TY  - JOUR
A1  - Vahabi, Mahsa
A1  - Schulz, Johannes H. P.
A1  - Shokri, Babak
A1  - Metzler, Ralf
T1  - Area coverage of radial Levy flights with periodic boundary conditions
JF  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - We consider the area coverage of radial Levy flights in a finite square area with periodic boundary conditions. From simulations we show how the fractal path dimension d(f) and thus the degree of area coverage depends on the number of steps of the trajectory, the size of the area, and the resolution of the applied box counting algorithm. For sufficiently long trajectories and not too high resolution, the fractal dimension returned by the box counting method equals two, and in that sense the Levy flight fully covers the area. Otherwise, the determined fractal dimension equals the stable index of the distribution of jump lengths of the Levy flight. We provide mathematical expressions for the turnover between these two scaling regimes. As complementary methods to analyze confined Levy flights we investigate fractional order moments of the position for which we also provide scaling arguments. Finally, we study the time evolution of the probability density function and the first passage time density of Levy flights in a square area. Our findings are of interest for a general understanding of Levy flights as well as for the analysis of recorded trajectories of animals searching for food or for human motion patterns.
Y1  - 2013
U6  - https://doi.org/10.1103/PhysRevE.87.042136
SN  - 1539-3755
VL  - 87
IS  - 4
PB  - American Physical Society
CY  - College Park
ER  - 
TY  - JOUR
A1  - Talukder, Srijeeta
A1  - Sen, Shrabani
A1  - Metzler, Ralf
A1  - Banik, Suman K.
A1  - Chaudhury, Pinaki
T1  - Stochastic optimization-based study of dimerization kinetics
JF  - JOURNAL OF CHEMICAL SCIENCES
N2  - We investigate the potential of numerical algorithms to decipher the kinetic parameters involved in multi-step chemical reactions. To this end, we study dimerization kinetics of protein as a model system. We follow the dimerization kinetics using a stochastic simulation algorithm and combine it with three different optimization techniques (genetic algorithm, simulated annealing and parallel tempering) to obtain the rate constants involved in each reaction step. We find good convergence of the numerical scheme to the rate constants of the process. We also perform a sensitivity test on the reaction kinetic parameters to see the relative effects of the parameters for the associated profile of the monomer/dimer distribution.
KW  - Stochastic optimization
KW  - dimerization kinetics
KW  - sensitivity analysis
KW  - stochastic simulation algorithm
KW  - probability distribution function
Y1  - 2013
SN  - 0974-3626
SN  - 0973-7103
VL  - 125
IS  - 6
SP  - 1619
EP  - 1627
PB  - INDIAN ACAD SCIENCES
CY  - BANGALORE
ER  - 
TY  - JOUR
A1  - Schulz, Johannes H. P.
A1  - Chechkin, Aleksei V.
A1  - Metzler, Ralf
T1  - Correlated continuous time random walks - combining scale-invariance with long-range memory for spatial and temporal dynamics
JF  - Journal of physics : A, Mathematical and theoretical
N2  - Standard continuous time random walk (CTRW) models are renewal processes in the sense that at each jump a new, independent pair of jump length and waiting time are chosen. Globally, anomalous diffusion emerges through scale-free forms of the jump length and/or waiting time distributions by virtue of the generalized central limit theorem. Here we present a modified version of recently proposed correlated CTRW processes, where we incorporate a power-law correlated noise on the level of both jump length and waiting time dynamics. We obtain a very general stochastic model, that encompasses key features of several paradigmatic models of anomalous diffusion: discontinuous, scale-free displacements as in Levy flights, scale-free waiting times as in subdiffusive CTRWs, and the long-range temporal correlations of fractional Brownian motion (FBM). We derive the exact solutions for the single-time probability density functions and extract the scaling behaviours. Interestingly, we find that different combinations of the model parameters lead to indistinguishable shapes of the emerging probability density functions and identical scaling laws. Our model will be useful for describing recent experimental single particle tracking data that feature a combination of CTRW and FBM properties.
Y1  - 2013
U6  - https://doi.org/10.1088/1751-8113/46/47/475001
SN  - 1751-8113
SN  - 1751-8121
VL  - 46
IS  - 47
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  - 
TY  - JOUR
A1  - Schulz, Johannes H. P.
