Undersampled Critical Branching Processes on Small-World and Random Networks Fail to Reproduce the Statistics of Spike Avalanches

The power-law size distributions obtained experimentally for neuronal avalanches are an important evidence of criticality in the brain. This evidence is supported by the fact that a critical branching process exhibits the same exponent t~3=2. Models at criticality have been employed to mimic avalanche propagation and explain the statistics observed experimentally. However, a crucial aspect of neuronal recordings has been almost completely neglected in the models: undersampling. While in a typical multielectrode array hundreds of neurons are recorded, in the same area of neuronal tissue tens of thousands of neurons can be found. Here we investigate the consequences of undersampling in models with three different topologies (two-dimensional, small-world and random network) and three different dynamical regimes (subcritical, critical and supercritical). We found that undersampling modifies avalanche size distributions, extinguishing the power laws observed in critical systems. Distributions from subcritical systems are also modified, but the shape of the undersampled distributions is more similar to that of a fully sampled system. Undersampled supercritical systems can recover the general characteristics of the fully sampled version, provided that enough neurons are measured. Undersampling in two-dimensional and small-world networks leads to similar effects, while the random network is insensitive to sampling density due to the lack of a well-defined neighborhood. We conjecture that neuronal avalanches recorded from local field potentials avoid undersampling effects due to the nature of this signal, but the same does not hold for spike avalanches. We conclude that undersampled branching-process-like models in these topologies fail to reproduce the statistics of spike avalanches.

Likelihood-Based Inference for Partially Observed Multi-Type Markov Branching Processes

Thesis (Ph.D.)--University of Washington, 2016-08

LATERAL BRANCHING OXIDOREDUCTASE acts in the final stages of strigolactone biosynthesis inArabidopsis

Strigolactones are a group of plant compounds of diverse but related chemical structures. They have similar bioactivity across a broad range of plant species, act to optimize plant growth and development, and promote soil microbe interactions. Carlactone, a common precursor to strigolactones, is produced by conserved enzymes found in a number of diverse species. Versions of the MORE AXILLARY GROWTH1 (MAX1) cytochrome P450 from rice and Arabidopsis thaliana make specific subsets of strigolactones from carlactone. However, the diversity of natural strigolactones suggests that additional enzymes are involved and remain to be discovered. Here, we use an innovative method that has revealed a missing enzyme involved in strigolactone metabolism. By using a transcriptomics approach involving a range of treatments that modify strigolactone biosynthesis gene expression coupled with reverse genetics, we identified LATERAL BRANCHING OXIDOREDUCTASE (LBO), a gene encoding an oxidoreductase-like enzyme of the 2-oxoglutarate and Fe(II)-dependent dioxygenase superfamily. Arabidopsis lbo mutants exhibited increased shoot branching, but the lbo mutation did not enhance the max mutant phenotype. Grafting indicated that LBO is required for a graft-transmissible signal that, in turn, requires a product of MAX1. Mutant lbo backgrounds showed reduced responses to carlactone, the substrate of MAX1, and methyl carlactonoate (MeCLA), a product downstream of MAX1. Furthermore, lbo mutants contained increased amounts of these compounds, and the LBO protein specifically converts MeCLA to an unidentified strigolactone-like compound. Thus, LBO function may be important in the later steps of strigolactone biosynthesis to inhibit shoot branching in Arabidopsis and other seed plants.

Branching dendrites with resonant membrane: a "sum-over-trips" approach

Dendrites form the major components of neurons. They are complex branching structures that receive and process thousands of synaptic inputs from other neurons. It is well known that dendritic morphology plays an important role in the function of dendrites. Another important contribution to the response characteristics of a single neuron comes from the intrinsic resonant properties of dendritic membrane. In this paper we combine the effects of dendritic branching and resonant membrane dynamics by generalising the "sum-over-trips" approach [Abbott, L.F., Fahri, E., Gutmann, S.: The path integral for dendritic trees. Biological Cybernetics 66, 49--60 (1991)]. To illustrate how this formalism can shed light on the role of architecture and resonances in determining neuronal output we consider dual recording and reconstruction data from a rat CA1 hippocampal pyramidal cell. Specifically we explore the way in which an $I_{h}$ current contributes to a voltage overshoot at the soma.

