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1.  Different scaling of white matter volume, cortical connectivity, and gyrification across rodent and primate brains 
Expansion of the cortical gray matter in evolution has been accompanied by an even faster expansion of the subcortical white matter volume and by folding of the gray matter surface, events traditionally considered to occur homogeneously across mammalian species. Here we investigate how white matter expansion and cortical folding scale across species of rodents and primates as the gray matter gains neurons. We find very different scaling rules of white matter expansion across the two orders, favoring volume conservation and smaller propagation times in primates. For a similar number of cortical neurons, primates have a smaller connectivity fraction and less white matter volume than rodents; moreover, as the cortex gains neurons, there is a much faster increase in white matter volume and in its ratio to gray matter volume in rodents than in primates. Order-specific scaling of the white matter can be attributed to different scaling of average fiber caliber and neuronal connectivity in rodents and primates. Finally, cortical folding increases as different functions of the number of cortical neurons in rodents and primates, scaling faster in the latter than in the former. While the neuronal rules that govern gray and white matter scaling are different across rodents and primates, we find that they can be explained by the same unifying model, with order-specific exponents. The different scaling of the white matter has implications for the scaling of propagation time and computational capacity in evolution, and calls for a reappraisal of developmental models of cortical expansion in evolution.
PMCID: PMC3620553  PMID: 23576961
white matter; number of neurons; allometry; brain size; cortical expansion; gyrification
2.  The human cerebral cortex is neither one nor many: neuronal distribution reveals two quantitatively different zones in the gray matter, three in the white matter, and explains local variations in cortical folding 
The human prefrontal cortex has been considered different in several aspects and relatively enlarged compared to the rest of the cortical areas. Here we determine whether the white and gray matter of the prefrontal portion of the human cerebral cortex have similar or different cellular compositions relative to the rest of the cortical regions by applying the Isotropic Fractionator to analyze the distribution of neurons along the entire anteroposterior axis of the cortex, and its relationship with the degree of gyrification, number of neurons under the cortical surface, and other parameters. The prefrontal region shares with the remainder of the cerebral cortex (except for occipital cortex) the same relationship between cortical volume and number of neurons. In contrast, both occipital and prefrontal areas vary from other cortical areas in their connectivity through the white matter, with a systematic reduction of cortical connectivity through the white matter and an increase of the mean axon caliber along the anteroposterior axis. These two parameters explain local differences in the distribution of neurons underneath the cortical surface. We also show that local variations in cortical folding are neither a function of local numbers of neurons nor of cortical thickness, but correlate with properties of the white matter, and are best explained by the folding of the white matter surface. Our results suggest that the human cerebral cortex is divided in two zones (occipital and non-occipital) that differ in how neurons are distributed across their gray matter volume and in three zones (prefrontal, occipital, and non-occipital) that differ in how neurons are connected through the white matter. Thus, the human prefrontal cortex has the largest fraction of neuronal connectivity through the white matter and the smallest average axonal caliber in the white matter within the cortex, although its neuronal composition fits the pattern found for other, non-occipital areas.
PMCID: PMC3759024  PMID: 24032005
human; prefrontal cortex; occipital cortex; evolution; cortical expansion
3.  Axons Pull on the Brain, But Tension Does Not Drive Cortical Folding 
During human brain development, the cerebral cortex undergoes substantial folding, leading to its characteristic highly convoluted form. Folding is necessary to accommodate the expansion of the cerbral cortex; abnormal cortical folding is linked to various neurological disorders, including schizophrenia, epilepsy, autism and mental retardation. Although this process requires mechanical forces, the specific force-generating mechanisms that drive folding remain unclear. The two most widely accepted hypotheses are (1) folding is caused by differential growth of the cortex and (2) folding is caused by mechanical tension generated in axons. Direct evidence supporting either theory, however, is lacking. Here we show that axons are indeed under considerable tension in the developing ferret brain, but the patterns of tissue stress are not consistent with a causal role for axonal tension. In particular, microdissection assays reveal that significant tension exists along axons aligned circumferentially in subcortical white matter tracts, as well as those aligned radially inside developing gyri (outward folds). Contrary to previous speculation, however, axonal tension is not directed across developing gyri, suggesting that axon tension does not drive folding. On the other hand, using computational (finite element) models, we show that differential cortical growth accompanied by remodeling of the subplate leads to outward folds and stress fields that are consistent with our microdissection experiments, supporting a mechanism involving differential growth. Local perturbations, such as temporal differences in the initiation of cortical growth, can ensure consistent folding patterns. This study shows that a combination of experimental and computational mechanics can be used to evaluate competing hypotheses of morphogenesis, and illuminate the biomechanics of cortical folding.
