Critical Tokunaga model for river networks.

The hierarchical organization and self-similarity in river basins have been topics of extensive research in hydrology and geomorphology starting with the pioneering work of Horton in 1945. Despite significant theoretical and applied advances, however, the mathematical origin of and relation among Horton's laws for different stream attributes remain unsettled. Here we capitalize on a recently developed theory of random self-similar trees to elucidate the origin of Horton's laws, Hack's laws, basin fractal dimensions, power-law distributions of link attributes, and power-law relations between distinct attributes. In particular, we introduce a one-parametric family of self-similar critical Tokunaga trees that includes the celebrated Shreve's random topology model and extends to trees that approximate the observed river networks with realistic exponents. The results offer tools to increase our understanding of landscape organization under different hydroclimatic forcings, and to extend scaling relationships useful for hydrologic prediction to resolutions higher than those observed.

Climate Signatures on Lake And Wetland Size Distributions in Arctic Deltas.

Understanding how thermokarst lakes on arctic river deltas will respond to rapid warming is critical for projecting how carbon storage and fluxes will change in those vulnerable environments. Yet, this understanding is currently limited partly due to the complexity of disentangling significant interannual variability from the longer-term surface water signatures on the landscape, using the short summertime window of optical spaceborne observations. Here, we rigorously separate perennial lakes from ephemeral wetlands on 12 arctic deltas and report distinct size distributions and climate trends for the two waterbodies. Namely, we find a lognormal distribution for lakes and a power-law distribution for wetlands, consistent with a simple proportionate growth model and inundated topography, respectively. Furthermore, while no trend with temperature is found for wetlands, a statistically significant decreasing trend of mean lake size with warmer temperatures is found, attributed to colder deltas having deeper and thicker permafrost preserving larger lakes.

Tokunaga self-similarity arises naturally from time invariance.

The Tokunaga condition is an algebraic rule that provides a detailed description of the branching structure in a self-similar tree. Despite a solid empirical validation and practical convenience, the Tokunaga condition lacks a theoretical justification. Such a justification is suggested in this work. We define a geometric branching process G(s) that generates self-similar rooted trees. The main result establishes the equivalence between the invariance of G(s) with respect to a time shift and a one-parametric version of the Tokunaga condition. In the parameter region where the process satisfies the Tokunaga condition (and hence is time invariant), G(s) enjoys many of the symmetries observed in a critical binary Galton-Watson branching process and reproduces the latter for a particular parameter value.

Entropy and optimality in river deltas.

The form and function of river deltas is intricately linked to the evolving structure of their channel networks, which controls how effectively deltas are nourished with sediments and nutrients. Understanding the coevolution of deltaic channels and their flux organization is crucial for guiding maintenance strategies of these highly stressed systems from a range of anthropogenic activities. To date, however, a unified theory explaining how deltas self-organize to distribute water and sediment up to the shoreline remains elusive. Here, we provide evidence for an optimality principle underlying the self-organized partition of fluxes in delta channel networks. By introducing a suitable nonlocal entropy rate ([Formula: see text]) and by analyzing field and simulated deltas, we suggest that delta networks achieve configurations that maximize the diversity of water and sediment flux delivery to the shoreline. We thus suggest that prograding deltas attain dynamically accessible optima of flux distributions on their channel network topologies, thus effectively decoupling evolutionary time scales of geomorphology and hydrology. When interpreted in terms of delta resilience, high nER configurations reflect an increased ability to withstand perturbations. However, the distributive mechanism responsible for both diversifying flux delivery to the shoreline and dampening possible perturbations might lead to catastrophic events when those perturbations exceed certain intensity thresholds.

Scale-dependent erosional patterns in steady-state and transient-state landscapes.

Landscape topography is the expression of the dynamic equilibrium between external forcings (for example, climate and tectonics) and the underlying lithology. The magnitude and spatial arrangement of erosional and depositional fluxes dictate the evolution of landforms during both statistical steady state (SS) and transient state (TS) of major landscape reorganization. For SS landscapes, the common expectation is that any point of the landscape has an equal chance to erode below or above the landscape median erosion rate. We show that this is not the case. Afforded by a unique experimental landscape that provided a detailed space-time recording of erosional fluxes and by defining the so-called E50-area curve, we reveal for the first time that there exists a hierarchical pattern of erosion. Specifically, hillslopes and fluvial channels erode more rapidly than the landscape median erosion rate, whereas intervening parts of the landscape in terms of upstream contributing areas (colluvial regime) erode more slowly. We explain this apparent paradox by documenting the dynamic nature of SS landscapes-landscape locations may transition from being a hillslope to being a valley and then to being a fluvial channel due to ridge migration, channel piracy, and small-scale landscape dynamics through time. Under TS conditions caused by increased precipitation, we show that the E50-area curve drastically changes shape during landscape reorganization. Scale-dependent erosional patterns, as observed in this study, suggest benchmarks in evaluating numerical models and interpreting the variability of sampled erosional rates in field landscapes.

