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  <doc>
    <id>10110</id>
    <completedYear/>
    <publishedYear>2025</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
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    <type>article</type>
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    <title language="eng">Unfolding the geometric structure and multiple timescales of the urea-urease pH oscillator</title>
    <abstract language="eng">We study a two-variable dynamical system modeling pH oscillations in the urea–urease reaction within giant lipid vesicles – a problem that intrinsically contains multiple, well-separated timescales. Building on an existing, deterministic formulation via ordinary differential equations, we resolve different orders of magnitude within a small parameter and analyze the system's limit cycle behavior using geometric singular perturbation theory (GSPT). By introducing two different coordinate scalings – each valid in a distinct region of the phase space – we resolve the local dynamics near critical fold points, using the extension of GSPT through such singular points due to Krupa and Szmolyan. This framework enables a geometric decomposition of the periodic orbits into slow and fast segments and yields closed-form estimates for the period of oscillation. In particular, we link the existence of such oscillations to an underlying biochemical asymmetry, namely, the differential transport across the vesicle membrane.</abstract>
    <identifier type="arxiv">2508.07275</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="SubmissionStatus">under review</enrichment>
    <enrichment key="PeerReviewed">no</enrichment>
    <submitter>Arthur Straube</submitter>
    <author>Arthur Straube</author>
    <author>Guillermo Olicón Méndez</author>
    <author>Stefanie Winkelmann</author>
    <author>Felix Höfling</author>
    <author>Maximilian Engel</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="persons" number="hoefling">Höfling, Felix</collection>
    <collection role="persons" number="straube">Straube, Arthur</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="institutes" number="PaDC">Parallel and Distributed Computing</collection>
    <collection role="projects" number="MathPlusAA1-18">MathPlusAA1-18</collection>
  </doc>
  <doc>
    <id>8405</id>
    <completedYear/>
    <publishedYear>2022</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
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    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>49</issue>
    <volume>112</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
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    <belongsToBibliography>0</belongsToBibliography>
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    <title language="eng">A probabilistic framework for particle-based reaction–diffusion dynamics using classical Fock space representations</title>
    <parentTitle language="eng">Letters in Mathematical Physics</parentTitle>
    <identifier type="arxiv">arXiv:2109.13616</identifier>
    <identifier type="doi">10.1007/s11005-022-01539-w</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="AcceptedDate">2022-04-21</enrichment>
    <author>Mauricio del Razo</author>
    <submitter>Stefanie Winkelmann</submitter>
    <author>Daniela Frömberg</author>
    <author>Arthur Straube</author>
    <author>Christof Schütte</author>
    <author>Felix Höfling</author>
    <author>Stefanie Winkelmann</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="SFB1114-C3">SFB1114-C3</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="persons" number="hoefling">Höfling, Felix</collection>
    <collection role="persons" number="straube">Straube, Arthur</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="projects" number="MathPlusAA1-5">MathPlusAA1-5</collection>
    <collection role="persons" number="delrazo">del Razo Sarmina, Mauricio</collection>
    <collection role="projects" number="DFG-OpenMultiscaleBiochem">DFG-OpenMultiscaleBiochem</collection>
  </doc>
  <doc>
    <id>8412</id>
    <completedYear/>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>9888</pageFirst>
    <pageLast>9893</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>12</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2021-10-05</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Stochastic pH oscillations in a model of the urea–urease reaction confined to lipid vesicles</title>
    <abstract language="eng">The urea-urease clock reaction is a pH switch from acid to basic that can turn into a pH oscillator if it occurs inside a suitable open reactor. We numerically study the confinement of the reaction to lipid vesicles, which permit the exchange with an external reservoir by differential transport, enabling the recovery of the pH level and yielding a constant supply of urea molecules. For microscopically small vesicles, the discreteness of the number of molecules requires a stochastic treatment of the reaction dynamics. Our analysis shows that intrinsic noise induces a significant statistical variation of the oscillation period, which increases as the vesicles become smaller.&#13;
The mean period, however, is found to be remarkably robust for vesicle sizes down to approximately 200 nm, but the periodicity of the rhythm is gradually destroyed for smaller vesicles. The observed oscillations are explained as a canard-like limit cycle that differs from the wide class of conventional feedback oscillators.</abstract>
    <parentTitle language="deu">J. Phys. Chem. Lett.</parentTitle>
    <identifier type="doi">10.1021/acs.jpclett.1c03016</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Arthur Straube</author>
    <submitter>Arthur Straube</submitter>
    <author>Stefanie Winkelmann</author>
    <author>Christof Schütte</author>