A1  - Barkai, Eli
A1  - Metzler, Ralf
T1  - Aging effects and population splitting in single-particle trajectoryaverages
JF  - Physical review letters
N2  - We study time averages of single particle trajectories in scale-free anomalous diffusion processes, in which the measurement starts at some time t(a) > 0 after initiation of the process at t = 0. Using aging renewal theory, we show that for such nonstationary processes a large class of observables are affected by a unique aging function, which is independent of boundary conditions or the external forces. Moreover, we discuss the implications of aging induced population splitting: with growing age ta of the process, an increasing fraction of particles remains motionless in a measurement of fixed duration. Consequences for single biomolecule tracking in live cells are discussed.
Y1  - 2013
U6  - https://doi.org/10.1103/PhysRevLett.110.020602
SN  - 0031-9007
SN  - 1079-7114
VL  - 110
IS  - 2
PB  - American Physical Society
CY  - College Park
ER  - 
TY  - JOUR
A1  - Pulkkinen, Otto
A1  - Metzler, Ralf
T1  - Distance matters the impact of gene proximity in bacterial gene regulation
JF  - Physical review letters
N2  - Following recent discoveries of colocalization of downstream-regulating genes in living cells, the impact of the spatial distance between such genes on the kinetics of gene product formation is increasingly recognized. We here show from analytical and numerical analysis that the distance between a transcription factor (TF) gene and its target gene drastically affects the speed and reliability of transcriptional regulation in bacterial cells. For an explicit model system, we develop a general theory for the interactions between a TF and a transcription unit. The observed variations in regulation efficiency are linked to the magnitude of the variation of the TF concentration peaks as a function of the binding site distance from the signal source. Our results support the role of rapid binding site search for gene colocalization and emphasize the role of local concentration differences.
Y1  - 2013
U6  - https://doi.org/10.1103/PhysRevLett.110.198101
SN  - 0031-9007
VL  - 110
IS  - 19
PB  - American Physical Society
CY  - College Park
ER  - 
TY  - JOUR
A1  - Maity, Alok Kumar
A1  - Bandyopadhyay, Arnab
A1  - Chattopadhyay, Sudip
A1  - Chaudhuri, Jyotipratim Ray
A1  - Metzler, Ralf
A1  - Chaudhury, Pinaki
A1  - Banik, Suman K.
T1  - Quantification of noise in bifunctionality-induced post-translational modification
JF  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - We present a generic analytical scheme for the quantification of fluctuations due to bifunctionality-induced signal transduction within the members of a bacterial two-component system. The proposed model takes into account post-translational modifications in terms of elementary phosphotransfer kinetics. Sources of fluctuations due to autophosphorylation, kinase, and phosphatase activity of the sensor kinase have been considered in the model via Langevin equations, which are then solved within the framework of linear noise approximation. The resultant analytical expression of phosphorylated response regulators are then used to quantify the noise profile of biologically motivated single and branched pathways. Enhancement and reduction of noise in terms of extra phosphate outflux and influx, respectively, have been analyzed for the branched system. Furthermore, the role of fluctuations of the network output in the regulation of a promoter with random activation-deactivation dynamics has been analyzed.
Y1  - 2013
U6  - https://doi.org/10.1103/PhysRevE.88.032716
SN  - 1539-3755
VL  - 88
IS  - 3
PB  - American Physical Society
CY  - College Park
ER  - 
TY  - JOUR
A1  - Lomholt, Michael A.
A1  - Lizana, Ludvig
A1  - Metzler, Ralf
A1  - Ambjoernsson, Tobias
T1  - Microscopic origin of the logarithmic time evolution of aging processes in complex systems
JF  - Physical review letters
N2  - There exists compelling experimental evidence in numerous systems for logarithmically slow time evolution, yet its full theoretical understanding remains elusive. We here introduce and study a generic transition process in complex systems, based on nonrenewal, aging waiting times. Each state n of the system follows a local clock initiated at t = 0. The random time tau between clock ticks follows the waiting time density psi (tau). Transitions between states occur only at local clock ticks and are hence triggered by the local forward waiting time, rather than by psi (tau). For power-law forms psi (tau) similar or equal to tau(-1-alpha) (0 < alpha < 1) we obtain a logarithmic time evolution of the state number < n(t)> similar or equal to log(t/t(0)), while for alpha > 2 the process becomes normal in the sense that < n(t)> similar or equal to t. In the intermediate range 1 < alpha < 2 we find the power-law growth < n(t)> similar or equal to t(alpha-1). Our model provides a universal description for transition dynamics between aging and nonaging states.
