Fluoxetine increased adult neurogenesis is mediated by 5-HT3 receptor.

Adult neurogenesis is an aspect of structural plasticity that remains active during adulthood in some brain regions. One of them is the subgranular zone (SGZ) of the dentate gyrus of the hippocampus. Adult neurogenesis is reduced by different factors and in disorders of the CNS, including major depression. Antidepressant treatments, such as chronic fluoxetine administration, recover the normal level of adult neurogenesis. Fluoxetine treatment increases the free concentration of the neurotransmitter serotonin and this monoamine is implicated in the regulation of the neurogenic process; however, the target of the action of this neurotransmitter has not been fully elucidated. In this study, we have tried to determine the relevance of the serotonin receptor 3 (5-HT3) in the hippocampal neurogenesis of adult rats. We have used fluorescent immunohistochemistry to study the expression of the 5-HT3 receptor in different neurogenesis stages in the SGZ, identifying its expression in stem cells, amplifying neural progenitors and immature neurons. Moreover, we have studied the impact of a 5-HT3 antagonist (ondansetron) in the fluoxetine-induced adult neurogenesis. We observed that fluoxetine alone increases the number of both proliferating cells (ki67 positive) and immature neurons (DCX positive) in the SGZ. By contrast, co-treatment with ondansetron blocked the increase in proliferation and neurogenesis. This study demonstrates that the activation of 5-HT3 receptors is necessary for the increase of adult neurogenesis induced by fluoxetine.

Characterization and isolation of immature neurons of the adult mouse piriform cortex.

Physiological studies indicate that the piriform or primary olfactory cortex of adult mammals exhibits a high degree of synaptic plasticity. Interestingly, a subpopulation of cells in the layer II of the adult piriform cortex expresses neurodevelopmental markers, such as the polysialylated form of neural cell adhesion molecule (PSA-NCAM) or doublecortin (DCX). This study analyzes the nature, origin, and potential function of these poorly understood cells in mice. As previously described in rats, most of the PSA-NCAM expressing cells in layer II could be morphologically classified as tangled cells and only a small proportion of larger cells could be considered semilunar-pyramidal transitional neurons. Most were also immunoreactive for DCX, confirming their immature nature. In agreement with this, detection of PSA-NCAM combined with that of different cell lineage-specific antigens revealed that most PSA-NCAM positive cells did not co-express markers of glial cells or mature neurons. Their time of origin was evaluated by birthdating experiments with halogenated nucleosides performed at different developmental stages and in adulthood. We found that virtually all cells in this paleocortical region, including PSA-NCAM-positive cells, are born during fetal development. In addition, proliferation analyses in adult mice revealed that very few cells were cycling in layer II of the piriform cortex and that none of them was PSA-NCAM-positive. Moreover, we have established conditions to isolate and culture these immature neurons in the adult piriform cortex layer II. We find that although they can survive under certain conditions, they do not proliferate in vitro either. © 2015 Wiley Periodicals, Inc. Develop Neurobiol 76: 748-763, 2016.

Characterization of a population of tyrosine hydroxylase-containing interneurons in the external plexiform layer of the rat olfactory bulb.

The olfactory bulb (OB) of mammals contains the major endogenous dopamine-producing system in the forebrain. The vast majority of dopaminergic neurons consists of juxtaglomerular cells, which innervate the olfactory glomeruli and modulate the entrance of sensory information to the OB. Although dopaminergic juxtaglomerular cells have been widely investigated, the presence of dopaminergic interneurons other than juxtaglomerular cells has been largely unexplored. In this study, we analyze a population of tyrosine hydroxylase (TH)-containing interneurons located in the external plexiform layer (EPL) of the rat OB. These interneurons are GABAergic and morphologically heterogeneous. They have an axon and two to four dendrites running throughout the EPL. Frequently, they have appendages similar to spines in the dendrites and, sometimes, the distal portions of the dendritic branches show enlargements or swellings similar to varicosities. Contrary to other interneurons of the EPL, the TH-containing ones do not form dendro-dendritic synapses on principal cells and do not receive dendro-dendritic synapses from them. In fact, no synapses were found from the dendrites of these interneurons. When their dendrites are involved in synaptic contacts, they are always the postsynaptic element. They receive symmetrical and asymmetrical synapses from GABAergic and non-GABAergic axons of unidentified origin. Our data indicate that the local circuits of the EPL are more complex than previously thought. Although most of the interneurons of this layer establish dendro-dendritic synaptic relationships with principal cells, the TH-containing interneurons constitute an exception to this rule, resembling interneurons from other cortical areas.