PMCID: PMC3170872  PMID: 20590291
biomechanics; morphogenesis; differential growth; finite element model; diffusion tensor imaging
4.  Conical expansion of the outer subventricular zone and the role of neocortical folding in evolution and development 
There is a basic rule to mammalian neocortical expansion: as it expands, so does it fold. The degree to which it folds, however, cannot strictly be attributed to its expansion. Across species, cortical volume does not keep pace with cortical surface area, but rather folds appear more rapidly than expected. As a result, larger brains quickly become disproportionately more convoluted than smaller brains. Both the absence (lissencephaly) and presence (gyrencephaly) of cortical folds is observed in all mammalian orders and, while there is likely some phylogenetic signature to the evolutionary appearance of gyri and sulci, there are undoubtedly universal trends to the acquisition of folds in an expanding neocortex. Whether these trends are governed by conical expansion of neocortical germinal zones, the distribution of cortical connectivity, or a combination of growth- and connectivity-driven forces remains an open question. But the importance of cortical folding for evolution of the uniquely mammalian neocortex, as well as for the incidence of neuropathologies in humans, is undisputed. In this hypothesis and theory article, we will summarize the development of cortical folds in the neocortex, consider the relative influence of growth- vs. connectivity-driven forces for the acquisition of cortical folds between and within species, assess the genetic, cell-biological, and mechanistic implications for neocortical expansion, and discuss the significance of these implications for human evolution, development, and disease. We will argue that evolutionary increases in the density of neuron production, achieved via maintenance of a basal proliferative niche in the neocortical germinal zones, drive the conical migration of neurons toward the cortical surface and ultimately lead to the establishment of cortical folds in large-brained mammal species.
PMCID: PMC3729979  PMID: 23914167
neocortex; gyrencephaly; subventricular zone; neural progenitors; mammals; extracellular matrix; phylogenetics
5.  Uniformity, specificity and variability of corticocortical connectivity. 
In many studies of the mammalian brain, subjective assessments of connectivity patterns and connection strengths have been used to subdivide the cortex into separate but linked areas and to make deductions about the flow of information through the cortical network. Here we describe the results of applying statistical analyses to quantitative corticocortical connection data, and the conclusions that can be drawn from such quantitative approaches. Injections of the tracer WGA-HRP were made into different visual areas either side of the middle suprasylvian sulcus (MSS) in 11 adult cats. Retrogradely labelled cells produced by these injections were counted in selected coronal sections taken at regularly spaced intervals (1 mm) through the entire visual cortex, and their cumulative sums and relative proportions in each of 16 recognized visual cortical areas were computed. The surface dimensions of these areas were measured in each cat, from contour lines made on enlarged drawings of the same sections. A total of 116,149 labelled neurons were assigned to all visual cortical areas in the 11 cats, with 5212 others excluded because of their uncertain location. The distribution of relative connection strengths, that is, the percentage of labelled cells per cortical area, was evaluated using non-parametric cluster analyses and Monte Carlo simulation, and relationships between connection strength and area size were examined by linear regression. The absolute size of each visual cortical area was uniform across individual cats, whereas the strengths of connections between the same area pairs were extremely variable for injections in different animals. The overall distribution of labelling strengths for corticocortical connections was continuous and monotonic, rather than inherently clustered, with the highest frequencies presented by the absent (zero density) and the very-low-density connections. These two categories could not, on analytical grounds, be separated from each other. Thus it seems that any subjective description of corticocortical connectivity strengths by ordinal classes (such as 'absent', 'weak', 'moderate' or 'strong') imposes a categorization on the data, rather than recognizes a structure inherent in the data themselves. Despite the great variability of connections, similarities in the distribution profiles for the relative strengths of labelled cells in all areas could be used to identify clusters of different injection sites in the MSS. This supported the conclusion that there are four connectionally distinct subdivisions of this cortex, corresponding to areas 21a, PMLS and AMLS (in the medial bank) and to area PLLS (in the lateral bank). Even for tracer deposits in the same cortical subdivision, however, the strength of connections projecting to the site from other cortical areas varied greatly across injection in different individual animals. We further demonstrated that, on average, the strength of connections originating from any given cortical area was positively and linearly correlated with the size of its surface dimensions. When analysed by specific injection site location, however, this relationship was shown to hold for the individual connections to the medial bank MSS areas, but not for connections leading to the lateral bank area. The data suggest that connectivity of the cat's visual cortex possesses a number of uniform global features, which are locally organized in such a way as to give each cortical area unique characteristics.
