNA for 8 bp on average before making a microscopic dissociation. By combining the microscopic molecular-dynamics calculations with Brownian simulation including rotational diffusion from the microscopically dissociated state we estimate a macroscopic residence time of 48 ms at the same DNA segment and an in vitro sliding distance of 240 bp. The sliding distance is in agreement with previous in vitro sliding-length estimates. The in vitro prediction for the macroscopic residence time also compares favorably to what we measure by single-molecule imaging of nonspecifically bound fluorescently labeled LacI in living cells. The investigation adds to our understanding of transcription-factor search kinetics and connects the macro-/mesoscopic rate constants to the microscopic dynamics.

Keyword
facilitated diffusion, lac operon, lac repressors, gene regulation
National Category
Natural Sciences
Identifiers
urn:nbn:se:uu:diva-213898 (URN)10.1073/pnas.1307905110 (DOI)000327744900041 ()
External cooperation:
Available from: 2014-01-06 Created: 2014-01-05 Last updated: 2017-12-06Bibliographically approved
4. MesoRD 1.0: Stochastic reaction-diffusion simulations in the microscopic limit
Open this publication in new window or tab >>MesoRD 1.0: Stochastic reaction-diffusion simulations in the microscopic limit
2012 (English)In: Bioinformatics, ISSN 1367-4803, E-ISSN 1367-4811, Vol. 28, no 23, 3155-3157 p.Article in journal (Refereed) Published
Abstract [en]

MesoRD is a tool for simulating stochastic reaction-diffusion systems as modeled by the reaction diffusion master equation. The simulated systems are defined in the Systems Biology Markup Language with additions to define compartment geometries. MesoRD 1.0 supports scale-dependent reaction rate constants and reactions between reactants in neighbouring subvolumes. These new features make it possible to construct physically consistent models of diffusion-controlled reactions also at fine spatial discretization.

National Category
Natural Sciences
Identifiers
urn:nbn:se:uu:diva-192453 (URN)10.1093/bioinformatics/bts584 (DOI)000311902700025 ()
Available from: 2013-01-23 Created: 2013-01-21 Last updated: 2017-12-06Bibliographically approved
5. The lac repressor displays facilitated diffusion in living cells
Open this publication in new window or tab >>The lac repressor displays facilitated diffusion in living cells
Show others...
2012 (English)In: Science, ISSN 0036-8075, E-ISSN 1095-9203, Vol. 336, no 6088, 1595-1598 p.Article in journal (Refereed) Published
Abstract [en]

Transcription factors (TFs) are proteins that regulate the expression of genes by binding sequence-specific sites on the chromosome. It has been proposed that to find these sites fast and accurately, TFs combine one-dimensional (1D) sliding on DNA with 3D diffusion in the cytoplasm. This facilitated diffusion mechanism has been demonstrated in vitro, but it has not been shown experimentally to be exploited in living cells. We have developed a single-molecule assay that allows us to investigate the sliding process in living bacteria. Here we show that the lac repressor slides 45 ± 10 base pairs on chromosomal DNA and that sliding can be obstructed by other DNA-bound proteins near the operator. Furthermore, the repressor frequently (>90%) slides over its natural lacO(1) operator several times before binding. This suggests a trade-off between rapid search on nonspecific sequences and fast binding at the specific sequence.

National Category
Natural Sciences
Identifiers
urn:nbn:se:uu:diva-176861 (URN)10.1126/science.1221648 (DOI)000305507500062 ()22723426 (PubMedID)
External cooperation:
Available from: 2012-06-26 Created: 2012-06-26 Last updated: 2017-12-07Bibliographically approved
6. The helical structure of DNA facilitates binding
Open this publication in new window or tab >>The helical structure of DNA facilitates binding
2016 (English)In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 9, no 36, 364002Article in journal (Other academic) Published
Abstract [en]

The helical structure of DNA imposes constraints on the rate of diffusion-limited protein binding. Here we solve the reaction-diffusion equations for DNA-like geometries and extend with simulations when necessary. We find that the helical structure can make binding to the DNA more than twice as fast compared to a case where DNA would be reactive only along one side. We also find that this rate advantage remains when the contributions from steric constraints and rotational diffusion of the DNA-binding protein are included. Furthermore, we find that the association rate is insensitive to changes in the steric constraints on the DNA in the helix geometry, while it is much more dependent on the steric constraints on the DNA-binding protein. We conclude that the helical structure of DNA facilitates the nonspecific binding of transcription factors and structural DNA-binding proteins in general.

Keyword
reaction-diffusion equation; steric constraints; helix geometry; diffusion limited
National Category
Biophysics
Identifiers
urn:nbn:se:uu:diva-263526 (URN)10.1088/1751-8113/49/36/364002 (DOI)000383512000002 ()
Funder
EU, European Research CouncilKnut and Alice Wallenberg Foundation
Available from: 2015-10-02 Created: 2015-10-02 Last updated: 2017-12-01Bibliographically approved

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