Olfactory bulbectomy, but not odor conditioned aversion, induces the differentiation of immature neurons in the adult rat piriform cortex.

The piriform cortex layer II of young-adult rats presents a population of prenatally generated cells, which express immature neuronal markers, such as the polysialylated form of the neural cell adhesion molecule (PSA-NCAM) or doublecortin (DCX), and display structural characteristics of immature neurons. The number of PSA-NCAM/DCX expressing cells in this region decreases markedly as age progresses, suggesting that these cells differentiate or die. Since the piriform cortex receives a major input from the olfactory bulb and participates in olfactory information processing, it is possible that the immature neurons in layer II are affected by manipulations of the olfactory bulb or olfactory learning. It is not known whether these cells can be induced to differentiate and, if so, what would be their fate. In order to address these questions, we have performed unilateral olfactory bulbectomy (OBX) and an olfactory learning paradigm (taste-potentiated odor aversion, TPOA), in young-adult rats and have studied the expression of different mature and immature neuronal markers, as well as the presence of cell death. We have found that 14 h after OBX there was a dramatic decrease in the number of both PSA-NCAM and DCX expressing cells in piriform cortex layer II, whereas that of cells expressing NeuN, a mature neuronal marker, increased. By contrast, the number of cells expressing glutamate decarboxylase, isoform 67 (GAD67), a marker for interneurons, decreased slightly. Additionally, we have not found evidence of numbers of dying cells high enough to justify the disappearance of immature neurons. Analysis of animals subjected to TPOA revealed that this paradigm does not affect PSA-NCAM expressing cells. Our results strongly suggest that OBX can induce the maturation of immature neurons in the piriform cortex layer II and that these cells do not become interneurons. By contrast, these cells do not seem to play a crucial role in olfactory memory.

"Arrested development". Immature, but not recently generated, neurons in the adult brain.

After the division of neuronal precursors, many of the newly generated cells become immature neurons, which migrate to their final destination in the nervous system, extend neurites and make appropriate connections. For most neurons these events occur in a narrow time window and, once in their definitive location, they immediately start the final stages of their differentiation program, remaining immature only for a short time. The main objective of this review is to present and discuss recent data on a peculiar population of cells in the adult brain, which retain an immature neuronal phenotype for an unusually prolonged time. We review and discuss recent evidence on the temporal and spatial origin of these cells, their distribution in rodents and other mammals, their structure and neurochemical phenotype, and their putative fate and function. The review is mainly focused on the population of immature neurons located in the layer II of certain cortical regions, but we will also describe similar populations found in other regions of the peripheral and central nervous systems.

GABAergic basal forebrain afferents innervate selectively GABAergic targets in the main olfactory bulb.

In this work we have analyzed the targets of the GABAergic afferents to the main olfactory bulb originating in the basal forebrain of the rat. We combined anterograde tracing of 10 kD biotinylated dextran amine (BDA) injected in the region of the horizontal limb of the diagonal band of Broca that projects to the main olfactory bulb, with immunocytochemical detection of GABA under electron microscopy or vesicular GABA transporter (vGABAt) under confocal fluorescent microscopy. GABAergic afferents were identified as double labeled BDA-GABA boutons. Their targets were identified by their ultrastructure and GABA content. We found that GABAergic afferents from the basal forebrain were distributed all over the bulbar lamination, but were more abundant in the glomerular and inframitral layers (i.e. internal plexiform layer and granule cell layer). The fibers had thick varicosities with abundant mitochondria and large perforated synaptic specializations. They contacted exclusively GABAergic cells, corresponding to type 1 periglomerular cells in the glomerular layer, and to granule cells in inframitral layers. This innervation will synchronize the bulbar inhibition and consequently the response of the principal cells to the olfactory input. The effect of the activation of this pathway will produce a disinhibition of the bulbar principal cells. This facilitation might occur at two separate levels: first in the terminal tufts of mitral and tufted cells via inhibition of type 1 periglomerular cells; second at the level of the firing of the principal cells via inhibition of granule cells. The GABAergic projection from the basal forebrain ends selectively on interneurons, specifically on type 1 periglomerular cells and granule cells, and is likely to control the activity of the olfactory bulb via disinhibition of principal cells. Possible similarities of this pathway with the septo-hippocampal loop are discussed.

