TY - JOUR A1 - Delle Site, Luigi A1 - Krekeler, Christian A1 - Whittaker, John A1 - Agarwal, Animesh A1 - Klein, Rupert A1 - Höfling, Felix T1 - Molecular Dynamics of Open Systems: Construction of a Mean‐Field Particle Reservoir JF - Advanced Theory and Simulations N2 - The simulation of open molecular systems requires explicit or implicit reservoirs of energy and particles. Whereas full atomistic resolution is desired in the region of interest, there is some freedom in the implementation of the reservoirs. Here, a combined, explicit reservoir is constructed by interfacing the atomistic region with regions of point-like, non-interacting particles (tracers) embedded in a thermodynamic mean field. The tracer molecules acquire atomistic resolution upon entering the atomistic region and equilibrate with this environment, while atomistic molecules become tracers governed by an effective mean-field potential after crossing the atomistic boundary. The approach is extensively tested on thermodynamic, structural, and dynamic properties of liquid water. Conceptual and numerical advantages of the procedure as well as new perspectives are highlighted and discussed. Y1 - 2019 U6 - https://doi.org/10.1002/adts.201900014 VL - 2 SP - 1900014 ER - TY - JOUR A1 - Dibak, Manuel A1 - Fröhner, Christoph A1 - Noé, Frank A1 - Höfling, Felix T1 - Diffusion-influenced reaction rates in the presence of pair interactions JF - The Journal of Chemical Physics N2 - The kinetics of bimolecular reactions in solution depends, among other factors, on intermolecular forces such as steric repulsion or electrostatic interaction. Microscopically, a pair of molecules first has to meet by diffusion before the reaction can take place. In this work, we establish an extension of Doi’s volume reaction model to molecules interacting via pair potentials, which is a key ingredient for interacting-particle-based reaction–diffusion (iPRD) simulations. As a central result, we relate model parameters and macroscopic reaction rate constants in this situation. We solve the corresponding reaction–diffusion equation in the steady state and derive semi- analytical expressions for the reaction rate constant and the local concentration profiles. Our results apply to the full spectrum from well-mixed to diffusion-limited kinetics. For limiting cases, we give explicit formulas, and we provide a computationally inexpensive numerical scheme for the general case, including the intermediate, diffusion-influenced regime. The obtained rate constants decompose uniquely into encounter and formation rates, and we discuss the effect of the potential on both subprocesses, exemplified for a soft harmonic repulsion and a Lennard-Jones potential. The analysis is complemented by extensive stochastic iPRD simulations, and we find excellent agreement with the theoretical predictions. Y1 - 2019 U6 - https://doi.org/10.1063/1.5124728 VL - 151 SP - 164105 ER - TY - JOUR A1 - Straube, Arthur A1 - Kowalik, Bartosz G. A1 - Netz, Roland R. A1 - Höfling, Felix T1 - Rapid onset of molecular friction in liquids bridging between the atomistic and hydrodynamic pictures JF - Commun. Phys. N2 - Friction in liquids arises from conservative forces between molecules and atoms. Although the hydrodynamics at the nanoscale is subject of intense research and despite the enormous interest in the non-Markovian dynamics of single molecules and solutes, the onset of friction from the atomistic scale so far could not be demonstrated. Here, we fill this gap based on frequency-resolved friction data from high-precision simulations of three prototypical liquids, including water. Combining with theory, we show that friction in liquids emerges abruptly at a characteristic frequency, beyond which viscous liquids appear as non-dissipative, elastic solids. Concomitantly, the molecules experience Brownian forces that display persistent correlations. A critical test of the generalised Stokes–Einstein relation, mapping the friction of single molecules to the visco-elastic response of the macroscopic sample, disproves the relation for Newtonian fluids, but substantiates it exemplarily for water and a moderately supercooled liquid. The employed approach is suitable to yield insights into vitrification mechanisms and the intriguing mechanical properties of soft materials. Y1 - 2020 U6 - https://doi.org/10.1038/s42005-020-0389-0 VL - 3 SP - 126 PB - Nature ER - TY - GEN A1 - Mokhtari, Zahra A1 - Patterson, Robert I. A. A1 - Höfling, Felix T1 - Spontaneous trail formation in populations of