Uphill Motion of Active Brownian Particles in Piecewise Linear Potentials

We consider Brownian particles with the ability to take up energy from the environment, to store it in an internal depot, and to convert internal energy into kinetic energy of motion. Provided a supercritical supply of energy, these particles are able to move in a ``high velocity'' or active mode, which allows them to move also against the gradient of an external potential. We investigate the critical energetic conditions of this self-driven motion for the case of a linear potential and a ratchet potential. In the latter case, we are able to find two different critical conversion rates for the internal energy, which describe the onset of a directed net current into the two different directions. The results of computer simulations are confirmed by analytical expressions for the critical parameters and the average velocity of the net current. Further, we investigate the influence of the asymmetry of the ratchet potential on the net current and estimate a critical value for the asymmetry in order to obtain a positive or negative net current.Comment: accepted for publication in European Journal of Physics B (1999), for related work see http://summa.physik.hu-berlin.de/~frank/active.htm

Directed motion of Brownian particles with internal energy depot

A model of Brownian particles with the ability to take up energy from the environment, to store it in an internal depot, and to convert internal energy into kinetic energy of motion, is discussed. The general dynamics outlined in Sect. 2 is investigated for the deterministic and stochastic particle's motion in a non-fluctuating ratchet potential. First, we discuss the attractor structure of the ratchet system by means of computer simulations. Dependent on the energy supply, we find either periodic bound attractors corresponding to localized oscillations, or one/two unbound attractors corresponding to directed movement in the ratchet potential. Considering an ensemble of particles, we show that in the deterministic case two currents into different directions can occur, which however depend on a supercritical supply of energy. Considering stochastic influences, we find the current only in one direction. We further investigate how the current reversal depends on the strength of the stochastic force and the asymmetry of the potential. We find both a critical value of the noise intensity for the onset of the current and an optimal value where the net current reaches a maximum. Eventually, the dynamics of our model is compared with other ratchet models previously suggested.Comment: 24 pages, 11 Figs., For related work see http://summa.physik.hu-berlin.de/~frank/active.htm

Spin dynamics calculations of electron and nuclear spin relaxation times in paramagnetic solutions

Spin dynamics (SD) methods have been developed to compute NMR paramagnetic relaxation enhancements (NMR-PRE) produced by solutes with electron spin S ≥ 1S⩾1 in solution. The spin dynamics algorithms, which are implemented as the computer program SpinDyn.f, are similar in spirit to molecular dynamics calculations in statistical mechanics, except that the spin motion is propagated numerically in time using quantum mechanical equations of motion of the spin operators, rather than Newtonian equations of motion of the molecular degrees of freedom as in MD simulations. SD simulations as implemented in SpinDyn.f provide accurate, flexible, and rapid calculations of NMR-PRE phenomena with few of the assumptions or limitations of previous analytical theories. The program calculates inter- and intramolecular NMR-PRE phenomena for both integer and half-integer spin systems processing under arbitrary Zeeman and zfs Hamiltonians in the presence of Brownian reorientation. Isotropic Brownian reorientation is simulated by means of a finite-step algorithm with adjustable step size. Simulations computed by SpinDyn.f have been used in a systematic study aimed at better understanding the influence of Brownian reorientation on the NMR-PRE of an S = 1S=1 ion in a non-Zeeman-limit physical situation. Conditions required for the validity of zfs-limit analytical theory are given. SpinDyn.f has also been used to assess quantitatively the effects of molecular reorientation on a prior analysis of NMR-PRE data for the model S = 2S=2 complex ion [tris-(acetylacetonato)manganese(III)] in acetone solution; this system was found to be well described by zfs-limit analytical theory. © 1997 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69991/2/JCPSA6-106-22-9032-1.pd

Anomalous transport in the crowded world of biological cells

A ubiquitous observation in cell biology is that diffusion of macromolecules and organelles is anomalous, and a description simply based on the conventional diffusion equation with diffusion constants measured in dilute solution fails. This is commonly attributed to macromolecular crowding in the interior of cells and in cellular membranes, summarising their densely packed and heterogeneous structures. The most familiar phenomenon is a power-law increase of the MSD, but there are other manifestations like strongly reduced and time-dependent diffusion coefficients, persistent correlations, non-gaussian distributions of the displacements, heterogeneous diffusion, and immobile particles. After a general introduction to the statistical description of slow, anomalous transport, we summarise some widely used theoretical models: gaussian models like FBM and Langevin equations for visco-elastic media, the CTRW model, and the Lorentz model describing obstructed transport in a heterogeneous environment. Emphasis is put on the spatio-temporal properties of the transport in terms of 2-point correlation functions, dynamic scaling behaviour, and how the models are distinguished by their propagators even for identical MSDs. Then, we review the theory underlying common experimental techniques in the presence of anomalous transport: single-particle tracking, FCS, and FRAP. We report on the large body of recent experimental evidence for anomalous transport in crowded biological media: in cyto- and nucleoplasm as well as in cellular membranes, complemented by in vitro experiments where model systems mimic physiological crowding conditions. Finally, computer simulations play an important role in testing the theoretical models and corroborating the experimental findings. The review is completed by a synthesis of the theoretical and experimental progress identifying open questions for future investigation.Comment: review article, to appear in Rep. Prog. Phy

Statistical Mechanics of Canonical-Dissipative Systems and Applications to Swarm Dynamics

We develop the theory of canonical-dissipative systems, based on the assumption that both the conservative and the dissipative elements of the dynamics are determined by invariants of motion. In this case, known solutions for conservative systems can be used for an extension of the dynamics, which also includes elements such as the take-up/dissipation of energy. This way, a rather complex dynamics can be mapped to an analytically tractable model, while still covering important features of non-equilibrium systems. In our paper, this approach is used to derive a rather general swarm model that considers (a) the energetic conditions of swarming, i.e. for active motion, (b) interactions between the particles based on global couplings. We derive analytical expressions for the non-equilibrium velocity distribution and the mean squared displacement of the swarm. Further, we investigate the influence of different global couplings on the overall behavior of the swarm by means of particle-based computer simulations and compare them with the analytical estimations.Comment: 14 pages incl. 13 figures. v2: misprints in Eq. (40) corrected, ref. updated. For related work see also: http://summa.physik.hu-berlin.de/~frank/active.htm

A flexible architecture for modeling and simulation of diffusional association

Up to now, it is not possible to obtain analytical solutions for complex molecular association processes (e.g. Molecule recognition in Signaling or catalysis). Instead Brownian Dynamics (BD) simulations are commonly used to estimate the rate of diffusional association, e.g. to be later used in mesoscopic simulations. Meanwhile a portfolio of diffusional association (DA) methods have been developed that exploit BD. However, DA methods do not clearly distinguish between modeling, simulation, and experiment settings. This hampers to classify and compare the existing methods with respect to, for instance model assumptions, simulation approximations or specific optimization strategies for steering the computation of trajectories. To address this deficiency we propose FADA (Flexible Architecture for Diffusional Association) - an architecture that allows the flexible definition of the experiment comprising a formal description of the model in SpacePi, different simulators, as well as validation and analysis methods. Based on the NAM (Northrup-Allison-McCammon) method, which forms the basis of many existing DA methods, we illustrate the structure and functioning of FADA. A discussion of future validation experiments illuminates how the FADA can be exploited in order to estimate reaction rates and how validation techniques may be applied to validate additional features of the model