The role of internal duplication in the evolution of multi-domain proteins.

Many proteins consist of several structural domains. These multi-domain proteins have likely been generated by selective genome growth dynamics during evolution to perform new functions as well as to create structures that fold on a biologically feasible time scale. Domain units frequently evolved through a variety of genetic shuffling mechanisms. Here we examine the protein domain statistics of more than 1000 organisms including eukaryotic, archaeal and bacterial species. The analysis extends earlier findings on asymmetric statistical laws for proteome to a wider variety of species. While proteins are composed of a wide range of domains, displaying a power-law decay, the computation of domain families for each protein reveals an exponential distribution, characterizing a protein universe composed of a thin number of unique families. Structural studies in proteomics have shown that domain repeats, or internal duplicated domains, represent a small but significant fraction of genome. In spite of its importance, this observation has been largely overlooked until recently. We model the evolutionary dynamics of proteome and demonstrate that these distinct distributions are in fact rooted in an internal duplication mechanism. This process generates the contemporary protein structural domain universe, determines its reduced thickness, and tames its growth. These findings have important implications, ranging from protein interaction network modeling to evolutionary studies based on fundamental mechanisms governing genome expansion.

Synaptic connectivity of serotonergic axons in the olfactory glomeruli of the rat olfactory bulb.

Although the major mode of transmission for serotonin in the brain is volume transmission, previous anatomical studies have demonstrated that serotonergic axons do form synaptic contacts. The olfactory glomeruli of the olfactory bulb of mammals receive a strong serotonergic innervation from the dorsal and medial raphe nuclei. In the present report, we investigate the synaptic connectivity of these serotonergic axons in the glomerular neuropil of the rat olfactory bulb. Our study shows that serotonergic axons form asymmetrical synaptic contacts on dendrites within the glomerular neuropil. Analyzing the neurochemical nature of the synaptic targets, we have found that 55% of the synapses were on GABA-immunopositive profiles and 45% on GABA-immunonegative profiles. These data indicate that barely half of the contacts were found in GABA-immunonegative profiles and half of the synapses in GABA-positive dendrites belonging to type 1 periglomerular cells. Synaptic contacts from serotonergic axons on dendrites of principal cells cannot be excluded, since some of the GABA-immunonegative postsynaptic profiles contacted by serotonergic axons had the typical ultrastructural features of bulbar principal cell dendrites. Altogether, our results suggest a complex action of the serotonergic system in the modulation of the bulbar circuitry.

Divergent impact of the polysialyltransferases ST8SiaII and ST8SiaIV on polysialic acid expression in immature neurons and interneurons of the adult cerebral cortex.

Polysialic acid (PSA) is a negatively charged carbohydrate polymer, which confers antiadhesive properties to the neural cell adhesion molecule NCAM and facilitates cellular plasticity during brain development. In mice, PSA expression decreases drastically during the first postnatal weeks and it gets confined to immature neurons and regions displaying structural plasticity during adulthood. In the brain, PSA is exclusively synthesized by the two polysialyltransferases ST8SiaII and ST8SiaIV. To study their individual contribution to polysialylation in the adult, we analyzed PSA expression in mice deficient for either polysialyltransferase. Focusing on the cerebral cortex, our results indicate that ST8SiaIV is solely responsible for PSA expression in mature interneurons and in most regions of cortical neuropil. By contrast, ST8SiaII is the major polysialyltransferase in immature neurons of the paleocortex layer II and the hippocampal subgranular zone. The numbers of cells expressing PSA or doublecortin, another marker of immature neurons, were increased in the paleocortex layer II of ST8SiaIV-deficient mice, indicating altered differentiation of these cells. Analysis of doublecortin expression also indicated that the production of new granule neurons in the subgranular zone of ST8SiaII-deficient mice is not affected. However, many of the immature granule neurons showed aberrant locations and morphology, suggesting a role of ST8SiaII in their terminal differentiation.

Structural characterization and modeling of ncRNA-protein interactions.