Undersampled Critical Branching Processes on Small-World and Random Networks Fail to Reproduce the Statistics of Spike Avalanches

The power-law size distributions obtained experimentally for neuronal avalanches are an important evidence of criticality in the brain. This evidence is supported by the fact that a critical branching process exhibits the same exponent t~3=2. Models at criticality have been employed to mimic avalanche propagation and explain the statistics observed experimentally. However, a crucial aspect of neuronal recordings has been almost completely neglected in the models: undersampling. While in a typical multielectrode array hundreds of neurons are recorded, in the same area of neuronal tissue tens of thousands of neurons can be found. Here we investigate the consequences of undersampling in models with three different topologies (two-dimensional, small-world and random network) and three different dynamical regimes (subcritical, critical and supercritical). We found that undersampling modifies avalanche size distributions, extinguishing the power laws observed in critical systems. Distributions from subcritical systems are also modified, but the shape of the undersampled distributions is more similar to that of a fully sampled system. Undersampled supercritical systems can recover the general characteristics of the fully sampled version, provided that enough neurons are measured. Undersampling in two-dimensional and small-world networks leads to similar effects, while the random network is insensitive to sampling density due to the lack of a well-defined neighborhood. We conjecture that neuronal avalanches recorded from local field potentials avoid undersampling effects due to the nature of this signal, but the same does not hold for spike avalanches. We conclude that undersampled branching-process-like models in these topologies fail to reproduce the statistics of spike avalanches.

Diurnal temporal patterns of the diversity and the abundance of reef fishes in a branching coral patch in New Caledonia

Small-scale spatial and temporal variability in animal abundance is an intrinsic characteristic of marine ecosystems but remains largely unknown for most animals, including coral reef fishes. In this study, we used a remote autonomous unbaited video system and recorded reef fish assemblages during daylight hours, 10 times a day for 34 consecutive days in a branching coral patch of the lagoon of New Caledonia. In total, 50 031 fish observations belonging to 114 taxa, 66 genera and 31 families were recorded in 256 recorded videos. Carnivores and herbivore-detritus feeders dominated the trophic structure. We found significant variations in the composition of fish assemblages between times of day. Taxa richness and fish abundance were greater in the early morning and in the late afternoon than during the day. Fourteen taxa displayed well-defined temporal patterns in abundance with one taxon influenced by time of day, six influenced by tidal state and seven influenced by both time of day and tidal state. None of these 14 taxa were piscivores, 10 were herbivore-detritus feeders, three were carnivores and one was plankton feeder. Our results suggest a diel migration from feeding grounds to shelter areas and highlight the importance of taking into account small-scale temporal variability in animal diversity and abundance when studying connectivity between habitats and monitoring communities.

Branching bisimulation games.

Branching bisimilarity and branching bisimilarity with explicit divergences are typically used in process algebras with silent steps when relating implementations to specifications. When an implementation fails to conform to its specification, i.e., when both are not related by branching bisimilarity [with explicit divergence], pinpointing the root causes can be challenging. In this paper, we provide characterisations of branching bisimilarity [with explicit divergence] as games between Spoiler and Duplicator, offering an operational understanding of both relations. Moreover, we show how such games can be used to assist in diagnosing non-conformance between implementation and specification.

Morphogenesis of the Arabidopsis Shoot Apical Meristem

Phyllotaxis patterns in plants, or the arrangement of leaves and flowers radially around the shoot, have fascinated both biologists and mathematicians for centuries. The current model of this process involves the lateral transport of the hormone auxin through the first layer of cells in the shoot apical meristem via the auxin efflux carrier protein PIN1. Locations around the meristem with high auxin concentration are sites of organ formation and differentiation. Many of the molecular players in this process are well known and characterized. Computer models composed of all these components are able to produce many of the observed phyllotaxis patterns. To understand which parts of this model have a large effect on the phenotype I automated parameter testing and tried many different parameter combinations. Results of this showed that cell size and meristem size should have the largest effect on phyllotaxis. This lead to three questions: (1) How is cell geometry regulated? (2) Does cell size affect auxin distribution? (3) Does meristem size affect phyllotaxis? To answer the first question I tracked cell divisions in live meristems and quantified the geometry of the cells and the division planes using advanced image processing techniques. The results show that cell shape is maintained by minimizing the length of the new wall and by minimizing the difference in area of the daughter cells. To answer the second question I observed auxin patterning in the meristem, shoot, leaves, and roots of Arabidopsis mutants with larger and smaller cell sizes. In the meristem and shoot, cell size plays an important role in determining the distribution of auxin. Observations of auxin in the root and leaves are less definitive. To answer the third question I measured meristem sizes and phyllotaxis patterns in mutants with altered meristem sizes. These results show that there is no correlation between meristem size and average divergence angle. But in an extreme case, making the meristem very small does lead to a switch on observed phyllotaxis in accordance with the model.

