Local optimization of neuron arbors

How parsimoniously is brain wiring laid out, that is, how well does a neuron minimize costs of connections among its synapses? Neural optimization of dentritic and axonic arbors can be evaluated using a generalization of the Steiner tree concept from combinatorial network optimization theory. Local branch-junction geometry of neuronal connecting structures fits a volume minimization model well. In addition, volume of the arborizations at this neighborhood level is significantly more strongly minimized than their length, signal propagation speed, or surface area. The mechanism of this local volume optimization resembles those involved in formation of nonliving tree structures such as river junctions and electric-discharge patterns, and appears to govern initial nerve growth-cone behavior through vector-mechanical energy minimization.     

Trade-off between Multiple Constraints Enables Simultaneous Formation of Modules and Hubs in Neural Systems

The formation of the complex network architecture of neural systems is subject to multiple structural and functional constraints. Two obvious but apparently contradictory constraints are low wiring cost and high processing efficiency, characterized by short overall wiring length and a small average number of processing steps, respectively. Growing evidence shows that neural networks are results from a trade-off between physical cost and functional value of the topology. However, the relationship between these competing constraints and complex topology is not well understood quantitatively. We explored this relationship systematically by reconstructing two known neural networks, Macaque cortical connectivity and C. elegans neuronal connections, from combinatory optimization of wiring cost and processing efficiency constraints, using a control parameter , and comparing the reconstructed networks to the real networks. We found that in both neural systems, the reconstructed networks derived from the two constraints can reveal some important relations between the spatial layout of nodes and the topological connectivity, and match several properties of the real networks. The reconstructed and real networks had a similar modular organization in a broad range of , resulting from spatial clustering of network nodes. Hubs emerged due to the competition of the two constraints, and their positions were close to, and partly coincided, with the real hubs in a range of values. The degree of nodes was correlated with the density of nodes in their spatial neighborhood in both reconstructed and real networks. Generally, the rebuilt network matched a significant portion of real links, especially short-distant ones. These findings provide clear evidence to support the hypothesis of trade-off between multiple constraints on brain networks. The two constraints of wiring cost and processing efficiency, however, cannot explain all salient features in the real networks. The discrepancy suggests that there are further relevant factors that are not yet captured here.     

The wiring economy principle: connectivity determines anatomy in the human brain

Minimization of the wiring cost of white matter fibers in the human brain appears to be an organizational principle. We investigate this aspect in the human brain using whole brain connectivity networks extracted from high resolution diffusion MRI data of 14 normal volunteers. We specifically address the question of whether brain anatomy determines its connectivity or vice versa. Unlike previous studies we use weighted networks, where connections between cortical nodes are real-valued rather than binary off-on connections. In one set of analyses we found that the connectivity structure of the brain has near optimal wiring cost compared to random networks with the same number of edges, degree distribution and edge weight distribution. A specifically designed minimization routine could not find cheaper wiring without significantly degrading network performance. In another set of analyses we kept the observed brain network topology and connectivity but allowed nodes to freely move on a 3D manifold topologically identical to the brain. An efficient minimization routine was written to find the lowest wiring cost configuration. We found that beginning from any random configuration, the nodes invariably arrange themselves in a configuration with a striking resemblance to the brain. This confirms the widely held but poorly tested claim that wiring economy is a driving principle of the brain. Intriguingly, our results also suggest that the brain mainly optimizes for the most desirable network connectivity, and the observed brain anatomy is merely a result of this optimization.     

Nonoptimal component placement, but short processing paths, due to long-distance projections in neural systems

It has been suggested that neural systems across several scales of organization show optimal component placement, in which any spatial rearrangement of the components would lead to an increase of total wiring. Using extensive connectivity datasets for diverse neural networks combined with spatial coordinates for network nodes, we applied an optimization algorithm to the network layouts, in order to search for wire-saving component rearrangements. We found that optimized component rearrangements could substantially reduce total wiring length in all tested neural networks. Specifically, total wiring among 95 primate (Macaque) cortical areas could be decreased by 32%, and wiring of neuronal networks in the nematode Caenorhabditis elegans could be reduced by 48% on the global level, and by 49% for neurons within frontal ganglia. Wiring length reductions were possible due to the existence of long-distance projections in neural networks. We explored the role of these projections by comparing the original networks with minimally rewired networks of the same size, which possessed only the shortest possible connections. In the minimally rewired networks, the number of processing steps along the shortest paths between components was significantly increased compared to the original networks. Additional benchmark comparisons also indicated that neural networks are more similar to network layouts that minimize the length of processing paths, rather than wiring length. These findings suggest that neural systems are not exclusively optimized for minimal global wiring, but for a variety of factors including the minimization of processing steps.     