    <author>Felix Höfling</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="vas">Distributed Algorithms and Supercomputing</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="SFB1114-C3">SFB1114-C3</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="persons" number="hoefling">Höfling, Felix</collection>
    <collection role="persons" number="straube">Straube, Arthur</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="projects" number="MathPlusAA1-18">MathPlusAA1-18</collection>
  </doc>
  <doc>
    <id>8927</id>
    <completedYear/>
    <publishedYear>2023</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>2955</pageFirst>
    <pageLast>2967</pageLast>
    <pageNumber/>
    <edition/>
    <issue>13</issue>
    <volume>127</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2023-03-28</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Accurate reduced models for the pH oscillations in the urea-urease reaction confined to giant lipid vesicles</title>
    <abstract language="eng">This theoretical study concerns a pH oscillator based on the urea-urease reaction confined to giant lipid vesicles. Under suitable conditions, differential transport of urea and hydrogen ion across the unilamellar vesicle membrane periodically resets the pH clock that switches the system from acid to basic, resulting in self-sustained oscillations. We analyse the structure of the phase flow and of the limit cycle, which controls the dynamics for giant vesicles and dominates the pronouncedly stochastic oscillations in small vesicles of submicrometer size. To this end, we derive reduced models, which are amenable to analytic treatments that are complemented by numerical solutions, and obtain the period and amplitude of the oscillations as well as the parameter domain, where oscillatory behavior persists. We show that the accuracy of these predictions is highly sensitive to the employed reduction scheme. In particular, we suggest an accurate two-variable model and show its equivalence to a three-variable model that admits an interpretation in terms of a chemical reaction network. The faithful modeling of a single pH oscillator appears crucial for rationalizing experiments and understanding communication of vesicles and synchronization of rhythms.</abstract>
    <parentTitle language="eng">The Journal of Physical Chemistry B</parentTitle>
    <identifier type="arxiv">arXiv:2212.14503</identifier>
    <identifier type="doi">10.1021/acs.jpcb.2c09092</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2023-03-13</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-88179</enrichment>
    <author>Arthur Straube</author>
    <submitter>Stefanie Winkelmann</submitter>
    <author>Stefanie Winkelmann</author>
    <author>Felix Höfling</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="projects" number="SFB1114-C3">SFB1114-C3</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="persons" number="hoefling">Höfling, Felix</collection>
    <collection role="persons" number="straube">Straube, Arthur</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="projects" number="MathPlusAA1-18">MathPlusAA1-18</collection>
  </doc>
  <doc>
    <id>8817</id>
    <completedYear/>
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    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
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    <creatingCorporation/>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2022-11-12</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Accurate reduced models for the pH oscillations in the urea-urease reaction confined to giant lipid vesicles</title>
    <abstract language="eng">Our theoretical study concerns an urea-urease-based pH oscillator confined to giant lipid vesicles. Under suitable conditions, differential transport of urea and hydrogen ion across the unilamellar vesicle membrane periodically resets the pH clock that switches the system from acid to basic, resulting in self-sustained oscillations. We analyse the structure of the limit cycle, which controls the dynamics for giant vesicles and dominates the strongly stochastic oscillations in small vesicles of submicrometer size. To this end, we derive reduced models, amenable to analytic treatments, and show that the accuracy of predictions, including the period of oscillations, is highly sensitive to the choice of the reduction scheme. In particular, we suggest an accurate two-variable model and show its equivalence to a three-variable model that admits an interpretation in terms of a chemical reaction network. The accurate description of a single pH oscillator appears crucial for rationalizing experiments and understanding communication of vesicles and synchronization of rhythms.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="doi">10.12752/8817</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-88179</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Arthur Straube</author>
    <submitter>Arthur Straube</submitter>
    <author>Stefanie Winkelmann</author>
    <author>Felix Höfling</author>
    <series>
      <title>ZIB-Report</title>
      <number>22-21</number>
    </series>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="vas">Distributed Algorithms and Supercomputing</collection>
    <collection role="projects" number="SFB1114-C3">SFB1114-C3</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="persons" number="hoefling">Höfling, Felix</collection>
    <collection role="persons" number="straube">Straube, Arthur</collection>
    <collection role="institutes" number="MfLMS">Mathematics for Life and Materials Science</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="projects" number="MathPlusAA1-18">MathPlusAA1-18</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/8817/ZIB-Report-Preprint.pdf</file>
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