tRNA anticodon loop modifications ensure protein homeostasis and cell morphogenesis in yeast

Using budding yeast, we investigated a negative interaction network among genes for tRNA modifications previously implicated in anticodon-codon interaction: 5-methoxy-carbonyl-methyl-2-thio-uridine (mcm5s2U34: ELP3, URM1), pseudouridine (Ψ38/39: DEG1) and cyclic N6-threonyl-carbamoyl-adenosine (ct6A37: TCD1). In line with functional cross talk between these modifications, we find that combined removal of either ct6A37 or Ψ38/39 and mcm5U34 or s2U34 results in morphologically altered cells with synthetic growth defects. Phenotypic suppression by tRNA overexpression suggests that these defects are caused by malfunction of tRNALysUUU or tRNAGlnUUG, respectively. Indeed, mRNA translation and synthesis of the Gln-rich prion Rnq1 are severely impaired in the absence of Ψ38/39 and mcm5U34 or s2U34, and this defect can be rescued by overexpression of tRNAGlnUUG. Surprisingly, we find that combined modification defects in the anticodon loops of different tRNAs induce similar cell polarity- and nuclear segregation defects that are accompanied by increased aggregation of cellular proteins. Since conditional expression of an artificial aggregation-prone protein triggered similar cytological aberrancies, protein aggregation is likely responsible for loss of morphogenesis and cytokinesis control in mutants with inappropriate tRNA anticodon loop modifications.

Numb/Numbl-Opo antagonism controls retinal epithelium morphogenesis by regulating integrin endocytosis

Polarized trafficking of adhesion receptors plays a pivotal role in controlling cellular behavior during morphogenesis. Particularly, clathrin-dependent endocytosis of integrins has long been acknowledged as essential for cell migration. However, little is known about the contribution of integrin trafficking to epithelial tissue morphogenesis. Here we show how the transmembrane protein Opo, previously described for its essential role during optic cup folding, plays a fundamental role in this process. Through interaction with the PTB domain of the clathrin adaptors Numb and Numbl via an integrin-like NPxF motif, Opo antagonizes Numb/Numbl function and acts as a negative regulator of integrin endocytosis in vivo. Accordingly, numb/numbl gain-of-function experiments in teleost embryos mimic the retinal malformations observed in opo mutants. We propose that developmental regulator Opo enables polarized integrin localization by modulating Numb/Numbl, thus directing the basal constriction that shapes the vertebrate retina epithelium.

Analysis of opo cis-regulatory landscape uncovers Vsx2 requirement in early eye morphogenesis

The self-organized morphogenesis of the vertebrate optic cup entails coupling the activation of the retinal gene regulatory network to the constriction-driven infolding of the retinal epithelium. Yet the genetic mechanisms underlying this coordination remain largely unexplored. Through phylogenetic footprinting and transgenesis in zebrafish, here we examine the cis-regulatory landscape of opo, an endocytosis regulator essential for eye morphogenesis. Among the different conserved enhancers identified, we isolate a single retina-specific element (H6_10137) and show that its activity depends on binding sites for the retinal determinant Vsx2. Gain- and loss-of-function experiments and ChIP analyses reveal that Vsx2 regulates opo expression through direct binding to this retinal enhancer. Furthermore, we show that vsx2 knockdown impairs the primary optic cup folding. These data support a model by which vsx2, operating through the effector gene opo, acts as a central transcriptional node that coordinates neural retina patterning and optic cup invagination in zebrafish.