Y1  - 2013
U6  - https://doi.org/10.1103/PhysRevLett.110.208301
SN  - 0031-9007
VL  - 110
IS  - 20
PB  - American Physical Society
CY  - College Park
ER  - 
TY  - JOUR
A1  - Kursawe, Jochen
A1  - Schulz, Johannes H. P.
A1  - Metzler, Ralf
T1  - Transient aging in fractional brownian and langevin-equation motion
JF  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - Stochastic processes driven by stationary fractional Gaussian noise, that is, fractional Brownian motion and fractional Langevin-equation motion, are usually considered to be ergodic in the sense that, after an algebraic relaxation, time and ensemble averages of physical observables coincide. Recently it was demonstrated that fractional Brownian motion and fractional Langevin-equation motion under external confinement are transiently nonergodic-time and ensemble averages behave differently-from the moment when the particle starts to sense the confinement. Here we show that these processes also exhibit transient aging, that is, physical observables such as the time-averaged mean-squared displacement depend on the time lag between the initiation of the system at time t = 0 and the start of the measurement at the aging time t(a). In particular, it turns out that for fractional Langevin-equation motion the aging dependence on ta is different between the cases of free and confined motion. We obtain explicit analytical expressions for the aged moments of the particle position as well as the time-averaged mean-squared displacement and present a numerical analysis of this transient aging phenomenon.
Y1  - 2013
U6  - https://doi.org/10.1103/PhysRevE.88.062124
SN  - 1539-3755
SN  - 1550-2376
VL  - 88
IS  - 6
PB  - American Physical Society
CY  - College Park
ER  - 
TY  - JOUR
A1  - Jeon, Jae-Hyung
A1  - Leijnse, Natascha
A1  - Oddershede, Lene B.
A1  - Metzler, Ralf
T1  - Anomalous diffusion and power-law relaxation of the time averaged mean squared displacement in worm-like micellar solutions
JF  - New journal of physics : the open-access journal for physics
N2  - We report the results of single tracer particle tracking by optical tweezers and video microscopy in micellar solutions. From careful analysis in terms of different stochastic models, we show that the polystyrene tracer beads of size 0.52-2.5 mu m after short-time normal diffusion turn over to perform anomalous diffusion of the form < r(2)(t)> similar or equal to t(alpha) with alpha approximate to 0.3. This free anomalous diffusion is ergodic and consistent with a description in terms of the generalized Langevin equation with a power-law memory kernel. With optical tweezers tracking, we unveil a power-law relaxation over several decades in time to the thermal plateau value under the confinement of the harmonic tweezer potential, as predicted previously (Phys. Rev. E 85 021147 (2012)). After the subdiffusive motion in the millisecond range, the motion becomes faster and turns either back to normal Brownian diffusion or to even faster superdiffusion, depending on the size of the tracer beads.
Y1  - 2013
U6  - https://doi.org/10.1088/1367-2630/15/4/045011
SN  - 1367-2630
VL  - 15
IS  - 4
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  - 
TY  - JOUR
A1  - Jeon, Jae-Hyung
A1  - Barkai, Eli
A1  - Metzler, Ralf
T1  - Noisy continuous time random walks
JF  - The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr
N2  - Experimental studies of the diffusion of biomolecules within biological cells are routinely confronted with multiple sources of stochasticity, whose identification renders the detailed data analysis of single molecule trajectories quite intricate. Here, we consider subdiffusive continuous time random walks that represent a seminal model for the anomalous diffusion of tracer particles in complex environments. This motion is characterized by multiple trapping events with infinite mean sojourn time. In real physical situations, however, instead of the full immobilization predicted by the continuous time random walk model, the motion of the tracer particle shows additional jiggling, for instance, due to thermal agitation of the environment. We here present and analyze in detail an extension of the continuous time random walk model. Superimposing the multiple trapping behavior with additive Gaussian noise of variable strength, we demonstrate that the resulting process exhibits a rich variety of apparent dynamic regimes. In particular, such noisy continuous time random walks may appear ergodic, while the bare continuous time random walk exhibits weak ergodicity breaking. Detailed knowledge of this behavior will be useful for the truthful physical analysis of experimentally observed subdiffusion.