Development of wiring specificity in the olfactory system

The olfactory system discriminates a large number of odorants using precisely wired neural circuits. It offers an excellent opportunity to study mechanisms of neuronal wiring specificity at the single synapse level. Each olfactory receptor neuron typically expresses only one olfactory receptor from many receptor genes (1000 in mice). In mice, this striking singularity appears to be ensured by a negative feedback mechanism. Olfactory receptor neurons expressing the same receptor converge their axons to stereotypical positions with high precision, a feature that is conserved from insects to mammals. Several molecules have recently been identified that control this process, including olfactory receptors themselves in mice. The second order neurons, mitral cells in mammals and projection neurons in insects, have a similar degree of wiring specificity: studies in Drosophila suggest that projection neuron-intrinsic mechanisms regulate their precise dendritic targeting. Finally, recent studies have revealed interactions of different cell types during circuit assembly, including axon-axon interactions among olfactory receptor neurons and dendro-dendritic interactions of projection neurons, that are essential in establishing wiring specificity of the olfactory circuit.     

Linking dynamical and functional properties of intrinsically bursting neurons

Several studies have shown that bursting neurons can encode information in the number of spikes per burst: As the stimulus varies, so does the length of individual bursts.Therepresented stimuli, however, vary substantially among different sensory modalities and different neurons.The goal of this paper is to determine which kind of stimulus features can be encoded in burst length, and how those features depend on the mathematical properties of the underlying dynamical system.We show that the initiation and termination of each burst is triggered by specific stimulus features whose temporal characteristsics are determined by the types of bifurcations that initiate and terminate firing in each burst. As only a few bifurcations are possible, only a restricted number of encoded features exists. Here we focus specifically on describing parabolic, square-wave and elliptic bursters. We find that parabolic bursters, whose firing is initiated and terminated by saddle-node bifurcations, behave as prototypical integrators: Firing is triggered by depolarizing stimuli, and lasts for as long as excitation is prolonged. Elliptic bursters, contrastingly, constitute prototypical resonators, since both the initiating and terminating bifurcations possess well-defined oscillation time scales. Firing is therefore triggered by stimulus stretches of matching frequency and terminated by a phase-inversion in the oscillation. The behavior of square-wave bursters is somewhat intermediate, since they are triggered by a fold bifurcation of cycles of well-defined frequency but are terminated by a homoclinic bifurcation lacking an oscillating time scale. These correspondences show that stimulus selectivity is determined by the type of bifurcations. By testing several neuron models, we also demonstrate that additional biological properties that do not modify the bifurcation structure play a minor role in stimulus encoding. Moreover, we show that burst-length variability (and thereby, the capacity to transmit information) depends on a trade-off between the variance of the external signal driving the cell and the strength of the slow internal currents modulating bursts. Thus, our work explicitly links the computational properties of bursting neurons to the mathematical properties of the underlying dynamical systems.     

Bifurcations in Turing systems of the second kind may explain blastula cleavage plane orientation

Spontaneous pattern formation (emergence of Turing structures) may take place in biological systems as primary and secondary bifurcations to nonlinear parabolic partial differential equations describing biochemical reaction-diffusion systems. Bipolarity in mitosis and cleavage planes in cytokinesis may be related to this formation of prepatterns. Cleavage planes in early blastulas have an apparently well controlled spatial relationship to the polarity known as the animal-vegetal (A-V) axis: the mitotic spindles form perpendicular to this axis in the first two division stages, with cleavage planes going strictly through the A-V poles. The third-stage spindles are parallel to the A-V axis, and cleavage is roughly in the equatorial plane, thus separating the A-V poles. The reason for these phenomena are poorly understood with current mitosis/cytokinesis models based on intrinsic spindle properties. It is shown here by numerical simulation that a simple modification to the usual Turing equations yields selection rules which lead directly to these orientations of the prepatterns, without any further ad hoc assumptions. These results strongly support the prepattern model for mitosis and cytokinesis and the viewpoint that prepatterns play a fundamental role in nature.     