PMCID: PMC1692717  PMID: 10703041
6.  An Adaptive Threshold in Mammalian Neocortical Evolution 
PLoS Biology  2014;12(11):e1002000.
A study of the evolutionary history of cortical folding in mammals, its relationship to physiological and life-history traits and the underlying cortical progenitor behavior during embryogenesis, explains the diversity of folding we see across modern mammals. The diversity of neocortical folding among mammals can be explained by two distinct neurogenic programs, which give rise to mammals with a highly folded neocortex and mammals with slightly folded or unfolded neocortex, each occupying a distinct ecological niche.
Expansion of the neocortex is a hallmark of human evolution. However, determining which adaptive mechanisms facilitated its expansion remains an open question. Here we show, using the gyrencephaly index (GI) and other physiological and life-history data for 102 mammalian species, that gyrencephaly is an ancestral mammalian trait. We find that variation in GI does not evolve linearly across species, but that mammals constitute two principal groups above and below a GI threshold value of 1.5, approximately equal to 109 neurons, which may be characterized by distinct constellations of physiological and life-history traits. By integrating data on neurogenic period, neuroepithelial founder pool size, cell-cycle length, progenitor-type abundances, and cortical neuron number into discrete mathematical models, we identify symmetric proliferative divisions of basal progenitors in the subventricular zone of the developing neocortex as evolutionarily necessary for generating a 14-fold increase in daily prenatal neuron production, traversal of the GI threshold, and thus establishment of two principal groups. We conclude that, despite considerable neuroanatomical differences, changes in the length of the neurogenic period alone, rather than any novel neurogenic progenitor lineage, are sufficient to explain differences in neuron number and neocortical size between species within the same principal group.
Author Summary
What are the key differences in the development and evolution of the cerebral cortex that underlie the differences in its size and degree of folding across mammals? Here, we present phylogenetic evidence that the Jurassic era mammalian ancestor may have been a relatively large-brained species with a folded neocortex. We then show that variation in the degree of cortical folding (gyrencephaly index [GI]) does not evolve linearly across species, as previously assumed, but that mammals fall into two principal groups associated with distinct ecological niches: low-GI mammals (such as mice and tarsiers) and high-GI mammals (such as dolphins and humans), which are found to generate on average 14-fold more brain weight per day of gestation. This greater daily brain weight production in mammals with a highly folded neocortex requires a specific class of progenitor cell-type to adopt a special mode of cell division, which is absent in mammals with slightly folded or unfolded neocortices. Differences among mammals within the same GI group (high or low) are not due to different programming, but rather the result of differences in the length of the neurogenic period. So, the impressively large and folded human neocortex, which is three times the size of the chimpanzee neocortex, can be explained by a modest evolutionary extension of the neurogenic period with respect to its closest primate ancestors.
PMCID: PMC4236020  PMID: 25405475
7.  Role of Mechanical Factors in the Morphology of the Primate Cerebral Cortex 
PLoS Computational Biology  2006;2(3):e22.
The convoluted cortex of primates is instantly recognizable in its principal morphologic features, yet puzzling in its complex finer structure. Various hypotheses have been proposed about the mechanisms of its formation. Based on the analysis of databases of quantitative architectonic and connection data for primate prefrontal cortices, we offer support for the hypothesis that tension exerted by corticocortical connections is a significant factor in shaping the cerebral cortical landscape. Moreover, forces generated by cortical folding influence laminar morphology, and appear to have a previously unsuspected impact on cellular migration during cortical development. The evidence for a significant role of mechanical factors in cortical morphology opens the possibility of constructing computational models of cortical develoment based on physical principles. Such models are particularly relevant for understanding the relationship of cortical morphology to the connectivity of normal brains, and structurally altered brains in diseases of developmental origin, such as schizophrenia and autism.
