Weak Pinning and Long-Range Anticorrelated Motion of Phase Boundaries in Driven Diffusive Systems.

We show that domain walls separating coexisting extremal current phases in driven diffusive systems exhibit complex stochastic dynamics with a subdiffusive temporal growth of position fluctuations due to long-range anticorrelated current fluctuations and a weak pinning at long times. This weak pinning manifests itself in a saturated width of the domain wall position fluctuations that increases sublinearly with the system size. As a function of time t and system size L, the width w(t,L) has a scaling behavior w(t,L)=L^{3/4}f(t/L^{9/4}), with f(u) constant for u≫1 and f(u)∼u^{1/3} for u≪1. An Orstein-Uhlenbeck process with long-range anticorrelated noise is shown to capture this scaling behavior. The exponent 9/4 is a new dynamical exponent for relaxation processes in driven diffusive systems.

Stochastic thermodynamics and modes of operation of a ribosome: A network theoretic perspective.

The ribosome is one of the largest and most complex macromolecular machines in living cells. It polymerizes a protein in a step-by-step manner as directed by the corresponding nucleotide sequence on the template messenger RNA (mRNA) and this process is referred to as "translation" of the genetic message encoded in the sequence of mRNA transcript. In each successful chemomechanical cycle during the (protein) elongation stage, the ribosome elongates the protein by a single subunit, called amino acid, and steps forward on the template mRNA by three nucleotides called a codon. Therefore, a ribosome is also regarded as a molecular motor for which the mRNA serves as the track, its step size is that of a codon and two molecules of GTP and one molecule of ATP hydrolyzed in that cycle serve as its fuel. What adds further complexity is the existence of competing pathways leading to distinct cycles, branched pathways in each cycle, and futile consumption of fuel that leads neither to elongation of the nascent protein nor forward stepping of the ribosome on its track. We investigate a model formulated in terms of the network of discrete chemomechanical states of a ribosome during the elongation stage of translation. The model is analyzed using a combination of stochastic thermodynamic and kinetic analysis based on a graph-theoretic approach. We derive the exact solution of the corresponding master equations. We represent the steady state in terms of the cycles of the underlying network and discuss the energy transduction processes. We identify the various possible modes of operation of a ribosome in terms of its average velocity and mean rate of GTP hydrolysis. We also compute entropy production as functions of the rates of the interstate transitions and the thermodynamic cost for accuracy of the translation process.

Kardar-Parisi-Zhang universality of the Nagel-Schreckenberg model.

Dynamical universality classes are distinguished by their dynamical exponent z and unique scaling functions encoding space-time asymmetry for, e.g., slow-relaxation modes or the distribution of time-integrated currents. So far the universality class of the Nagel-Schreckenberg (NaSch) model, which is a paradigmatic model for traffic flow on highways, was not known. Only the special case v_{max}=1, where the model corresponds to the totally asymmetric simple exclusion process, is known to belong to the superdiffusive Kardar-Parisi-Zhang (KPZ) class with z=3/2. In this paper, we show that the NaSch model also belongs to the KPZ class for general maximum velocities v_{max}>1. Using nonlinear fluctuating hydrodynamics theory we calculate the nonuniversal coefficients, fixing the exact asymptotic solutions for the dynamical structure function and the distribution of time-integrated currents. The results of large-scale Monte Carlo simulations match the exact asymptotic KPZ solutions without any fitting parameter left. Additionally, we find that nonuniversal early-time effects or the choice of initial conditions might have a strong impact on the numerical determination of the dynamical exponent and therefore lead to inconclusive results. We also show that the universality class is not changed by extending the model to a two-lane NaSch model with lane-changing rules.

Fibonacci family of dynamical universality classes.

Universality is a well-established central concept of equilibrium physics. However, in systems far away from equilibrium, a deeper understanding of its underlying principles is still lacking. Up to now, a few classes have been identified. Besides the diffusive universality class with dynamical exponent [Formula: see text], another prominent example is the superdiffusive Kardar-Parisi-Zhang (KPZ) class with [Formula: see text]. It appears, e.g., in low-dimensional dynamical phenomena far from thermal equilibrium that exhibit some conservation law. Here we show that both classes are only part of an infinite discrete family of nonequilibrium universality classes. Remarkably, their dynamical exponents [Formula: see text] are given by ratios of neighboring Fibonacci numbers, starting with either [Formula: see text] (if a KPZ mode exist) or [Formula: see text] (if a diffusive mode is present). If neither a diffusive nor a KPZ mode is present, all dynamical modes have the Golden Mean [Formula: see text] as dynamical exponent. The universal scaling functions of these Fibonacci modes are asymmetric Lévy distributions that are completely fixed by the macroscopic current density relation and compressibility matrix of the system and hence accessible to experimental measurement.