Single-neuron theory of consciousness

By most accounts, the mind arises from the integrated activity of large populations of neurons distributed across multiple brain regions. A contrasting model is presented in the present paper that places the mind/brain interface not at the whole brain level but at the level of single neurons. Specifically, it is proposed that each neuron in the nervous system is independently conscious, with conscious content corresponding to the spatial pattern of a portion of that neuron's dendritic electrical activity. For most neurons, such as those in the hypothalamus or posterior sensory cortices, the conscious activity would be assumed to be simple and unable to directly affect the organism's macroscopic conscious behavior. For a subpopulation of layer 5 pyramidal neurons in the lateral prefrontal cortices, however, an arrangement is proposed to be present such that, at any given moment: (i) the spatial pattern of electrical activity in a portion of the dendritic tree of each neuron in the subpopulation individually manifests a complexity and diversity sufficient to account for the complexity and diversity of conscious experience; (ii) the dendritic trees of the neurons in the subpopulation all contain similar spatial electrical patterns; (iii) the spatial electrical pattern in the dendritic tree of each neuron interacts non-linearly with the remaining ambient dendritic electrical activity to determine the neuron's overall axonal response; (iv) the dendritic spatial pattern is reexpressed at the population level by the spatial pattern exhibited by a synchronously firing subgroup of the conscious neurons, thereby providing a mechanism by which conscious activity at the neuronal level can influence overall behavior. The resulting scheme is one in which conscious behavior appears to be the product of a single macroscopic mind, but is actually the integrated output of a chorus of minds, each associated with a different neuron.     

Planar molecular arrangements aid the design of MHC class II binding peptides

The coupling between peptides and MHC-II proteins in the human immune system is not well understood. This work presents an evidence-based hypothesis of a guiding intermolecular force present in every human MHC-II protein (HLA-II). Previously, we examined the spatial positions of the fully conserved residues in all HLA-II protein types. In each one, constant planar patterns were revealed. These molecular planes comprise of amino acid groups of the same chemical species (for example, Gly) distributed across the protein structure. Each amino acid plane has a unique direction and this directional element offers spatial selectivity. Constant within all planes, too, is the presence of an aromatic residue possessing electrons in movement, leading the authors to consider that the planes generate electromagnetic fields that could serve as an attractive force in a single direction. Selection and attraction between HLA-II molecules and antigen peptides would, therefore, be non-random, resulting in a coupling mechanism as effective and rapid as is clearly required in the immune response. On the basis of planar projections onto the HLA-II groove, modifications were made by substituting the key residues in the class II-associated invariant chain peptide—a peptide with a universal binding affinity—resulting in eight different modified peptides with affinities greater than that of the unmodified peptide. Accurate and reliable prediction of MHC class II-binding peptides may facilitate the design of universal vaccine-peptides with greatly enhanced binding affinities. The proposed mechanisms of selection, attraction and coupling between HLA-II and antigen peptides are explained further in the paper.     

基于改进PSO的洞庭湖水源涵养林空间优化模型

以结构化森林经营思想为理论基础,从与水源林涵养水源、保持水土功能密切相关的林分物种组成(树种混交)、种内及种间竞争、空间分布格局、垂直结构4个方面选择混交度、竞争指数、角尺度、林层指数、空间密度指数、开阔比数作为水源林健康经营和林分空间结构优化的目标函数,建立洞庭湖水源林林分多目标空间优化模型,应用改进的群智能粒子群算法求解林分空间结构优化模型,并针对模型输出的目标树空间结构单元制定周密的经营策略.研究结果表明,优化模型能准确定位林分空间关系的薄弱环节,调控措施能显著改善林分空间结构,有利于促进森林生态系统的正向演替,为恢复洞庭湖水源林生态功能和健康经营提供理论依据和技术支撑.应用优化模型进行水源涵养林健康经营突破了传统森林经营模式,为智能信息技术在森林空间经营中的应用提供了新的思路.     

Lights,cytoskeleton, action: Optogenetic control of cell dynamics

Cell biology is moving from observing molecules to controlling them in real time, a critical step towards a mechanistic understanding of how cells work. Initially developed from light-gated ion channels to control neuron activity, optogenetics now describes any genetically encoded protein system designed to accomplish specific light-mediated tasks. Recent photosensitive switches use many ingenious designs that bring spatial and temporal control within reach for almost any protein or pathway of interest. This next generation optogenetics includes light-controlled protein–protein interactions and shape-shifting photosensors, which in combination with live microscopy enable acute modulation and analysis of dynamic protein functions in living cells. We provide a brief overview of various types of optogenetic switches. We then discuss how diverse approaches have been used to control cytoskeleton dynamics with light through Rho GTPase signaling, microtubule and actin assembly, mitotic spindle positioning and intracellular transport and highlight advantages and limitations of different experimental strategies.     