Y1  - 2013
U6  - https://doi.org/10.1063/1.4816635
SN  - 0021-9606
SN  - 1089-7690
VL  - 139
IS  - 12
PB  - American Institute of Physics
CY  - Melville
ER  - 
TY  - JOUR
A1  - Javanainen, Matti
A1  - Hammaren, Henrik
A1  - Monticelli, Luca
A1  - Jeon, Jae-Hyung
A1  - Miettinen, Markus S.
A1  - Martinez-Seara, Hector
A1  - Metzler, Ralf
A1  - Vattulainen, Ilpo
T1  - Anomalous and normal diffusion of proteins and lipids in crowded lipid membranes
JF  - Faraday discussions
N2  - Lateral diffusion plays a crucial role in numerous processes that take place in cell membranes, yet it is quite poorly understood in native membranes characterized by, e.g., domain formation and large concentration of proteins. In this article, we use atomistic and coarse-grained simulations to consider how packing of membranes and crowding with proteins affect the lateral dynamics of lipids and membrane proteins. We find that both packing and protein crowding have a profound effect on lateral diffusion, slowing it down. Anomalous diffusion is observed to be an inherent property in both protein-free and protein-rich membranes, and the time scales of anomalous diffusion and the exponent associated with anomalous diffusion are found to strongly depend on packing and crowding. Crowding with proteins also has a striking effect on the decay rate of dynamical correlations associated with lateral single-particle motion, as the transition from anomalous to normal diffusion is found to take place at macroscopic time scales: while in protein-poor conditions normal diffusion is typically observed in hundreds of nanoseconds, in protein-rich conditions the onset of normal diffusion is tens of microseconds, and in the most crowded systems as large as milliseconds. The computational challenge which results from these time scales is not easy to deal with, not even in coarse-grained simulations. We also briefly discuss the physical limits of protein motion. Our results suggest that protein concentration is anything but constant in the plane of cell membranes. Instead, it is strongly dependent on proteins' preference for aggregation.
Y1  - 2013
U6  - https://doi.org/10.1039/c2fd20085f
SN  - 1359-6640
VL  - 161
IS  - 1
SP  - 397
EP  - 417
PB  - Royal Society of Chemistry
CY  - Cambridge
ER  - 
TY  - JOUR
A1  - Godec, Aljaz
A1  - Metzler, Ralf
T1  - Finite-Time effects and ultraweak ergodicity breaking in superdiffusive dynamics
JF  - Physical review letters
N2  - We study the ergodic properties of superdiffusive, spatiotemporally coupled Levy walk processes. For trajectories of finite duration, we reveal a distinct scatter of the scaling exponents of the time averaged mean squared displacement (delta x(2)) over bar around the ensemble value 3 - alpha (1 < alpha < 2) ranging from ballistic motion to subdiffusion, in strong contrast to the behavior of subdiffusive processes. In addition we find a significant dependence of the average of (delta x(2)) over bar over an ensemble of trajectories as a function of the finite measurement time. This so-called finite-time amplitude depression and the scatter of the scaling exponent is vital in the quantitative evaluation of superdiffusive processes. Comparing the long time average of the second moment with the ensemble mean squared displacement, these only differ by a constant factor, an ultraweak ergodicity breaking.
Y1  - 2013
U6  - https://doi.org/10.1103/PhysRevLett.110.020603
SN  - 0031-9007
VL  - 110
IS  - 2
PB  - American Physical Society
CY  - College Park
ER  - 
TY  - JOUR
A1  - Eliazar, Iddo
A1  - Metzler, Ralf
T1  - Anomalous statistics of random relaxations in random environments
JF  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - We comprehensively analyze the emergence of anomalous statistics in the context of the random relaxation ( RARE) model [Eliazar and Metzler, J. Chem. Phys. 137, 234106 ( 2012)], a recently introduced versatile model of random relaxations in random environments. The RARE model considers excitations scattered randomly across a metric space around a reaction center. The excitations react randomly with the center, the reaction rates depending on the excitations' distances from this center. Relaxation occurs upon the first reaction between an excitation and the center. Addressing both the relaxation time and the relaxation range, we explore when these random variables display anomalous statistics, namely, heavy tails at zero and at infinity that manifest, respectively, exceptionally high occurrence probabilities of very small and very large outliers. A cohesive set of closed-form analytic results is established, determining precisely when such anomalous statistics emerge.