Network robustness assessed within a dual connectivity framework: joint dynamics of the Active and Idle Networks.

Network robustness against attacks has been widely studied in fields as diverse as the Internet, power grids and human societies. But current definition of robustness is only accounting for half of the story: the connectivity of the nodes unaffected by the attack. Here we propose a new framework to assess network robustness, wherein the connectivity of the affected nodes is also taken into consideration, acknowledging that it plays a crucial role in properly evaluating the overall network robustness in terms of its future recovery from the attack. Specifically, we propose a dual perspective approach wherein at any instant in the network evolution under attack, two distinct networks are defined: (i) the Active Network (AN) composed of the unaffected nodes and (ii) the Idle Network (IN) composed of the affected nodes. The proposed robustness metric considers both the efficiency of destroying the AN and that of building-up the IN. We show, via analysis of well-known prototype networks and real world data, that trade-offs between the efficiency of Active and Idle Network dynamics give rise to surprising robustness crossovers and re-rankings, which can have significant implications for decision making.

Engineered Tug-of-War Between Kinesin and Dynein Controls Direction of Microtubule Based Transport In Vivo.

Bidirectional transport of membrane organelles along microtubules (MTs) is driven by plus-end directed kinesins and minus-end directed dynein bound to the same cargo. Activities of opposing MT motors produce bidirectional movement of membrane organelles and cytoplasmic particles along MT transport tracks. Directionality of MT-based transport might be controlled by a protein complex that determines which motor type is active at any given moment of time, or determined by the outcome of a tug-of-war between MT motors dragging cargo organelles in opposite directions. However, evidence in support of each mechanisms of regulation is based mostly on the results of theoretical analyses or indirect experimental data. Here, we test whether the direction of movement of membrane organelles in vivo can be controlled by the tug-of-war between opposing MT motors alone, by attaching a large number of kinesin-1 motors to organelles transported by dynein to minus-ends of MTs. We find that recruitment of kinesin significantly reduces the length and velocity of minus-end-directed dynein-dependent MT runs, leading to a reversal of the overall direction of dynein-driven organelles in vivo. Therefore, in the absence of external regulators tug-of-war between opposing MT motors alone is sufficient to determine the directionality of MT transport in vivo.

Regulation of microtubule-based transport by MAP4.

Microtubule (MT)-based transport of organelles driven by the opposing MT motors kinesins and dynein is tightly regulated in cells, but the underlying molecular mechanisms remain largely unknown. Here we tested the regulation of MT transport by the ubiquitous protein MAP4 using Xenopus melanophores as an experimental system. In these cells, pigment granules (melanosomes) move along MTs to the cell center (aggregation) or to the periphery (dispersion) by means of cytoplasmic dynein and kinesin-2, respectively. We found that aggregation signals induced phosphorylation of threonine residues in the MT-binding domain of the Xenopus MAP4 (XMAP4), thus decreasing binding of this protein to MTs. Overexpression of XMAP4 inhibited pigment aggregation by shortening dynein-dependent MT runs of melanosomes, whereas removal of XMAP4 from MTs reduced the length of kinesin-2-dependent runs and suppressed pigment dispersion. We hypothesize that binding of XMAP4 to MTs negatively regulates dynein-dependent movement of melanosomes and positively regulates kinesin-2-based movement. Phosphorylation during pigment aggregation reduces binding of XMAP4 to MTs, thus increasing dynein-dependent and decreasing kinesin-2-dependent motility of melanosomes, which stimulates their accumulation in the cell center, whereas dephosphorylation of XMAP4 during dispersion has an opposite effect.

Stimulation of the CLIP-170--dependent capture of membrane organelles by microtubules through fine tuning of microtubule assembly dynamics.