Recent studies have suggested that noncoding RNA (ncRNA) molecules could play an important role in the regulatory architecture of eukaryotic cells. This new RNA-based regulation might indicate the existence of a hidden layer in the central dogma. In spite of its importance, the large-scale structure as well as the local interaction pattern of the ncRNA regulatory network has not been investigated. In this work, we collected regulatory interactions between ncRNA molecules and their regulated protein targets. We then constructed the ncRNA-protein interaction network corresponding to six model organisms, including Homo sapiens. The large-scale network analysis of ncRNA-protein interactions revealed a high degree of similarity for the degree distribution to that of the transcription regulatory network. Moreover, characterization of the local interaction structure of these networks based on motifs abundance also reveals significant similarities between ncRNA-protein and TFs-gene regulatory networks. Based on the identified motif abundance, we propose an evolutionary model that rebuilds the degree distribution and predicts the observed degree exponent. Taken together, our findings offer insights into the noncoding RNA-mediated regulation and provide knowledge about its structure and evolutionary mechanisms.

Alteration of inhibitory circuits in the somatosensory cortex of Ts65Dn mice, a model for Down's syndrome.

Down's syndrome (DS), with an incidence of one in 800 live births, is the most common genetic disorder associated with mental retardation. This trisomy on chromosome 21 induces a variable phenotype in which the only common feature is the presence of mental retardation. The neural mechanisms underlying mental retardation might include defects in the formation of neuronal networks and neural plasticity. DS patients have alterations in the morphology, the density and the distribution of dendritic spines in the pyramidal neurons of the cortex. Our hypothesis is that the deficits in dendritic arborization observed in the principal neurons of DS patients and Ts65Dn mice (a model for DS that mimics most of the structural alterations observed in humans) may be mediated to some extent by changes in their inhibitory inputs. Different types of interneurons control different types of inhibition. Therefore, to understand well the changes in inhibition in DS, it is necessary to study the different types of interneurons separately. We have studied the expression of synaptophysin, Glutamic acid decarboxylase-67 (GAD-67) and calcium-binding protein-expressing cells in the primary somatosensory cortex of 4-5 month old Ts65Dn mice. We have observed an increment of GAD67 immunoreactivity that is related mainly to an increment of calretinin-immunoreactive cells and among them the ones with bipolar morphology. Since there is a propensity for epilepsy in DS patients, this increase in interneurons might reflect an attempt by the system to block overexcitation rather than an increment in total inhibition and could explain the deficit in interneurons and principal cells observed in elderly DS patients.

Effects of chronic fluoxetine treatment on the rat somatosensory cortex: activation and induction of neuronal structural plasticity.

Recent hypotheses support the idea that disruption of normal neuronal plasticity mechanisms underlies depression and other psychiatric disorders, and that antidepressant treatment may counteract these changes. In a previous report we found that chronic fluoxetine treatment increases the expression of the polysialylated form of the neural cell adhesion molecule (PSA-NCAM), a molecule involved in neuronal structural plasticity, in the somatosensory cortex. In the present study we intended to find whether, in fact, cell activation and neuronal structural remodeling occur in parallel to changes in the expression of this molecule. Using immunohistochemistry, we found that chronic fluoxetine treatment caused an increase in the expression of the early expression gene c-fos. Golgi staining revealed that this treatment also increased spine density in the principal apical dendrite of pyramidal neurons. These results indicate that, apart from the medial prefrontal cortex or the hippocampus, other cortical regions can respond to chronic antidepressant treatment undergoing neuronal structural plasticity.

Emergence of scale-free distribution in protein-protein interaction networks based on random selection of interacting domain pairs.

Recent analyses of biological and artificial networks have revealed a common network architecture, called scale-free topology. The origin of the scale-free topology has been explained by using growth and preferential attachment mechanisms. In a cell, proteins are the most important carriers of function, and are composed of domains as elemental units responsible for the physical interaction between protein pairs. Here, we propose a model for protein-protein interaction networks that reveals the emergence of two possible topologies. We show that depending on the number of randomly selected interacting domain pairs, the connectivity distribution follows either a scale-free distribution, even in the absence of the preferential attachment, or a normal distribution. This new approach only requires an evolutionary model of proteins (nodes) but not for the interactions (edges). The edges are added by means of random interaction of domain pairs. As a result, this model offers a new mechanistic explanation for understanding complex networks with a direct biological interpretation because only protein structures and their functions evolved through genetic modifications of amino acid sequences. These findings are supported by numerical simulations as well as experimental data.