auto-chemotactic walkers N2 - We study the formation of trails in populations of self-propelled agents that make oriented deposits of pheromones and also sense such deposits to which they then respond with gradual changes of their direction of motion. Based on extensive off-lattice computer simulations aiming at the scale of insects, e.g., ants, we identify a number of emerging stationary patterns and obtain qualitatively the non-equilibrium \add{state} diagram of the model, spanned by the strength of the agent--pheromone interaction and the number density of the population. In particular, we demonstrate the spontaneous formation of persistent, macroscopic trails, and highlight some behaviour that is consistent with a dynamic phase transition. This includes a characterisation of the mass of system-spanning trails as a potential order parameter. We also propose a dynamic model for a few macroscopic observables, including the sub-population size of trail-following agents, which captures the early phase of trail formation. T3 - ZIB-Report - 21-36 Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-84466 SN - 1438-0064 ER - TY - JOUR A1 - Pathania, Yogyata A1 - Chakraborty, Dipanjan A1 - Höfling, Felix T1 - Continuous demixing transition of binary liquids: finite-size scaling from the analysis of sub-systems JF - Advances Theory and Simulation Y1 - 2021 U6 - https://doi.org/10.1002/adts.202000235 VL - 4 SP - 2000235 ER - TY - JOUR A1 - Frömberg, Daniela A1 - Höfling, Felix T1 - Generalized master equation for first-passage problems in partitioned spaces JF - Journal of Physics A: Mathematical and Theoretical Y1 - 2021 U6 - https://doi.org/10.1088/1751-8121/abf2ec VL - 54 SP - 215601 ER - TY - JOUR A1 - Klein, Rupert A1 - Ebrahimi Viand, Roya A1 - Höfling, Felix A1 - Delle Site, Luigi T1 - Nonequilibrium induced by reservoirs: Physico-mathematical model and numerical tests JF - Advances Theory and Simulation Y1 - 2021 U6 - https://doi.org/10.1002/adts.202100071 VL - 4 SP - 2100071 ER - TY - JOUR A1 - Gholami, Abbas A1 - Höfling, Felix A1 - Klein, Rupert A1 - Delle Site, Luigi T1 - Thermodynamic relations at the coupling boundary in adaptive resolution simulations for open systems JF - Advances Theory and Simulation Y1 - 2021 U6 - https://doi.org/10.1002/adts.202000303 VL - 4 SP - 2000303 ER - TY - JOUR A1 - Mokhtari, Zahra A1 - Patterson, Robert I. A. A1 - Höfling, Felix T1 - Spontaneous trail formation in populations of auto-chemotactic walkers JF - New Journal of Physics Y1 - 2022 U6 - https://doi.org/10.1088/1367-2630/ac43ec VL - 24 SP - 013012 ER - TY - JOUR A1 - Höfling, Felix A1 - Dietrich, Siegfried T1 - Structure of liquid–vapor interfaces: perspectives from liquid state theory, large-scale simulations, and potential grazing-incidence X-ray diffraction JF - The Journal of Chemical Physics N2 - Grazing-incidence X-ray diffraction (GIXRD) is a scattering technique which allows one to characterize the structure of fluid interfaces down to the molecular scale, including the measurement of the surface tension and of the interface roughness. However, the corresponding standard data analysis at non-zero wave numbers has been criticized as to be inconclusive because the scattering intensity is polluted by the unavoidable scattering from the bulk. Here we overcome this ambiguity by proposing a physically consistent model of the bulk contribution which is based on a minimal set of assumptions of experimental relevance. To this end, we derive an explicit integral expression for the background scattering, which can be determined numerically from the static structure factors of the coexisting bulk phases as independent input. Concerning the interpretation of GIXRD data inferred from computer simulations, we account also for the finite sizes of the bulk phases, which are unavoidable in simulations. The corresponding leading-order correction beyond the dominant contribution to the scattered intensity is revealed by asymptotic analysis, which is characterized by the competition between the linear system size and the X-ray penetration depth in the case of simulations. Specifically, we have calculated the expected GIXRD intensity for scattering at the planar liquid--vapor interface of Lennard-Jones fluids with truncated pair interactions via extensive, high-precision simulations. The reported data cover interfacial and bulk properties of fluid states along the whole liquid--vapor coexistence line. A sensitivity analysis demonstrates the robustness of our findings concerning the detailed