Cytoplasmic microtubules (MTs) continuously grow and shorten at their free plus ends, a behavior that allows them to capture membrane organelles destined for MT minus end-directed transport. In Xenopus melanophores, the capture of pigment granules (melanosomes) involves the +TIP CLIP-170, which is enriched at growing MT plus ends. Here we used Xenopus melanophores to test whether signals that stimulate minus end MT transport also enhance CLIP-170-dependent binding of melanosomes to MT tips. We found that these signals significantly (>twofold) increased the number of growing MT plus ends and their density at the cell periphery, thereby enhancing the likelihood of interaction with dispersed melanosomes. Computational simulations showed that local and global increases in the density of CLIP-170-decorated MT plus ends could reduce the half-time of melanosome aggregation by ~50%. We conclude that pigment granule aggregation signals in melanophores stimulate MT minus end-directed transport by the increasing number of growing MT plus ends decorated with CLIP-170 and redistributing these ends to more efficiently capture melanosomes throughout the cytoplasm.

CK1 activates minus-end-directed transport of membrane organelles along microtubules.

Microtubule (MT)-based organelle transport is driven by MT motor proteins that move cargoes toward MT minus-ends clustered in the cell center (dyneins) or plus-ends extended to the periphery (kinesins). Cells are able to rapidly switch the direction of transport in response to external cues, but the signaling events that control switching remain poorly understood. Here, we examined the signaling mechanism responsible for the rapid activation of dynein-dependent MT minus-end-directed pigment granule movement in Xenopus melanophores (pigment aggregation). We found that, along with the previously identified protein phosphatase 2A (PP2A), pigment aggregation signaling also involved casein kinase 1ε (CK1ε), that both enzymes were bound to pigment granules, and that their activities were increased during pigment aggregation. Furthermore we found that CK1ε functioned downstream of PP2A in the pigment aggregation signaling pathway. Finally, we discovered that stimulation of pigment aggregation increased phosphorylation of dynein intermediate chain (DIC) and that this increase was partially suppressed by CK1ε inhibition. We propose that signal transduction during pigment aggregation involves successive activation of PP2A and CK1ε and CK1ε-dependent phosphorylation of DIC, which stimulates dynein motor activity and increases minus-end-directed runs of pigment granules.

CLIP-170-dependent capture of membrane organelles by microtubules initiates minus-end directed transport.

Cytoplasmic microtubules (MTs) continuously grow and shorten at free plus ends. During mitosis, this dynamic behavior allows MTs to capture chromosomes to initiate their movement to the spindle poles; however, the role of MT dynamics in capturing organelles for transport in interphase cells has not been demonstrated. Here we use Xenopus melanophores to test the hypothesis that MT dynamics significantly contribute to the efficiency of MT minus-end directed transport of membrane organelles. We demonstrate that initiation of transport of membrane-bounded melanosomes (pigment granules) to the cell center involves their capture by MT plus ends, and that inhibition of MT dynamics or loss of the MT plus-end tracking protein CLIP-170 from MT tips dramatically inhibits pigment aggregation. We conclude that MT dynamics are required for the initiation of MT transport of membrane organelles in interphase cells, and that +TIPs such as CLIP-170 play an important role in this process.

Actin dynamics is essential for myosin-based transport of membrane organelles.

Actin filaments that serve as "rails" for the myosin-based transport of membrane organelles [1-4] continuously turn over by concurrent growth and shortening at the opposite ends [5]. Although it is known that dynamics of actin filaments is essential for many of the actin cytoskeleton functions, the role of such dynamics in myosin-mediated organelle transport was never studied before. Here, we addressed the role of turnover of actin filaments in the myosin-based transport of membrane organelles by treating cells with the drugs that suppress actin-filament dynamics and found that such a suppression significantly inhibited organelle transport along the actin filaments without inhibiting their intracellular distribution or the activity of the myosin motors. We conclude that dynamics of actin filaments is essential for myosin-based transport of membrane organelles and suggest a previously unknown role of actin-filament dynamics in providing the "rails" for continuous organelle movement resulting in the increased distances traveled by membrane organelles along the actin filaments.

Clustering analysis of seismicity and aftershock identification.