[Correct placement of left-sided double lumen endotracheal tubes: a simple verification technique]. / Un método sencillo para ayudar a la comprobación del correcto posicionamiento de los tubos endotraqueales de doble luz izquierdos.

OBJECTIVE: Double lumen endotracheal tubes (DLTs) are used in thoracic surgery for selective bronchial intubation, which is required for single lung ventilation. Correct placement of the tube is checked by means of fiberoptic bronchoscopy. We present a simple alternative method to help confirm the correct placement of left-sided DLTs. The method consists of passing a suction catheter through the tracheal lumen of the tube. Our hypothesis was that if the catheter can be inserted without difficulty, the tube is correctly placed. The objective was to determine the sensitivity and specificity of that criterion. MATERIAL AND METHODS: We studied patients scheduled for elective left pneumonectomy or lobectomy. After passing the catheter through the left-sided DLT, placement was checked by means of fiberoptic bronchoscopy (gold standard) and the results were compared with the placement assessment based on ease of insertion. RESULTS: One hundred patients were included. The DLT was judged to be correctly placed in 88% of patients in whom the catheter was inserted without resistance. Bronchoscopy corroborated this finding in 84% of cases; the tube was found to be incorrectly placed in the remaining 4% of cases and had to be reinserted. Resistance was noted in 12% of cases and bronchoscopy confirmed that the tube was incorrectly placed in those patients. CONCLUSIONS: This technique can be very useful in placing left-sided DLTs in situations where fiberoptic bronchoscopy is not available and if the anesthesiologist has a thorough command of the method. Our results support the routine use of this criterion as it is simple and easy to learn. It should be remembered, however, that confirmation of placement by means of fiberoptic bronchoscopy is currently the gold standard technique.

Distribution of the A3 subunit of the cyclic nucleotide-gated ion channels in the main olfactory bulb of the rat.

Previous data suggest that cyclic GMP (cGMP) signaling can play key roles in the circuitry of the olfactory bulb (OB). Therefore, the expression of cGMP-selective subunits of the cyclic nucleotide-gated ion channels (CNGs) can be expected in this brain region. In the present study, we demonstrate a widespread expression of the cGMP-selective A3 subunit of the cyclic nucleotide-gated ion channels (CNGA3) in the rat OB. CNGA3 appears in principal cells, including mitral cells and internal, medium and external tufted cells. Moreover, it appears in two populations of interneurons, including a subset of periglomerular cells and a group of deep short-axon cells. In addition to neurons, CNGA3-immunoreactivity is found in the ensheathing glia of the olfactory nerve. Finally, an abundant population of CNGA3-containing cells with fusiform morphology and radial processes is found in the inframitral layers. These cells express doublecortin and have a morphology similar to that of the undifferentiated cells that leave the rostral migratory stream and migrate radially through the layers of the OB. Altogether, our results suggest that CNGA3 can play important and different roles in the OB. Channels composed of this subunit can be involved in the processing of the olfactory information taking place in the bulbar circuitry. Moreover, they can be involved in the function of the ensheathing glia and in the radial migration of immature cells through the bulbar layers.

Transcription and noise in negative feedback loops.

Recently, several studies have investigated the transcription process associated to specific genetic regulatory networks. In this work, we present a stochastic approach for analyzing the dynamics and effect of negative feedback loops (FBL) on the transcriptional noise. First, our analysis allows us to identify a bimodal activity depending on the strength of self-repression coupling D. In the strong coupling region D>>1, our findings indicate that the variance of the transcriptional noise is reduced 28% more than described earlier. Secondly, the contribution of the noise effect to the abundance of regulating protein becomes manifest when the coefficient of variation is computed. In the strong coupling region, this coefficient was found to be independent of all parameters and in fair agreement with the experimentally observed values. Finally, our analysis reveals that the regulating protein is significantly induced by the intrinsic and external noise in the strong coupling region. In short, it indicates that the existence of inherent noise in FBL makes it possible to produce a basal amount of proteins even though the repression level D is very strong.

Recent progress on the analysis of power-law features in complex cellular networks.