Y1  - 2013
U6  - https://doi.org/10.1103/PhysRevE.87.022141
SN  - 1539-3755
SN  - 1550-2376
VL  - 87
IS  - 2
PB  - American Physical Society
CY  - College Park
ER  - 
TY  - GEN
A1  - Cherstvy, Andrey G.
A1  - Metzler, Ralf
T1  - Population splitting, trapping, and non-ergodicity in heterogeneous diffusion processes
N2  - We consider diffusion processes with a spatially varying diffusivity giving rise to anomalous diffusion. Such heterogeneous diffusion processes are analysed for the cases of exponential, power-law, and logarithmic dependencies of the diffusion coefficient on the particle position. Combining analytical approaches with stochastic simulations, we show that the functional form of the space-dependent diffusion coefficient and the initial conditions of the diffusing particles are vital for their statistical and ergodic properties. In all three cases a weak ergodicity breaking between the time and ensemble averaged mean squared displacements is observed. We also demonstrate a population splitting of the time averaged traces into fast and slow diffusers for the case of exponential variation of the diffusivity as well as a particle trapping in the case of the logarithmic diffusivity. Our analysis is complemented by the quantitative study of the space coverage, the diffusive spreading of the probability density, as well as the survival probability.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 236 
KW  - anomalous diffusion
KW  - disordered media
KW  - fractional dynamics
KW  - infection pathway
KW  - inhomogeneous-media
KW  - intracellular-transport
KW  - langevin equation
KW  - living cells
KW  - random-walks
KW  - single-particle tracking
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-94468
SP  - 20220
EP  - 20235
ER  - 
TY  - JOUR
A1  - Cherstvy, Andrey G.
A1  - Metzler, Ralf
T1  - Population splitting, trapping, and non-ergodicity in heterogeneous diffusion processes
JF  - Physical chemistry, chemical physics : a journal of European Chemical Societies
N2  - We consider diffusion processes with a spatially varying diffusivity giving rise to anomalous diffusion. Such heterogeneous diffusion processes are analysed for the cases of exponential, power-law, and logarithmic dependencies of the diffusion coefficient on the particle position. Combining analytical approaches with stochastic simulations, we show that the functional form of the space-dependent diffusion coefficient and the initial conditions of the diffusing particles are vital for their statistical and ergodic properties. In all three cases a weak ergodicity breaking between the time and ensemble averaged mean squared displacements is observed. We also demonstrate a population splitting of the time averaged traces into fast and slow diffusers for the case of exponential variation of the diffusivity as well as a particle trapping in the case of the logarithmic diffusivity. Our analysis is complemented by the quantitative study of the space coverage, the diffusive spreading of the probability density, as well as the survival probability.
Y1  - 2013
U6  - https://doi.org/10.1039/c3cp53056f
SN  - 1463-9076
SN  - 1463-9084
VL  - 15
IS  - 46
SP  - 20220
EP  - 20235
PB  - Royal Society of Chemistry
CY  - Cambridge
ER  - 
TY  - JOUR
A1  - Cherstvy, Andrey G.
A1  - Chechkin, Aleksei V.
A1  - Metzler, Ralf
T1  - Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes
JF  - New journal of physics : the open-access journal for physics
N2  - We demonstrate the non-ergodicity of a simple Markovian stochastic process with space-dependent diffusion coefficient D(x). For power-law forms D(x) similar or equal to vertical bar x vertical bar(alpha), this process yields anomalous diffusion of the form < x(2)(t)> similar or equal to t(2/(2-alpha)). Interestingly, in both the sub- and superdiffusive regimes we observe weak ergodicity breaking: the scaling of the time-averaged mean-squared displacement <(delta(2)(Delta))over bar> remains linear in the lag time Delta and thus differs from the corresponding ensemble average < x(2)(t)>. We analyse the non-ergodic behaviour of this process in terms of the time-averaged mean- squared displacement (delta(2)) over bar and its random features, i.e. the statistical distribution of (delta(2)) over bar and the ergodicity breaking parameters. The heterogeneous diffusion model represents an alternative approach to non- ergodic, anomalous diffusion that might be particularly relevant for diffusion in heterogeneous media.
Y1  - 2013
U6  - https://doi.org/10.1088/1367-2630/15/8/083039
SN  - 1367-2630
VL  - 15
IS  - 15
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  - 
TY  - GEN
A1  - Chechkin, Aleksei V.
