It has been hypothesized that topological structures of biological transport networks are consequences of energy optimization. Motivated by experimental observation, we propose that adaptation dynamics may underlie this optimization. In contrast to the global nature of optimization, our adaptation dynamics responds only to local information and can naturally incorporate fluctuations in flow distributions. The adaptation dynamics minimizes the global energy consumption to produce optimal networks, which may possess hierarchical loop structures in the presence of strong fluctuations in flow distribution. We further show that there may exist a new phase transition as there is a critical open probability of sinks, above which there are only trees for network structures whereas below which loops begin to emerge.

This in vivo time-lapse imaging study in zebrafish reveals how changes to brain blood flow drive vessel pruning via endothelial cell migration, and how pruning leads to the simplification of the brain vasculature during development.

A coarse-grained representation of neuronal network dynamics is developed in terms of kinetic equations, which are derived by a moment closure, directly from the original large-scale integrate-andfire (I&F) network. This powerful kinetic theory captures the full dynamic range of neuronal networks, from the mean-driven limit (a limit such as the number of neurons N 3 ؕ, in which the fluctuations vanish) to the fluctuation-dominated limit (such as in small N networks). Comparison with full numerical simulations of the original I&F network establishes that the reduced dynamics is very accurate and numerically efficient over all dynamic ranges. Both analytical insights and scale-up of numerical representation can be achieved by this kinetic approach. Here, the theory is illustrated by a study of the dynamical properties of networks of various architectures, including excitatory and inhibitory neurons of both simple and complex type, which exhibit rich dynamic phenomena, such as, transitions to bistability and hysteresis, even in the presence of large fluctuations. The implication for possible connections between the structure of the bifurcations and the behavior of complex cells is discussed. Finally, I&F networks and kinetic theory are used to discuss orientation selectivity of complex cells for ''ring-model'' architectures that characterize changes in the response of neurons located from near ''orientation pinwheel centers'' to far from them. N euronal networks, whether real cortical networks (1, 2) or computer models (3, 4), frequently operate in a regime in which spiking is caused by irregular temporal fluctuations of the membrane potential. At this ''cortical operating point,'' the mean membrane potential (e.g., obtained by averaging over many voltage traces under the same stimulus condition or by averaging locally in time), does not reach firing threshold. Thus, the spiking process is fluctuation-driven.A theoretical challenge is to construct efficient and effective representations of such fluctuation-driven networks, which are needed both to ''scale-up'' computational models to large enough regions of the cortex to capture interesting cortical processing (such as optical illusions related to ''contour completion''), and to gain qualitative understanding of the cortical mechanisms underlying this level of cortical processing. In this article, we develop such a construction: Starting with large-scale model networks of integrateand-fire (I&F) neurons, which are sufficiently detailed for modeling neuronal computation of large systems but are difficult to scale-up, we tile the cortex with coarse-grained (CG) patches. Each CG patch is sufficiently small that the cortical architecture does not change systematically across it, yet it is sufficiently large to contain many (hundreds) of neurons. We then derive an effective dynamics to capture the statistical behavior of the many neurons within each CG patch in their interaction with other CG patches. This representation is achieved by a kinetic theory, accomplished by ...

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Purpose PIK3CA gene encoding a catalytic subunit of the phosphatidylinositol-3-kinase (PI3K) is mutated and/or amplified in various neoplasia, including lung cancer. Here we investigated PIK3CA gene alterations, the expression of core components of PI3K pathway, and evaluated their clinical importance in non-small cell lung cancer (NSCLC).Materials and methodsOncogenic mutations/rearrangements in PIK3CA, EGFR, KRAS, HER2, BRAF, AKT1 and ALK genes were detected in tumors from 1117 patients with NSCLC. PIK3CA gene copy number was examined by fluorescent in situ hybridization and the expression of PI3K p110 subunit alpha (PI3K p110α), p-Akt, mTOR, PTEN was determined by immunohistochemistry in PIK3CA mutant cases and 108 patients without PIK3CA mutation.Results PIK3CA mutation was found in 3.9% of squamous cell carcinoma and 2.7% of adenocarcinoma. Among 34 PIK3CA mutant cases, 17 tumors harbored concurrent EGFR mutations and 4 had KRAS mutations. PIK3CA mutation was significantly associated with high expression of PI3K p110α (p<0.0001), p-Akt (p = 0.024) and mTOR (p = 0.001), but not correlated with PIK3CA amplification (p = 0.463). Patients with single PIK3CA mutation had shorter overall survival than those with PIK3CA-EGFR/KRAS co-mutation or wildtype PIK3CA (p = 0.004). A significantly worse survival was also found in patients with PIK3CA mutations than those without PIK3CA mutations in the EGFR/KRAS wildtype subgroup (p = 0.043)Conclusions PIK3CA mutations frequently coexist with EGFR/KRAS mutations. The poor prognosis of patients with single PIK3CA mutation in NSCLC and the prognostic value of PIK3CA mutation in EGFR/KRAS wildtype subgroup suggest the distinct mutation status of PIK3CA gene should be determined for individual therapeutic strategies in NSCLC.

Abstract. We present a detailed theoretical framework for statistical descriptions of neuronal networks and derive (1 + 1)-dimensional kinetic equations, without introducing any new parameters, directly from conductance-based integrate-and-fire neuronal networks. We describe the details of derivation of our kinetic equation, proceeding from the simplest case of one excitatory neuron, to coupled networks of purely excitatory neurons, to coupled networks consisting of both excitatory and inhibitory neurons. The dimension reduction in our theory is achieved via novel moment closures. We also describe the limiting forms of our kinetic theory in various limits, such as the limit of mean-driven dynamics and the limit of infinitely fast conductances. We establish accuracy of our kinetic theory by comparing its prediction with the full simulations of the original point-neuron networks. We emphasize that our kinetic theory is dynamically accurate, i.e., it captures very well the instantaneous statistical properties of neuronal networks under time-inhomogeneous inputs.Key words. Visual cortex, coarse-grain, fluctuation, diffusion, correlation.AMS subject classifications. 82C31, 92B99, 92C20 IntroductionMathematically, the vast hierarchy of the multiple spatial and temporal scales in the cortical dynamics presents a significant challenge to computational neuroscience. While we may devise ever more efficient numerical methods for simulations of dynamics of large-scale neuronal networks [1, 2, 3, 4, 5], basic computational constraints will eventually limit our simulation power. In order to "scale-up" computational models to sufficiently large regions of the cortex to capture interesting cortical processing (such as optical illusions related to "contour completion"), and to gain qualitative understanding of the cortical mechanisms underlying this level of cortical processing, a major theoretical issue is how to derive effective dynamics under a reduced representation of large-scale neuronal networks. Therefore, a theoretical challenge is to develop efficient and effective representations for simulating and understanding the dynamics of larger, multi-layered networks. As suggested, for example, by the laminar structure of cat's or monkey's primary visual cortex, in which many cellular properties such as orientation preference are arranged in regular patterns or maps across the cortex [6,7,8,9,10], some neuronal sub-populations may be effectively represented by coarse-grained substitutes. Thus, we may partition the two-dimensional cortical layers into coarse-grained patches, each sufficiently large to contain many neurons, yet sufficiently small that these regular response properties of the individual neurons within each patch are approximately the same for each neuron in the patch. These regular response properties are then treated as constants throughout each coarse-grained patch.