Scaling laws and thermodynamic analysis for vascular branching of microvessels

When blood flows through small vessels, the two-phase nature of blood as a suspension of red cells (erythrocytes) in plasma cannot be neglected, and with decreasing vessel size, a homogeneous continuum model become less adequate in describing blood flow. Following the Haynes’ marginal zone theory, and viewing the flow as the result of concentric laminae of fluid moving axially, the present work provides models for fluid flow in dichotomous branching composed by larger and smaller vessels, respectively. Expressions for the branching sizes of parent and daughter vessels, that provides easier flow access, are obtained by means of a constrained optimization approach using the Lagrange multipliers. This study shows that when blood behaves as a Newtonian fluid, Hess – Murray law that states that the daughters-to-parent diameter ratio must equal to 2^(-1/3) is valid. However, when the nature of blood as a suspension becomes important, the expression for optimum branching diameters of vessels is dependent on the separation phase lengths. It is also shown that the same effect occurs for the relative lengths of daughters and parent vessels. For smaller vessels (e. g., arterioles and capillaries), it is found that the daughters-to-parent diameter ratio may varies from 0,741 to 0,849, and the daughters-to-parent length ratio varies from 0,260 to 2,42. For larger vessels (e. g., arteries), the daughters-to-parent diameter ratio and the daughters-to-parent length ratio range from 0,458 to 0,819, and from 0,100 to 6,27, respectively. In this paper, it is also demonstrated that the entropy generated when blood behaves as a single phase fluid (i. e., continuum viscous fluid) is greater than the entropy generated when the nature of blood as a suspension becomes important. Another important finding is that the manifestation of the particulate nature of blood in small vessels reduces entropy generation due to fluid friction, thereby maintaining the flow through dichotomous branching vessels at a relatively lower cost.

Encephalization And Diversification Of The Cranial Base In Platyrrhine Primates.

The cranial base, composed of the midline and lateral basicranium, is a structurally important region of the skull associated with several key traits, which has been extensively studied in anthropology and primatology. In particular, most studies have focused on the association between midline cranial base flexion and relative brain size, or encephalization. However, variation in lateral basicranial morphology has been studied less thoroughly. Platyrrhines are a group of primates that experienced a major evolutionary radiation accompanied by extensive morphological diversification in Central and South America over a large temporal scale. Previous studies have also suggested that they underwent several evolutionarily independent processes of encephalization. Given these characteristics, platyrrhines present an excellent opportunity to study, on a large phylogenetic scale, the morphological correlates of primate diversification in brain size. In this study we explore the pattern of variation in basicranial morphology and its relationship with phylogenetic branching and with encephalization in platyrrhines. We quantify variation in the 3D shape of the midline and lateral basicranium and endocranial volumes in a large sample of platyrrhine species, employing high-resolution CT-scans and geometric morphometric techniques. We investigate the relationship between basicranial shape and encephalization using phylogenetic regression methods and calculate a measure of phylogenetic signal in the datasets. The results showed that phylogenetic structure is the most important dimension for understanding platyrrhine cranial base diversification; only Aotus species do not show concordance with our molecular phylogeny. Encephalization was only correlated with midline basicranial flexion, and species that exhibit convergence in their relative brain size do not display convergence in lateral basicranial shape. The evolution of basicranial variation in primates is probably more complex than previously believed, and understanding it will require further studies exploring the complex interactions between encephalization, brain shape, cranial base morphology, and ecological dimensions acting along the species divergence process.

Micrornas And Drought Responses In Sugarcane.

There is a growing demand for renewable energy, and sugarcane is a promising bioenergy crop. In Brazil, the largest sugarcane producer in the world, sugarcane plantations are expanding into areas where severe droughts are common. Recent evidence has highlighted the role of miRNAs in regulating drought responses in several species, including sugarcane. This review summarizes the data from miRNA expression profiles observed in a wide array of experimental conditions using different sugarcane cultivars that differ in their tolerance to drought. We uncovered a complex regulation of sugarcane miRNAs in response to drought and discussed these data with the miRNA profiles observed in other plant species. The predicted miRNA targets revealed different transcription factors, proteins involved in tolerance to oxidative stress, cell modification, as well as hormone signaling. Some of these proteins might regulate sugarcane responses to drought, such as reduction of internode growth and shoot branching and increased leaf senescence. A better understanding on the regulatory network from miRNAs and their targets under drought stress has a great potential to contribute to sugarcane improvement, either as molecular markers as well as by using biotechnological approaches.