A1  - Zaid, Irwin M.
A1  - Lomholt, Michael A.
A1  - Sokolov, Igor M.
A1  - Metzler, Ralf
T1  - Bulk-mediated surface diffusion on a cylinder in the fast exchange limit
T2  - Postprints der Universität Potsdam : Mathematisch Naturwissenschaftliche Reihe
N2  - In various biological systems and small scale technological applications particles transiently bind to a cylindrical surface. Upon unbinding the particles diffuse in the vicinal bulk before rebinding to the surface. Such bulk-mediated excursions give rise to an effective surface translation, for which we here derive and discuss the dynamic equations, including additional surface diffusion. We discuss the time evolution of the number of surface-bound particles, the effective surface mean squared displacement, and the surface propagator. In particular, we observe sub- and superdiffusive regimes. A plateau of the surface mean-squared displacement reflects a stalling of the surface diffusion at longer times. Finally, the corresponding first passage problem for the cylindrical geometry is analysed.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 593 
KW  - Bulk-mediated diffusion;
KW  - anomalous diffusion
KW  - Levy flights
KW  - stochastic processes
Y1  - 2019
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-415480
SN  - 1866-8372
IS  - 593
SP  - 114
EP  - 126
ER  - 
TY  - JOUR
A1  - Chechkin, Aleksei V.
A1  - Zaid, I. M.
A1  - Lomholt, M. A.
A1  - Sokolov, Igor M.
A1  - Metzler, Ralf
T1  - Bulk-mediated surface diffusion on a cylinder in the fast exchange limit
JF  - Mathematical modelling of natural phenomena
N2  - In various biological systems and small scale technological applications particles transiently bind to a cylindrical surface. Upon unbinding the particles diffuse in the vicinal bulk before rebinding to the surface. Such bulk-mediated excursions give rise to an effective surface translation, for which we here derive and discuss the dynamic equations, including additional surface diffusion. We discuss the time evolution of the number of surface-bound particles, the effective surface mean squared displacement, and the surface propagator. In particular, we observe sub- and superdiffusive regimes. A plateau of the surface mean-squared displacement reflects a stalling of the surface diffusion at longer times. Finally, the corresponding first passage problem for the cylindrical geometry is analysed.
KW  - Bulk-mediated diffusion
KW  - anomalous diffusion
KW  - Levy flights
KW  - stochastic processes
Y1  - 2013
U6  - https://doi.org/10.1051/mmnp/20138208
SN  - 0973-5348
VL  - 8
IS  - 2
SP  - 114
EP  - 126
PB  - EDP Sciences
CY  - Les Ulis
ER  - 
TY  - JOUR
A1  - Bauer, Maximilian
A1  - Metzler, Ralf
T1  - In vivo facilitated diffusion model
JF  - PLoS one
N2  - Under dilute in vitro conditions transcription factors rapidly locate their target sequence on DNA by using the facilitated diffusion mechanism. However, whether this strategy of alternating between three-dimensional bulk diffusion and one-dimensional sliding along the DNA contour is still beneficial in the crowded interior of cells is highly disputed. Here we use a simple model for the bacterial genome inside the cell and present a semi-analytical model for the in vivo target search of transcription factors within the facilitated diffusion framework. Without having to resort to extensive simulations we determine the mean search time of a lac repressor in a living E. coli cell by including parameters deduced from experimental measurements. The results agree very well with experimental findings, and thus the facilitated diffusion picture emerges as a quantitative approach to gene regulation in living bacteria cells. Furthermore we see that the search time is not very sensitive to the parameters characterizing the DNA configuration and that the cell seems to operate very close to optimal conditions for target localization. Local searches as implied by the colocalization mechanism are only found to mildly accelerate the mean search time within our model.
Y1  - 2013
U6  - https://doi.org/10.1371/journal.pone.0053956
SN  - 1932-6203
VL  - 8
IS  - 1
PB  - PLoS
CY  - San Fransisco
ER  - 
TY  - GEN
A1  - Barkai, Eli
A1  - Garini, Yuval
A1  - Metzler, Ralf
T1  - Electrostatic effects in living cells Reply
T2  - PHYSICS TODAY
Y1  - 2013
SN  - 0031-9228
SN  - 1945-0699
VL  - 66
IS  - 7
SP  - 11
EP  - 11
PB  - AMER INST PHYSICS
CY  - MELVILLE
ER  -