definition of the mean interface position. We conclude that previous claims of an enhanced surface tension at mesoscopic scales are amenable to unambiguous tests via scattering experiments. Y1 - 2024 U6 - https://doi.org/10.1063/5.0186955 VL - 160 SP - 104107 ER - TY - CHAP A1 - Skoblin, Viktor A1 - Höfling, Felix A1 - Christgau, Steffen T1 - Gaining Cross-Platform Parallelism for HAL’s Molecular Dynamics Package using SYCL T2 - 29. PARS-Workshop 2023 N2 - Molecular dynamics simulations are one of the methods in scientific computing that benefit from GPU acceleration. For those devices, SYCL is a promising API for writing portable codes. In this paper, we present the case study of HAL’s MD package that has been successfully migrated from CUDA to SYCL. We describe the different strategies that we followed in the process of porting the code. Following these strategies, we achieved code portability across major GPU vendors. Depending on the actual kernels, both significant performance improvements and regressions are observed. As a side effect of the migration process, we obtained impressing speedups also for execution on CPUs. Y1 - 2023 SN - 0177-0454 VL - 36 ER - TY - JOUR A1 - Straube, Arthur A1 - Höfling, Felix T1 - Memory effects in colloidal motion under confinement and driving JF - J. Phys. A: Math. Theor. N2 - The transport of individual particles in inhomogeneous environments is complex and exhibits non-Markovian responses. The latter may be quantified by a memory function within the framework of the linear generalised Langevin equation (GLE). Here, we exemplify the implications of steady driving on the memory function of a colloidal model system for Brownian motion in a corrugated potential landscape, specifically, for one-dimensional motion in a sinusoidal potential. To this end, we consider the overdamped limit of the GLE, which is facilitated by separating the memory function into a singular (Markovian) and a regular (non-Markovian) part. Relying on exact solutions for the investigated model, we show that the random force entering the GLE must display a bias far from equilibrium, which corroborates a recent general prediction. Based on data for the mean-square displacement (MSD) obtained from Brownian dynamics simulations, we estimate the memory function for different driving strengths and show that already moderate driving accelerates the decay of the memory function by several orders of magnitude in time. We find that the memory may persist on much longer timescales than expected from the convergence of the MSD to its long-time asymptote. Furthermore, the functional form of the memory function changes from a monotonic decay to a non-monotonic, damped oscillatory behaviour, which can be understood from a competition of confined motion and depinning. Our analysis of the simulation data further reveals a pronounced non-Gaussianity, which questions the Gaussian approximation of the random force entering the GLE. Y1 - 2024 U6 - https://doi.org/10.1088/1751-8121/ad5b2d SN - 1751-8113 VL - 57 SP - 295003 PB - IOP Publishing ER - TY - JOUR A1 - Höfling, Felix A1 - Straube, Arthur T1 - Langevin equations and a geometric integration scheme for the overdamped limit of rotational Brownian motion of axisymmetric particles JF - Physical Review Research N2 - The translational motion of anisotropic or self-propelled colloidal particles is closely linked with the particle’s orientation and its rotational Brownian motion. In the overdamped limit, the stochastic evolution of the orientation vector follows a diffusion process on the unit sphere and is characterized by an orientation-dependent (“multiplicative”) noise. As a consequence, the corresponding Langevin equation attains different forms depending on whether Itō’s or Stratonovich’s stochastic calculus is used. We clarify that both forms are equivalent and derive them in a top-down approach from a geometric construction of Brownian motion on the unit sphere, based on infinitesimal random rotations. Our approach suggests further a geometric integration scheme for rotational Brownian motion, which preserves the normalization constraint of the orientation vector exactly. We show that a simple implementation of the scheme, using Gaussian random rotations, converges weakly at order 1 of the integration time step, and we outline an advanced variant of the scheme that is weakly exact for an arbitrarily large time step. Due to a favorable prefactor of the discretization error, already the Gaussian scheme allows for integration time