Models of cortical networks with long-range patchy projections

The cortex exhibits an intricate vertical and horizontal architecture, the latter often featuring spatially clustered projection patterns, so-called patches. Many network studies of cortical dynamics ignore such spatial structures and assume purely random wiring. Here, we focus on non-random network structures provided by long-range horizontal (patchy) connections that remain inside the gray matter. We investigate how the spatial arrangement of patchy projections influences global network topology and predict its impact on the activity dynamics of the network. Since neuroanatomical data on horizontal projections is rather sparse, we suggest and compare four candidate scenarios of how patchy connections may be established. To identify a set of characteristic network properties that enables us to pin down the differences between the resulting network models, we employ the framework of stochastic graph theory. We find that patchy projections provide an exceptionally efficient way of wiring, as the resulting networks tend to exhibit small-world properties with significantly reduced wiring costs. Furthermore, the eigenvalue spectra, as well as the structure of common in- and output of the networks suggest that different spatial connectivity patterns support distinct types of activity propagation.     

大兴安岭次生林空间分布格局及其尺度效应

研究大兴安岭落叶松林、白桦林和落叶松+白桦混交林3种次生林中,不同树种(落叶松、白桦和其他)和不同大小级(Ⅰ～Ⅴ级)树木的空间分布格局及其尺度效应。结果表明:3个林型中,仅落叶松林的更新数量达到良好状态,其余2种林型均为更新不良;各林型中,更新层幼苗、幼树的数量组成均与乔木层存在显著差异,且各林型中树木的直径(落叶松林和落叶松+白桦混交林除外)和树高分布也不够合理,3个林型均属于不稳定群落。各林型内林木空间分布整体以聚集分布为主,但方差/均值比率、负二项指数、Green指数、平均拥挤度和Morisita指数5个判别指数随尺度的变化显著不同,并以线性递增(40%)、幂函数递增(22%)和负二次多项式(20%)趋势为主。Ⅰ～Ⅲ级的更新层林木在不同尺度上以聚集分布为主,而乔木层(Ⅳ～Ⅴ级)在多种分布格局间波动,其对尺度的响应同样以线性递增(44%)、幂函数递增(15%)和负二次多项式(12%)为主。同一林型和取样尺度下,林木空间聚集程度整体随着林木大小级的增加呈线性下降趋势。各林型中,非优势树种的种群格局规模往往大于优势树种,而更新层林木空间格局规模大于乔木层。     

Local Diameter Fully Constrains Dendritic Size in Basal but not Apical Trees of CA1 Pyramidal Neurons

Computational modeling of dendritic morphology is a powerful tool for quantitatively describing complex geometrical relationships, uncovering principles of dendritic development, and synthesizing virtual neurons to systematically investigate cellular biophysics and network dynamics. A feature common to many morphological models is a dependence of the branching probability on local diameter. Previous models of this type have been able to recreate a wide variety of dendritic morphologies. However, these diameter-dependent models have so far failed to properly constrain branching when applied to hippocampal CA1 pyramidal cells, leading to explosive growth. Here we present a simple modification of this basic approach, in which all parameter sampling, not just bifurcation probability, depends on branch diameter. This added constraint prevents explosive growth in both apical and basal trees of simulated CA1 neurons, yielding arborizations with average numbers and patterns of bifurcations extremely close to those observed in real cells. However, simulated apical trees are much more varied in size than the corresponding real dendrites. We show that, in this model, the excessive variability of simulated trees is a direct consequence of the natural variability of diameter changes at and between bifurcations observed in apical, but not basal, dendrites. Conversely, some aspects of branch distribution were better matched by virtual apical trees than by virtual basal trees. Dendritic morphometrics related to spatial position, such as path distance from the soma or branch order, may be necessary to fully constrain CA1 apical tree size and basal branching pattern.     

Functional multimodality of axonal tree in invertebrate neurons.

This review, based on invertebrate neuron examples, aims at highlighting the functional consequences of axonal tree organization. The axonal organization of invertebrate neurons is very complex both morphologically and physiologically. The first part shows how the transfer of information along sensory axons is modified by presynaptic inhibition mechanisms. In primary afferents, presynaptic inhibition is involved in: 1) increasing the dynamic range of the sensory response; 2) processing the sensory information such as increasing spatial and/or temporal selectivity; 3) discriminating environmental information from sensory activities generated by the animal's own movement; and 4) modulating the gain of negative feedback (resistance reflex) during active rhythmic movements such as locomotion. In a second part, the whole organization of other types of neurons is considered, and evidence is given that a neuron may not work as a unit, but rather as a mosaic of disconnected 'integrate-and-fire' units. Examples of invertebrate neurons are presented in which several spike initiating zones exist, such as in some stomatogastric neurons. The separation of a neuron into two functionally distinct entities may be almost total with distinct arborizations existing in different ganglia. However, this functional separation is not definitive and depends on the state of the neuron. In conclusion, the classical integrate-and-fire representation of the neuron, with its dendritic arborization, its spike initiating zone, its axon and axonal tree seems to be no more applicable to invertebrate neurons. A better knowledge of the function of vertebrate neurons would probably demonstrate that it is the case for a large number of them, as suggested by the complex architecture of some reticular interneurons in vertebrates.     