How are the characteristic folds of primate brains formed? New answers to this old question support the idea that folding occurs as nerve fibers connect the brain's different surface regions. The fibers pull together regions that are strongly connected, while unconnected regions drift apart. Furthermore, as the brain develops before birth and its surface expands, folding may affect the passage of new neurons into different regions, influencing the brain's architecture. These findings underscore the role of mechanical forces in shaping the normal brain. Moreover, the findings suggest that changes in brain shape in developmental diseases, such as schizophrenia and autism, may result from changes in the connections.
PMCID: PMC1409812  PMID: 16557292
8.  Axonal Velocity Distributions in Neural Field Equations 
PLoS Computational Biology  2010;6(1):e1000653.
By modelling the average activity of large neuronal populations, continuum mean field models (MFMs) have become an increasingly important theoretical tool for understanding the emergent activity of cortical tissue. In order to be computationally tractable, long-range propagation of activity in MFMs is often approximated with partial differential equations (PDEs). However, PDE approximations in current use correspond to underlying axonal velocity distributions incompatible with experimental measurements. In order to rectify this deficiency, we here introduce novel propagation PDEs that give rise to smooth unimodal distributions of axonal conduction velocities. We also argue that velocities estimated from fibre diameters in slice and from latency measurements, respectively, relate quite differently to such distributions, a significant point for any phenomenological description. Our PDEs are then successfully fit to fibre diameter data from human corpus callosum and rat subcortical white matter. This allows for the first time to simulate long-range conduction in the mammalian brain with realistic, convenient PDEs. Furthermore, the obtained results suggest that the propagation of activity in rat and human differs significantly beyond mere scaling. The dynamical consequences of our new formulation are investigated in the context of a well known neural field model. On the basis of Turing instability analyses, we conclude that pattern formation is more easily initiated using our more realistic propagator. By increasing characteristic conduction velocities, a smooth transition can occur from self-sustaining bulk oscillations to travelling waves of various wavelengths, which may influence axonal growth during development. Our analytic results are also corroborated numerically using simulations on a large spatial grid. Thus we provide here a comprehensive analysis of empirically constrained activity propagation in the context of MFMs, which will allow more realistic studies of mammalian brain activity in the future.
Author Summary
Due to the sheer number of neurons and the complexity of their interactions, the modelling of brain activity is particularly challenging. How can computationally tractable models of brain function be developed that are nevertheless biologically plausible? The “mean field” approach, borrowed from statistical physics, is to model the average activity of populations of neurons rather than the behaviour of individual neurons. While a large number of promising theories have been developed with this approach, they fall short of biological fidelity in the way interactions between distant populations have been modelled. In particular, it is often assumed that all neurons interact via connections of very similar conduction velocity, when in fact experiment suggests quite the opposite: populations of neurons are connected by axonal fibres with a broad range of velocities. We develop here activity propagators that provide for the first time the ability to realistically and efficiently simulate connectivity in mean field theories, and demonstrate how to use them to fit successfully experimental data from both human and rat. With our novel propagators, one can thus study on an empirical basis the role of activity propagation in both healthy and diseased mammalian brains.
PMCID: PMC2813262  PMID: 20126532
9.  Stochastic Simulations on the Reliability of Action Potential Propagation in Thin Axons 
PLoS Computational Biology  2007;3(5):e79.
It is generally assumed that axons use action potentials (APs) to transmit information fast and reliably to synapses. Yet, the reliability of transmission along fibers below 0.5 μm diameter, such as cortical and cerebellar axons, is unknown. Using detailed models of rodent cortical and squid axons and stochastic simulations, we show how conduction along such thin axons is affected by the probabilistic nature of voltage-gated ion channels (channel noise). We identify four distinct effects that corrupt propagating spike trains in thin axons: spikes were added, deleted, jittered, or split into groups depending upon the temporal pattern of spikes. Additional APs may appear spontaneously; however, APs in general seldom fail (<1%). Spike timing is jittered on the order of milliseconds over distances of millimeters, as conduction velocity fluctuates in two ways. First, variability in the number of Na channels opening in the early rising phase of the AP cause propagation speed to fluctuate gradually. Second, a novel mode of AP propagation (stochastic microsaltatory conduction), where the AP leaps ahead toward spontaneously formed clusters of open Na channels, produces random discrete jumps in spike time reliability. The combined effect of these two mechanisms depends on the pattern of spikes. Our results show that axonal variability is a general problem and should be taken into account when considering both neural coding and the reliability of synaptic transmission in densely connected cortical networks, where small synapses are typically innervated by thin axons. In contrast we find that thicker axons above 0.5 μm diameter are reliable.