Motor and behavioral phenotype in conditional mutants with targeted ablation of cortical D1 dopamine receptor-expressing cells.

D1-dopamine receptors (Drd1a) are highly expressed in the deep layers of the cerebral cortex and the striatum. A number of human diseases such as Huntington disease and schizophrenia are known to have cortical pathology involving dopamine receptor expressing neurons. To illuminate their functional role, we exploited a Cre/Lox molecular paradigm to generate Emx-1(tox) MUT mice, a transgenic line in which cortical Drd1a-expressing pyramidal neurons were selectively ablated. Emx-1(tox) MUT mice displayed prominent forelimb dystonia, hyperkinesia, ataxia on rotarod testing, heightened anxiety-like behavior, and age-dependent abnormalities in a test of social interaction. The latter occurred in the context of normal working memory on testing in the Y-maze and for novel object recognition. Some motor and behavioral abnormalities in Emx-1(tox) MUT mice overlapped with those in CamKIIα(tox) MUT transgenic mice, a line in which both striatal and cortical Drd1a-expressing cells were ablated. Although Emx-1(tox) MUT mice had normal striatal anatomy, both Emx-1(tox) MUT and CamKIIα(tox) MUT mice displayed selective neuronal loss in cortical layers V and VI. This study shows that loss of cortical Drd1a-expressing cells is sufficient to produce deficits in multiple motor and behavioral domains, independent of striatal mechanisms. Primary cortical changes in the D1 dopamine receptor compartment are therefore likely to model a number of core clinical features in disorders such as Huntington disease and schizophrenia.

Phenotyping dividing cells in mouse models of neurodegenerative basal ganglia diseases.

BACKGROUND: Mice generated by a Cre/LoxP transgenic paradigm were used to model neurodegenerative basal ganglia disease of which Huntington disease (HD) is the prototypical example. In HD, death occurs in striatal projection neurons as well as cortical neurons. Cortical and striatal neurons that express the D1 dopamine receptor (Drd1a) degenerate in HD. The contribution that death of specific neuronal cell populations makes to the HD disease phenotype and the response of the brain to loss of defined cell subtypes is largely unknown. METHODS: Drd1a-expressing cells were targeted for cell death and three independent lines generated; a striatal-restricted line, a cortical-restricted line and a global line in which Drd1a cells were deleted from both the striatum and cortex. Two independent experimental approaches were used. In the first, the proliferative marker Ki-67 was used to identify proliferating cells in eighty-week-old mice belonging to a generic global line, a global in which Drd1a cells express green fluorescent protein (GFP-global) and in eighty-week-old mice of a cortical line. In the second experiment, the proliferative response of four-week-old mice belonging to GFP-global and striatal lines was assessed using the thymidine analogue BrdU. The phenotype of proliferating cells was ascertained by double staining for BrdU and Olig2 (an oligodendrocyte marker), Iba1 (a microglial cell marker), S100ß (an astroglial cell marker), or NeuN (a neuronal cell marker). RESULTS: In the first study, we found that Ki-67-expressing cells were restricted to the striatal side of the lateral ventricles. Control mice had a greater number of Ki-67+ cells than mutant mice. There was no overlap between Ki-67 and GFP staining in control or mutant mice, suggesting that cells did not undergo cell division once they acquired a Drd1a phenotype. In contrast, in the second study we found that BrdU+ cells were identified throughout the cortex, striatum and periventricular region of control and mutant mice. Mutant mice from the GFP-global line showed increased BrdU+ cells in the cortex, striatum and periventricular region relative to control. Striatal line mutant mice had an increased number of BrdU+ cells in the striatum and periventricular region, but not the cortex. The number of microglia, astrocytes, oligodendrocytes and neurons generated from dividing progenitors was increased relative to control mice in most brain regions in mutant mice from the GFP-global line. In contrast, striatal line mutant mice displayed an increase only in the number of dividing microglia in striatal and periventricular regions. CONCLUSIONS: Genetically programmed post-natal ablation of Drd1a-expressing neurons is associated with an extensive proliferative response involving multiple cell lineages. The nature of the tissue response has the potential not only to remove cellular debris but also to forge physiologically meaningful brain repair. Age related deficits in proliferation are seen in mutant lines. A blunted endogenous reparative response may underlie the cumulative deficits characteristic of age related neurodegeneration.