steps that are one order of magnitude larger compared to a commonly used algorithm for rotational Brownian dynamics simulations based on projection on the constraining manifold. For torques originating from constant external fields, we prove by virtue of the Fokker-Planck equation that the constructed diffusion process satisfies detailed balance and converges to the correct equilibrium distribution. The analysis is restricted to time-homogeneous rotational Brownian motion (i.e., a single rotational diffusion constant), which is relevant for axisymmetric particles and also chemically anisotropic spheres, such as self-propelled Janus particles. Y1 - 2025 U6 - https://doi.org/10.1103/wzdn-29p4 VL - 7 SP - 043034 ER - TY - JOUR A1 - Roy, Sutapa A1 - Höfling, Felix T1 - Critical surface adsorption of confined binary liquids with locally conserved mass and composition JF - Molecular Physics N2 - Close to a solid surface, the properties of a fluid deviate significantly from their bulk values. In this context, we study the surface adsorption profiles of a symmetric binary liquid confined to a slit pore by means of molecular dynamics simulations; the latter naturally entails that mass and concentration are locally conserved. Near a bulk consolute point, where the liquid exhibits a demixing transition with the local concentration as the order parameter, we determine the order parameter profiles and characterise the relevant critical scaling behaviour, in the regime of strong surface attraction, for a range of pore widths and temperatures. The obtained order parameter profiles decay monotonically near the surfaces, also in the presence of a pronounced layering in the number density. Overall, our results agree qualitatively with recent theoretical predictions from a mesoscopic field-theoretical approach for the canonical ensemble. Y1 - 2024 U6 - https://doi.org/10.1080/00268976.2024.2391998 VL - 122 IS - 21-22 SP - e2391998 ER - TY - JOUR A1 - Marcelli, Giorgia A1 - Bottinelli Montandon, Tecla A1 - Ebrahimi Viand, Roya A1 - Höfling, Felix T1 - Fluid flow inside slit-shaped nanopores: the role of surface morphology at the molecular scale JF - The Journal of Chemical Physics N2 - Non-equilibrium molecular dynamics (NEMD) simulations of fluid flow have highlighted the peculiarities of nanoscale flows compared to classical fluid mechanics; in particular, boundary conditions can deviate from the no-slip behavior at macroscopic scales. For fluid flow in slit-shaped nanopores, we demonstrate that surface morphology provides an efficient control on the slip length, which approaches zero when matching the molecular structures of the pore wall and the fluid. Using boundary-driven, energy-conserving NEMD simulations with a pump-like driving mechanism, we examine two types of pore walls—mimicking a crystalline and an amorphous material—that exhibit markedly different surface resistances to flow. The resulting flow velocity profiles are consistent with Poiseuille theory for incompressible, Newtonian fluids when adjusted for surface slip. For the two pores, we observe partial slip and no-slip behavior, respectively. The hydrodynamic permeability corroborates that the simulated flows are in the Darcy regime. However, the confinement of the fluid gives rise to an effective viscosity below its bulk value; wide pores exhibit a crossover between boundary and bulk-like flows. In addition, the thermal isolation of the flow causes a linear increase in fluid temperature along the flow, which we relate to strong viscous dissipation and heat convection, utilizing conservation laws of fluid mechanics. Noting that the investigated fluid model does not form droplets, our findings challenge the universality of previously reported correlations between slippage, solvophobicity, and a depletion zone. Furthermore, they underscore the need for molecular-scale modeling to accurately capture the fluid dynamics near boundaries and in nanoporous materials, where macroscopic models may not be applicable. Y1 - 2025 U6 - https://doi.org/10.1063/5.0246573 VL - 162 SP - 104101 ER - TY - JOUR A1 - Zhong, Xin A1 - Höfling, Felix A1 - John, Timm T1 - Hydrogen diffusion in garnet: insights from atomistic simulations JF - Geochemistry Geophysics Geosystems N2 - Garnet has been widely used to decipher the pressure-temperature-time history of rocks, but its physical properties such as elasticity and diffusion are strongly affected by trace amounts of hydrogen. Experimental measurements of H diffusion in garnet are limited to room pressure. We