Author Summary
Neurons in cerebral cortex achieve wiring densities of 4 km per mm3 by using unmyelinated axons of 0.3 μm average diameter as wires. Many axons (e.g., pain fibers) are thinner. Although, as in computer chips, wire miniaturization economizes on space and energy, it increases the noise introduced by thermodynamic fluctuations in a neuron's “protein transistors,” voltage-gated ion channels. We investigated how well the relatively small number of ion channels found in the membranes of tiny axons propagate the brain's universal signal—the action potential. We built a stochastic model that incorporates the random behavior of individual ion channels and found noise effects much larger than previously assumed, because standard stochastic approximation techniques (Langevin) break down because single channels can produce whole-cell responses. Channel noise destroys information encoded in the timing of action potentials, by randomly varying the speed of conduction, and produces a novel mode of transmission, stochastic microsaltatory conduction. Ion channel populations retain memory of previous activity in the distribution of channel states, causing action potential reliability to vary with context. The effects and general relationships identified here will govern other cell-signaling systems that rely on inherently noisy protein switches to propagate signals, either for intracellular communication (Ca++/cAMP waves) or in nanotechnology.
PMCID: PMC1864994  PMID: 17480115
10.  3D Reconstruction and Standardization of the Rat Vibrissal Cortex for Precise Registration of Single Neuron Morphology 
PLoS Computational Biology  2012;8(12):e1002837.
The three-dimensional (3D) structure of neural circuits is commonly studied by reconstructing individual or small groups of neurons in separate preparations. Investigation of structural organization principles or quantification of dendritic and axonal innervation thus requires integration of many reconstructed morphologies into a common reference frame. Here we present a standardized 3D model of the rat vibrissal cortex and introduce an automated registration tool that allows for precise placement of single neuron reconstructions. We (1) developed an automated image processing pipeline to reconstruct 3D anatomical landmarks, i.e., the barrels in Layer 4, the pia and white matter surfaces and the blood vessel pattern from high-resolution images, (2) quantified these landmarks in 12 different rats, (3) generated an average 3D model of the vibrissal cortex and (4) used rigid transformations and stepwise linear scaling to register 94 neuron morphologies, reconstructed from in vivo stainings, to the standardized cortex model. We find that anatomical landmarks vary substantially across the vibrissal cortex within an individual rat. In contrast, the 3D layout of the entire vibrissal cortex remains remarkably preserved across animals. This allows for precise registration of individual neuron reconstructions with approximately 30 µm accuracy. Our approach could be used to reconstruct and standardize other anatomically defined brain areas and may ultimately lead to a precise digital reference atlas of the rat brain.
Author Summary
For studying the neural basis of perception and behavior, it would be ideal to directly monitor sensory-evoked excitation streams within neural circuits, at sub-cellular and millisecond resolution. To do so, reverse engineering approaches of reconstructing circuit anatomy and synaptic wiring have been suggested. The resulting anatomically realistic models may then allow for computer simulations (in silico experiments) of circuit function. A natural starting point for reconstructing neural circuits is a cortical column, which is thought to be an elementary functional unit of sensory cortices. In the vibrissal area of rodent somatosensory cortex, a cytoarchitectonic equivalent, designated as a ‘barrel column’, has been described. By reconstructing the 3D geometry of almost 1,000 barrel columns, we show that the somatotopic layout of the vibrissal cortex is highly preserved across animals. This allows generating a standard cortex and registering neuron morphologies, obtained from different experiments, to their ‘true’ location. Marking a crucial step towards reverse engineering of cortical circuits, the present study will allow estimating synaptic connectivity within an entire cortical area by structural overlap of registered axons and dendrites.
PMCID: PMC3527218  PMID: 23284282
11.  Emergence of Metastable State Dynamics in Interconnected Cortical Networks with Propagation Delays 
PLoS Computational Biology  2013;9(10):e1003304.