Non-Gaussian propagator for elephant random walks.

For almost a decade the consensus has held that the random walk propagator for the elephant random walk (ERW) model is a Gaussian. Here we present strong numerical evidence that the propagator is, in general, non-Gaussian and, in fact, non-Lévy. Motivated by this surprising finding, we seek a second, non-Gaussian solution to the associated Fokker-Planck equation. We prove mathematically, by calculating the skewness, that the ERW Fokker-Planck equation has a non-Gaussian propagator for the superdiffusive regime. Finally, we discuss some unusual aspects of the propagator in the context of higher order terms needed in the Fokker-Planck equation.

Emergent motion of condensates in mass-transport models.

We examine the effect of spatial correlations on the phenomenon of real-space condensation in driven mass-transport systems. We suggest that in a broad class of models with a spatially correlated steady state, the condensate drifts with a nonvanishing velocity. We present a robust mechanism leading to this condensate drift. This is done within the framework of a generalized zero-range process (ZRP) in which, unlike the usual ZRP, the steady state is not a product measure. The validity of the mechanism in other mass-transport models is discussed.

Behavioural and anatomical characterization of mutant mice with targeted deletion of D1 dopamine receptor-expressing cells: response to acute morphine.

Considerable topographic overlap exists between brain opioidergic and dopaminergic neurons. Pharmacological blockade of the dopamine D(1) receptor (Drd1a) reverses several behavioural phenomena elicited by opioids. The present study examines the effects of morphine in adult mutant (MUT) mice expressing the attenuated diphtheria toxin-176 gene in Drd1a-expressing cells, a mutant line shown previously to undergo post-natal striatal atrophy and loss of Drd1a-expression. MUT and wild-type mice were assessed behaviourally following acute administration of 10 mg/kg morphine. Treatment with morphine reduced locomotion and rearing similarly in both genotypes but reduced total grooming only in MUT mice. Morphine-induced Straub tail and stillness were heightened in MUT mice. Chewing and sifting were decreased in MUT mice and these effects were not modified by morphine. Loss of striatal Drd1-positive cells and up-regulated D(2)-expression, as reflected in down-regulated D(1)-like and up-regulated D(2)-like binding, respectively, is not uniform along the cranio-caudal extent in this model but appears to be greater in the caudal striatum. Preferential caudal loss of µ-opioid-expression, a marker for the striosomal compartment, was seen. These data indicate that Drd1a-positive cell loss modifies the exploratory behavioural response elicited by morphine, unmasking novel morphine-induced MUT-specific behaviours and generating a hypersensitivity to morphine for others.

Unusual shock wave in two-species driven systems with an umbilic point.

Using dynamical Monte Carlo simulations we observe the occurrence of an unexpected shock wave in driven diffusive systems with two conserved species of particles. This U shock is microscopically sharp, but does not satisfy the usual criteria for the stability of shocks. Exact analysis of the large-scale hydrodynamic equations of motion reveals the presence of an umbilical point which we show to be responsible for this phenomenon. We prove that such an umbilical point is a general feature of multispecies driven diffusive systems with reflection symmetry of the bulk dynamics. We argue that a U shock will occur whenever there are strong interactions between species such that the current-density relation develops a double well and the umbilical point becomes isolated.

Glucocorticoid receptor dimerization is required for survival in septic shock via suppression of interleukin-1 in macrophages.

Sepsis is controlled by endogenous glucocorticoids (GCs). Previous studies provided evidence that crosstalk of the monomeric GC receptor (GR) with proinflammatory transcription factors is the crucial mechanism underlying the suppressive GC effect. Here we demonstrate that mice with a dimerization-deficient GR (GR(dim)) are highly susceptible to sepsis in 2 different models, namely cecal ligation and puncture and lipopolysaccharide (LPS)-induced septic shock. TNF-α is normally regulated in these mice, but down-regulation of IL-6 and IL-1ß is diminished. LPS-treated macrophages derived from GR(dim) mice are largely resistant to GC actions in vitro in terms of morphology, surface marker expression, and gene expression. Treatment with recombinant IL-1 receptor antagonist improved survival of GR(dim) mice and mice lacking the GR in macrophages (GR(LysMCre)) mice. This suggests that regulation of IL-1ß in macrophages by GCs is pivotal to control sepsis.