use atomistic simulations to study H diffusion in perfect and defective garnet lattices, focusing on protonation defects at the Si and Mg sites, which are shown to be energetically favored. Transient trapping of H renders ab-initio simulations of H diffusion computationally challenging, which is overcome with machine learning techniques by training a deep neural network that encodes the interatomic potential. Our results from such deep potential molecular dynamics (DeePMD) simulations show high mobility of hydrogen in defect-free garnet lattices, whereas H diffusivity is significantly diminished in defective lattices. Tracer simulations focusing on H alone highlight the vital role of atomic vibrations of heavier atoms like Mg on the release of H atoms. Two regimes of H diffusion are identified: a diffuser-dominated regime at high hydrogen content with low activation energies due to saturation of vacancies by hydrogen, and a vacancy-dominated regime at low hydrogen content with high activation energies due to trapping of H atoms at vacancy sites. These regimes account for experimental observations, such as a H-concentration dependent diffusivity and the discrepancy in activation energy between deprotonation and D-H exchange experiments. This study underpins the crucial role of vacancies in H diffusion and demonstrates the utility of machine-learned interatomic potentials in studying kinetic processes in the Earth's interior. Y1 - 2025 U6 - https://doi.org/10.1029/2024GC011951 VL - 26 SP - e2024GC011951 ER - TY - JOUR A1 - Straube, Arthur A1 - Höfling, Felix T1 - Depinning transition of self-propelled particles JF - Physical Review E N2 - For self-propelled particles in a corrugated potential landscape, we describe a discontinuous change of the classical depinning transition and a host of unique behaviors sensitive to the persistence of the propulsion direction. Exact and semianalytic results for active Brownian particles corroborate a creep regime with a superexponentially suppressed drift velocity upon lowering the force towards the threshold value. This unusual nonlinear response emerges from the competition of two critical scaling laws with exponents of 1/2 for rapidly reorienting particles and 𝑑/2 for particles with a persistent orientation; the latter case depends on the dimensionality 𝑑 of rotational motion and also includes run-and-tumble particles. Additionally, different giant diffusion phenomena occur in the two regimes. Our findings extend to random dynamics with bounded noise near a saddle-node bifurcation and have potential applications in various nonequilibrium problems, including arrested active matter and cell migration. Y1 - 2024 U6 - https://doi.org/10.1103/PhysRevE.110.L062601 VL - 110 IS - 6 SP - L062601 ER - TY - JOUR A1 - Straube, Arthur A1 - Olicón Méndez, Guillermo A1 - Winkelmann, Stefanie A1 - Höfling, Felix A1 - Engel, Maximilian T1 - Unfolding the geometric structure and multiple timescales of the urea-urease pH oscillator N2 - 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. Y1 - 2025 ER - TY - JOUR A1 - del Razo, Mauricio A1 - Frömberg, Daniela A1 - Straube, Arthur A1 - Schütte, Christof A1 - Höfling, Felix A1 - Winkelmann, Stefanie T1 - A probabilistic framework for particle-based reaction–diffusion dynamics using classical Fock space representations JF - Letters in Mathematical Physics Y1 - 2022 U6 - https://doi.org/10.1007/s11005-022-01539-w VL - 112 IS - 49 ER - TY - JOUR A1 - Straube, Arthur A1 - Winkelmann, Stefanie A1 - Schütte, Christof A1 - Höfling, Felix T1 - Stochastic pH oscillations in a model of the urea–urease reaction confined to lipid vesicles JF - J. Phys. Chem. Lett. N2 - 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. 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. Y1 - 2021 U6 - https://doi.org/10.1021/acs.jpclett.1c03016 VL - 12 SP - 9888 EP - 9893 ER - TY - JOUR A1 - Straube, Arthur A1 - Winkelmann, Stefanie A1 - Höfling, Felix T1 - Accurate reduced models for the pH oscillations in the urea-urease reaction confined to giant lipid vesicles JF - The Journal of Physical Chemistry B N2 - 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. Y1 - 2023 U6 - https://doi.org/10.1021/acs.jpcb.2c09092 VL - 127 IS - 13 SP - 2955 EP - 2967 ER - TY - JOUR A1 - Höfling, Felix A1 - Dietrich, Siegfried T1 - Finite-size corrections for the static structure factor of a liquid slab with open boundaries JF - The Journal of Chemical Physics N2 - The presence of a confining boundary can modify the local structure of a