Complex interactions between different kinds of bio-molecules and essential nutrients are responsible for cellular functions. Rapid advances in theoretical modeling and experimental analyses have shown that drastically different biological and non-biological networks share a common architecture. That is, the probability that a selected node in the network has exactly k edges decays as a power-law. This finding has definitely opened an intense research and debate on the origin and implications of this ubiquitous pattern. In this review, we describe the recent progress on the emergence of power-law distributions in cellular networks. We first show the internal characteristics of the observed complex networks uncovered using graph theory. We then briefly review some works that have significantly contributed to the theoretical analysis of cellular networks and systems, from metabolic and protein networks to gene expression profiles. This prevalent topology observed in so many diverse biological systems suggests the existence of generic laws and organizing principles behind the cellular networks.

Chronic antidepressant treatment induces contrasting patterns of synaptophysin and PSA-NCAM expression in different regions of the adult rat telencephalon.

Structural modifications occur in the brain of severely depressed patients and they can be reversed by antidepressant treatment. Some of these changes do not occur in the same direction in different regions, such as the medial prefrontal cortex, the hippocampus or the amygdala. Differential structural plasticity also occurs in animal models of depression and it is also prevented by antidepressants. In order to know whether chronic fluoxetine treatment induces differential neuronal structural plasticity in rats, we have analyzed the expression of synaptophysin, a protein considered a marker of synaptic density, and the expression of the polysialylated form of the neural cell adhesion molecule (PSA-NCAM), a molecule involved in neurite and synaptic remodeling. Chronic fluoxetine treatment increases synaptophysin and PSA-NCAM expression in the medial prefrontal cortex and decreases them in the amygdala. The expression of these molecules is also affected in the entorhinal, the visual and the somatosensory cortices.

N-methyl-d-aspartate receptor expression during adult neurogenesis in the rat dentate gyrus.

N-methyl-d-aspartate (NMDA) receptors play a crucial role in the regulation of neuronal development during embryogenesis and they also regulate the rate of neurogenesis and proliferation in the adult dentate gyrus. However, the mechanism by which they influence these processes is not fully understood. NMDA receptors seem to be functional in hippocampal precursor cells and recently generated granule neurons, although there is no anatomical correlate of these physiological observations. We have analyzed the expression of the NMDA receptor subunits NR1 and NR2B in precursor cells and recently generated granule neurons of the adult rat dentate gyrus, using 5'bromodeoxyuridine, green fluorescent protein-retrovirus and immunohistochemistry. Our results indicate that NR1 and NR2B are expressed in some proliferating cells of the adult subgranular zone. These receptors are absent from transiently amplifying progenitors (type 2-3 cells) but they are found in glial fibrillar acidic protein expressing cells in the subgranular zone, suggesting its presence in bipotential (type-1) precursor cells. NR1 and NR2B are rarely found in granule cells younger than 60 h. By contrast, many granule cells generated 14 days before killing express both NMDA receptor subunits. These results demonstrate that adult hippocampal neurogenesis may be regulated by NMDA receptors present in precursor cells and in differentiating granule neurons, although these receptors are probably not located on synapses. However, an indirect effect through NMDA receptors located in other cell types should not be excluded.

The role of log-normal dynamics in the evolution of biochemical pathways.

The study of the scale-free topology in non-biological and biological networks and the dynamics that can explain this fascinating property of complex systems have captured the attention of the scientific community in the last years. Here, we analyze the biochemical pathways of three organisms (Methanococcus jannaschii, Escherichia coli, Saccharomyces cerevisiae) which are representatives of the main kingdoms Archaea, Bacteria and Eukaryotes during the course of the biological evolution. We can consider two complementary representations of the biochemical pathways: the enzymes network and the chemical compounds network. In this article, we propose a stochastic model that explains that the scale-free topology with exponent in the vicinity of gamma approximately 3/2 found across these three organisms is governed by the log-normal dynamics in the evolution of the enzymes network. Precisely, the fluctuations of the connectivity degree of enzymes in the biochemical pathways between evolutionary distant organisms follow the same conserved dynamical principle, which in the end is the origin of the stationary scale-free distribution observed among species, from Archaea to Eukaryotes. In particular, the log-normal dynamics guarantees the conservation of the scale-free distribution in evolving networks. Furthermore, the log-normal dynamics also gives a possible explanation for the restricted range of observed exponents gamma in the scale-free networks (i.e., gamma > or = 3/2). Finally, our model is also applied to the chemical compounds network of biochemical pathways and the Internet network.