Approach to equilibrium of diffusion in a logarithmic potential.

The late-time distribution function P(x,t) of a particle diffusing in a one-dimensional logarithmic potential is calculated for arbitrary initial conditions. We find a scaling solution with three surprising features: (i) the solution is given by two distinct scaling forms, corresponding to a diffusive (x∼t(1/2)) and a subdiffusive (x∼t(γ) with a given γ<1/2) length scale, respectively, (ii) the overall scaling function is selected by the initial condition, and (iii) depending on the tail of the initial condition, the scaling exponent that characterizes the scaling function is found to exhibit a transition from a continuously varying to a fixed value.

Strong molecular traffic control effect in TNU-9 zeolite channel topology.

Reactivity enhancement in a catalytic zeolite grain through molecular traffic control (MTC) rests on the basic notion that the reactant and product molecules prefer to diffuse along different channels inside the grain and therefore do not mutually hinder their transport in and out of the grain. We investigate the conditions of reactivity enhancement in the presence of MTC for a realistic channel topology that describes the pore structure of a TNU-9 zeolite. We compare the output current of an MTC system with a reference system, which does not show any channel selectivity. For a wide range of reaction rates and for different grain sizes, we find that there is a very significant enhancement of reactivity for the MTC system. This effect remains strong as the grain size increases. The mechanism behind reactivity enhancement is argued to be generic rather than being confined to the particular structure of TNU-9.

Phenotypic disruption to orofacial movement topography in conditional mutants with generalized CamKIIa/Cre D1Tox versus striatal-specific DARPP-32/Cre D1Tox ablation of D1 dopamine receptor-expressing cells.

Orofacial movements were quantified in (a) DARPP-32/Cre D1Tox mutants, having progressive loss of D1 dopamine receptor expressing striatal medium spiny neurons and (b) CamKIIa/Cre D1Tox mutants, having progressive, generalized loss of forebrain D1 receptor expressing cells. Horizontal jaw movements and tongue protrusions were reduced in DARPP-32/Cre but not in CamKIIa/Cre mutants; head and vibrissae movements were increased in DARPP-32/Cre but decreased in CamKIIa/Cre mutants. In drug challenge studies, tongue protrusions were increased in CamKIIa/Cre mutants following vehicle, suggesting a stress-related phenotype. These findings indicate that mice with progressive loss of striatal-specific D1 receptor expressing cells have an orofacial phenotype that may be modulated by the loss of extrastriatal D1 receptor expressing cells. As progressive loss of D1 dopamine receptor-expressing cells is a hallmark feature of Huntington's disease (HD), these findings may inform the functional role of loss of this cell population in the overall pathobiology of HD.

Age-related behavioural phenotype and cellular characterisation of mice with progressive ablation of D1 dopamine receptor-expressing cells.

In this study we characterize the behavioural and cellular phenotype of mutant (MUT) mice with progressive loss of D1 dopamine receptor (Drd1a)-expressing cells. Adult [14-19 weeks] MUT mice showed intact working memory in the spontaneous alternation test but evidenced anxiety-like behaviour in the elevated plus maze and the light-dark test. The ethogram of mature adult MUT [average age 22 weeks] was compared with that of young adult MUT mice [average age 12 weeks]. While MUT mice evidenced hyperactivity over initial exploration at both time points, the topography of hyperactivity shifted. Moreover, initial hyperactivity was sustained over habituation at 12 weeks, but not at 22 weeks. Thus, by 22 weeks MUT mice evidenced shifts in, and mitigation of, these early phenotypic effects. However, orofacial behaviours of chewing and sifting were reduced similarly at 12 and 22 weeks. These data support the hypothesis that aspects of the mutant phenotype change with time. Quantitative autoradiography at 20 weeks revealed loss of D1-like dopamine receptor binding in the entire basal ganglia, with upregulated D2-like binding. There appear to be topographically specific interactions between normal maturational processes and compensatory mechanisms evoked subsequent to targeted ablation of D1 dopamine receptor-expressing cells. Understanding the mechanistic bases of mitigation vs persistence of individual phenotypes in relation to neural adaptation consequent to cell loss may lead to novel therapeutic strategies for basal ganglia disorders.

Condensation in temporally correlated zero-range dynamics.