liquid markedly. In addition, small samples of finite size are known to exhibit systematic deviations of thermodynamic quantities relative to their bulk values. Here, we consider the static structure factor of a liquid sample in slab geometry with open boundaries at the surfaces, which can be thought of as virtually cutting out the sample from a macroscopically large, homogeneous fluid. This situation is a relevant limit for the interpretation of grazing-incidence diffraction experiments at liquid interfaces and films. We derive an exact, closed expression for the slab structure factor, with the bulk structure factor as the only input. This shows that such free boundary conditions cause significant differences between the two structure factors, in particular, at small wavenumbers. An asymptotic analysis of this result yields the scaling exponent and an accurate, useful approximation of these finite-size corrections. Furthermore, the open boundaries permit the interpretation of the slab as an open system, supporting particle exchange with a reservoir. We relate the slab structure factor to the particle number fluctuations and discuss conditions under which the subvolume of the slab represents a grand canonical ensemble with chemical potential μ and temperature T. Thus, the open slab serves as a test-bed for the small-system thermodynamics in a μT reservoir. We provide a microscopically justified and exact result for the size dependence of the isothermal compressibility. Our findings are corroborated by simulation data for Lennard-Jones liquids at two representative temperatures. Y1 - 2020 U6 - https://doi.org/10.1063/5.0017923 VL - 153 SP - 054119 ER - TY - JOUR A1 - Ebrahimi Viand, Roya A1 - Höfling, Felix A1 - Klein, Rupert A1 - Delle Site, Luigi T1 - Theory and simulation of open systems out of equilibrium JF - The Journal of Chemical Physics N2 - We consider the theoretical model of Bergmann and Lebowitz for open systems out of equilibrium and translate its principles in the adaptive resolution simulation molecular dynamics technique. We simulate Lennard-Jones fluids with open boundaries in a thermal gradient and find excellent agreement of the stationary responses with the results obtained from the simulation of a larger locally forced closed system. The encouraging results pave the way for a computational treatment of open systems far from equilibrium framed in a well-established theoretical model that avoids possible numerical artifacts and physical misinterpretations. Y1 - 2020 U6 - https://doi.org/10.1063/5.0014065 VL - 153 SP - 101102 ER - TY - GEN A1 - Straube, Arthur A1 - Winkelmann, Stefanie A1 - Höfling, Felix T1 - Accurate reduced models for the pH oscillations in the urea-urease reaction confined to giant lipid vesicles N2 - 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. T3 - ZIB-Report - 22-21 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-88179 SN - 1438-0064 ER - TY - JOUR A1 - del Razo, Mauricio A1 - Winkelmann, Stefanie A1 - Klein, Rupert A1 - Höfling, Felix T1 - Chemical diffusion master equation: formulations of reaction-diffusion processes on the molecular level JF - Journal of Mathematical Physics N2 - The chemical diffusion master equation (CDME) describes the probabilistic dynamics of reaction--diffusion systems at the molecular level [del Razo et al., Lett. Math. Phys. 112:49, 2022]; it can be considered the master equation for reaction--diffusion processes. The CDME consists of an infinite ordered family of Fokker--Planck equations, where each level of the ordered family corresponds to a certain number of particles and each particle represents a molecule. The equations at each level describe the spatial diffusion of the corresponding set of particles, and they are coupled to each other via reaction operators --linear operators representing chemical reactions. These operators change the number of particles in the system, and thus transport probability between different levels in the family. In this work, we present three approaches to formulate the CDME and show the relations between them. We further deduce the non-trivial combinatorial factors contained in the reaction operators, and we elucidate the relation to the original formulation of the CDME, which is based on creation and annihilation operators acting on many-particle probability density functions. Finally we discuss applications to multiscale simulations of biochemical systems among other future prospects. Y1 - 2023 U6 - https://doi.org/10.1063/5.0129620 VL - 64 IS - 1 ER -