We introduce a statistical methodology for clustering analysis of seismicity in the time-space-energy domain and use it to establish the existence of two statistically distinct populations of earthquakes: clustered and nonclustered. This result can be used, in particular, for nonparametric aftershock identification. The proposed approach expands the analysis of Baiesi and Paczuski [Phys. Rev. E 69, 066106 (2004)10.1103/PhysRevE.69.066106] based on the space-time-magnitude nearest-neighbor distance eta between earthquakes. We show that for a homogeneous Poisson marked point field with exponential marks, the distance eta has the Weibull distribution, which bridges our results with classical correlation analysis for point fields. The joint 2D distribution of spatial and temporal components of eta is used to identify the clustered part of a point field. The proposed technique is applied to several seismicity models and to the observed seismicity of southern California.

Switching of membrane organelles between cytoskeletal transport systems is determined by regulation of the microtubule-based transport.

Intracellular transport of membrane organelles occurs along microtubules (MTs) and actin filaments (AFs). Although transport along each type of the cytoskeletal tracks is well characterized, the switching between the two types of transport is poorly understood because it cannot be observed directly in living cells. To gain insight into the regulation of the switching of membrane organelles between the two major transport systems, we developed a novel approach that combines live cell imaging with computational modeling. Using this approach, we measured the parameters that determine how fast membrane organelles switch back and forth between MTs and AFs (the switching rate constants) and compared these parameters during different signaling states. We show that regulation involves a major change in a single parameter: the transferring rate from AFs onto MTs. This result suggests that MT transport is the defining factor whose regulation determines the choice of the cytoskeletal tracks during the transport of membrane organelles.

Inverse cascade in a percolation model: hierarchical description of time-dependent scaling.

The dynamics of a two-dimensional site percolation model on a square lattice is studied using the hierarchical approach introduced by Gabrielov [Phys. Rev. E 60, 5293 (1999)]. The key elements of the approach are the tree representation of clusters and their coalescence, and the Horton-Strahler scheme for cluster ranking. Accordingly, the evolution of the percolation model is considered as a hierarchical inverse cascade of cluster aggregation. A three-exponent time-dependent scaling for the cluster rank distribution is derived using the Tokunaga branching constraint and classical results on percolation in terms of cluster masses. Deviations from the pure scaling are described. An empirical constraint on the dynamics of a rank population is reported based on numerical simulations.

Multiscale trend analysis of microtubule transport in melanophores.

Microtubule-based transport is critical for trafficking of organelles, organization of endomembranes, and mitosis. The driving force for microtubule-based transport is provided by microtubule motors, which move organelles specifically to the plus or minus ends of the microtubules. Motor proteins of opposite polarities are bound to the surface of the same cargo organelle. Transport of organelles along microtubules is discontinuous and involves transitions between movements to plus or minus ends or pauses. Parameters of the movement, such as velocity and length of runs, provide important information about the activity of microtubule motors, but measurement of these parameters is difficult and requires a sophisticated decomposition of the organelle movement trajectories into directional runs and pauses. The existing algorithms are based on establishing threshold values for the length and duration of runs and thus do not allow to distinguish between slow runs and pauses, making the analysis of the organelle transport incomplete. Here we describe a novel algorithm based on multiscale trend analysis for the decomposition of organelle trajectories into plus- or minus-end runs, and pauses. This algorithm is self-adapted to the characteristic durations and velocities of runs, and allows reliable separation of pauses from runs. We apply the proposed algorithm to compare regulation of microtubule transport in fish and Xenopus melanophores and show that the general mechanisms of regulation are similar in the two pigment cell types.

Protein kinase A, which regulates intracellular transport, forms complexes with molecular motors on organelles.

Major signaling cascades have been shown to play a role in the regulation of intracellular organelle transport . Aggregation and dispersion of pigment granules in melanophores are regulated by the second messenger cAMP through the protein kinase A (PKA) signaling pathway ; however, the exact mechanisms of this regulation are poorly understood. To study the role of signaling molecules in the regulation of pigment transport in melanophores, we have asked the question whether the components of the cAMP-signaling pathway are bound to pigment granules and whether they interact with molecular motors to regulate the granule movement throughout the cytoplasm. We found that purified pigment granules contain PKA and scaffolding proteins and that PKA associates with pigment granules in cells. Furthermore, we found that the PKA regulatory subunit forms two separate complexes, one with cytoplasmic dynein ("aggregation complex") and one with kinesin II and myosin V ("dispersion complex"), and that the removal of PKA from granules causes dissociation of dynein and disruption of dynein-dependent pigment aggregation. We conclude that cytoplasmic organelles contain protein complexes that include motor proteins and signaling molecules involved in different components of intracellular transport. We propose to call such complexes 'regulated motor units' (RMU).