The impact of temporally correlated dynamics on nonequilibrium condensation is studied using a non-Markovian zero-range process (ZRP). We find that memory effects can modify the condensation scenario significantly: (i) For mean-field dynamics, the steady state corresponds to that of a Markovian ZRP, but with modified hopping rates which can affect condensation; (ii) for nearest-neighbor hopping dynamics in one dimension, the condensate is found to occupy two adjacent lattice sites and to drift with a finite velocity. The validity of these results in a more general context is discussed.

Instability of condensation in the zero-range process with random interaction.

The zero-range process is a stochastic interacting particle system that is known to exhibit a condensation transition. We present a detailed analysis of this transition in the presence of quenched disorder in the particle interactions. Using rigorous probabilistic arguments, we show that disorder changes the critical exponent in the interaction strength below which a condensation transition may occur. The local critical densities may exhibit large fluctuations, and their distribution shows an interesting crossover from exponential to algebraic behavior.

Asymmetric simple exclusion process with periodic boundary driving.

We consider the asymmetric simple exclusion process (ASEP) on a semi-infinite chain which is coupled at the end to a reservoir with a particle density that changes periodically in time. It is shown that the density profile assumes a time-periodic sawtoothlike shape. This shape does not depend on initial conditions and is found analytically in the hydrodynamic limit. In a finite system, the stationary state is shown to be governed by effective boundary densities and the extremal flux principle. Effective boundary densities are determined numerically via Monte Carlo simulations and compared with those given by mean-field approach and numerical integration of the hydrodynamic limit equation which is the Burgers equation. Our results extend straightforwardly beyond the ASEP to a wide class of driven diffusive systems with one conserved particle species.

Exact solution of a stochastic susceptible-infectious-recovered model.

The susceptible-infectious-recovered (SIR) model describes the evolution of three species of individuals which are subject to an infection and recovery mechanism. A susceptible S can become infectious with an infection rate beta by an infectious I type provided that both are in contact. The I type may recover with a rate gamma and from then on stay immune. Due to the coupling between the different individuals, the model is nonlinear and out of equilibrium. We adopt a stochastic individual-based description where individuals are represented by nodes of a graph and contact is defined by the links of the graph. Mapping the underlying master equation onto a quantum formulation in terms of spin operators, the hierarchy of evolution equations can be solved exactly for arbitrary initial conditions on a linear chain. In the case of uncorrelated random initial conditions, the exact time evolution for all three individuals of the SIR model is given analytically. Depending on the initial conditions and reaction rates beta and gamma , the I population may increase initially before decaying to zero. Due to fluctuations, isolated regions of susceptible individuals evolve, and unlike in the standard mean-field SIR model, one observes a finite stationary distribution of the S type even for large population size. The exact results for the ensemble-averaged population size are compared with simulations for single realizations of the process and also with standard mean-field theory, which is expected to be valid on large fully connected graphs.

Ablation of D1 dopamine receptor-expressing cells generates mice with seizures, dystonia, hyperactivity, and impaired oral behavior.

Huntington's disease is characterized by death of striatal projection neurons. We used a Cre/Lox transgenic approach to generate an animal model in which D1 dopamine receptor (Drd1a)+ cells are progressively ablated in the postnatal brain. Striatal Drd1a, substance P, and dynorphin expression is progressively lost, whereas D2 dopamine receptor (Drd2) and enkephalin expression is up-regulated. Magnetic resonance spectroscopic analysis demonstrated early elevation of the striatal choline/creatine ratio, a finding associated with extensive reactive striatal astrogliosis. Sequential MRI demonstrated a progressive reduction in striatal volume and secondary ventricular enlargement confirmed to be due to loss of striatal cells. Mutant mice had normal gait and rotarod performance but displayed hindlimb dystonia, locomotor hyperactivity, and handling-induced electrographically verified spontaneous seizures. Ethological assessment identified an increase in rearing and impairments in the oral behaviors of sifting and chewing. In line with the limbic seizure profile, cell loss, astrogliosis, microgliosis, and down-regulated dynorphin expression were seen in the hippocampal dentate gyrus. This study specifically implicates Drd1a+ cell loss with tail suspension hindlimb dystonia, hyperactivity, and abnormal oral function. The latter may relate to the speech and swallowing disturbances and the classic sign of tongue-protrusion motor impersistence observed in Huntington's disease. In addition, the findings of this study support the notion that Drd1a and Drd2 are segregated on striatal projection neurons.