Modelling of the qualitative discrimination of odours in the first two layers of olfactory system by Jutten and Hérault algorithm.

The olfactory system discriminates many different odours although membrane receptors, and neuroreceptors that bear them, are only broadly tuned to volatile molecules. We investigated how mixed and redundant information carried by neuroreceptors could be efficiently coded by output neurons in the second neuronal layer in the brain. We showed that a good discrimination is yielded if neuroreceptors that terminate on the same output neuron belong to several types, if these types are in different proportions for each output neuron, and if each output neuron exerts an action on all others so that their independence is maximized, according to the Jutten and Hérault algorithm for separating linear mixtures of independent sources. The proposed model details the computations made by neurons and leads to a better understanding of several observed properties of the olfactory system, among which the inhibitory actions of local neurons of the second layer and the identifiability of insect glomeruli.     

Random Wiring,Ganglion Cell Mosaics,and the Functional Architecture of the Visual Cortex

The architecture of iso-orientation domains in the primary visual cortex (V1) of placental carnivores and primates apparently follows species invariant quantitative laws. Dynamical optimization models assuming that neurons coordinate their stimulus preferences throughout cortical circuits linking millions of cells specifically predict these invariants. This might indicate that V1’s intrinsic connectome and its functional architecture adhere to a single optimization principle with high precision and robustness. To validate this hypothesis, it is critical to closely examine the quantitative predictions of alternative candidate theories. Random feedforward wiring within the retino-cortical pathway represents a conceptually appealing alternative to dynamical circuit optimization because random dimension-expanding projections are believed to generically exhibit computationally favorable properties for stimulus representations. Here, we ask whether the quantitative invariants of V1 architecture can be explained as a generic emergent property of random wiring. We generalize and examine the stochastic wiring model proposed by Ringach and coworkers, in which iso-orientation domains in the visual cortex arise through random feedforward connections between semi-regular mosaics of retinal ganglion cells (RGCs) and visual cortical neurons. We derive closed-form expressions for cortical receptive fields and domain layouts predicted by the model for perfectly hexagonal RGC mosaics. Including spatial disorder in the RGC positions considerably changes the domain layout properties as a function of disorder parameters such as position scatter and its correlations across the retina. However, independent of parameter choice, we find that the model predictions substantially deviate from the layout laws of iso-orientation domains observed experimentally. Considering random wiring with the currently most realistic model of RGC mosaic layouts, a pairwise interacting point process, the predicted layouts remain distinct from experimental observations and resemble Gaussian random fields. We conclude that V1 layout invariants are specific quantitative signatures of visual cortical optimization, which cannot be explained by generic random feedforward-wiring models.     

吉林蛟河针阔混交林树木生长的空间关联格局

以吉林蛟河21.12hm2(660m×320m)针阔混交林样地为对象,利用2009年和2014年森林生长观测数据,研究树木生长的空间自相关格局及其生境影响机制。在样地生境型划分结果的基础上,采用Ripley's L(r)函数分析不同生境型中树木种群空间分布特征;利用标记相关函数分析不同生境型中树木生长特征的空间关联格局。研究结果表明:(1)红松(生境型3:1—5m)、蒙古栎(生境型3:1—3m)、胡桃楸(生境型2:1—2m;生境型3:1—7m)、黄檗(生境型2:1—3m;生境型4:1—5m)、水曲柳(生境型3:1—2m;生境型4:1—2m)、瘤枝卫矛(生境型2:1—15m)在特定生境和空间尺度上呈随机分布,但空间格局仍以聚集性分布为主;其余10个物种则在全部0—30m尺度上呈聚集分布。(2)标记相关函数分析显示春榆、毛榛、色木槭、瘤枝卫矛和千金榆的径向生长至少在一个生境中表现出正相关格局;暴马丁香、胡桃楸、裂叶榆、瘤枝卫矛、水曲柳、紫椴、糠椴、毛榛、色木槭和白牛槭的径向生长至少在一个生境中表现出负相关格局;红松、黄檗、蒙古栎和簇毛槭的径向生长在全部尺度上均未检测到显著的空间关联格局。因此,不同树种径向生长的空间自相关特征不同,树种生长特征的空间关联格局具有明显的生境依赖性。