The importance of the large number of thin-diameter and unmyelinated axons that connect different cortical areas is unknown. The pronounced propagation delays in these axons may prevent synchronization of cortical networks and therefore hinder efficient information integration and processing. Yet, such global information integration across cortical areas is vital for higher cognitive function. We hypothesized that delays in communication between cortical areas can disrupt synchronization and therefore enhance the set of activity trajectories and computations interconnected networks can perform. To evaluate this hypothesis, we studied the effect of long-range cortical projections with propagation delays in interconnected large-scale cortical networks that exhibited spontaneous rhythmic activity. Long-range connections with delays caused the emergence of metastable, spatio-temporally distinct activity states between which the networks spontaneously transitioned. Interestingly, the observed activity patterns correspond to macroscopic network dynamics such as globally synchronized activity, propagating wave fronts, and spiral waves that have been previously observed in neurophysiological recordings from humans and animal models. Transient perturbations with simulated transcranial alternating current stimulation (tACS) confirmed the multistability of the interconnected networks by switching the networks between these metastable states. Our model thus proposes that slower long-range connections enrich the landscape of activity states and represent a parsimonious mechanism for the emergence of multistability in cortical networks. These results further provide a mechanistic link between the known deficits in connectivity and cortical state dynamics in neuropsychiatric illnesses such as schizophrenia and autism, as well as suggest non-invasive brain stimulation as an effective treatment for these illnesses.
Author Summary
The brain mediates behavior by orchestrating the activity of billions of neurons that communicate with each other through electric impulses. The transmission of these action potentials is surprisingly slow for a large fraction of these connections. Given the importance of precise timing of neuronal activity, the function of these slow connections has remained a puzzle. We here used computer simulations to investigate how slow connection speeds alter the overall activity patterns of two brain networks. We found that these connections enable the interconnected networks to generate distinct activity patterns such as different types of waves of electric activity. Our results therefore suggest that the slow transmission of electric impulses in the brain is not a “design flaw” but rather plays an important role in enabling the brain to generate a richer set of activity patterns. The ability of the brain to switch between different activity states is crucial to normal cognition, and abnormalities in switching behavior are associated with cognitive symptoms in psychiatric disorders such as schizophrenia and autism. It is therefore promising that we were able to control transitions between different activity states with non-invasive brain stimulation in our simulations, suggesting a novel approach to the treatment of these illnesses.
PMCID: PMC3812055  PMID: 24204238
12.  Cortical Gyrification Induced by Fibroblast Growth Factor 2 in the Mouse Brain 
The Journal of Neuroscience  2013;33(26):10802-10814.
Gyrification allows an expanded cortex with greater functionality to fit into a smaller cranium. However, the mechanisms of gyrus formation have been elusive. We show that ventricular injection of FGF2 protein at embryonic day 11.5—before neurogenesis and before the formation of intrahemispheric axonal connections—altered the overall size and shape of the cortex and induced the formation of prominent, bilateral gyri and sulci in the rostrolateral neocortex. We show increased tangential growth of the rostral ventricular zone (VZ) but decreased Wnt3a and Lef1 expression in the cortical hem and adjacent hippocampal promordium and consequent impaired growth of the caudal cortical primordium, including the hippocampus. At the same time, we observed ectopic Er81 expression, increased proliferation of Tbr2-expressing (Tbr2+) intermediate neuronal progenitors (INPs), and elevated Tbr1+ neurogenesis in the regions that undergo gyrification, indicating region-specific actions of FGF2 on the VZ and subventricular zone (SVZ). However, the relative number of basal radial glia—recently proposed to be important in gyrification—appeared to be unchanged. These findings are consistent with the hypothesis that increased radial unit production together with rapid SVZ growth and heightened localized neurogenesis can cause cortical gyrification in lissencephalic species. These data also suggest that the position of cortical gyri can be molecularly specified in mice. In contrast, a different ligand, FGF8b, elicited surface area expansion throughout the cortical primordium but no gyrification. Our findings demonstrate that individual members of the diverse Fgf gene family differentially regulate global as well as regional cortical growth rates while maintaining cortical layer structure.
PMCID: PMC3693057  PMID: 23804101
13.  Segregation of the Brain into Gray and White Matter: A Design Minimizing Conduction Delays 
PLoS Computational Biology  2005;1(7):e78.
A ubiquitous feature of the vertebrate anatomy is the segregation of the brain into white and gray matter. Assuming that evolution maximized brain functionality, what is the reason for such segregation? To answer this question, we posit that brain functionality requires high interconnectivity and short conduction delays. Based on this assumption we searched for the optimal brain architecture by comparing different candidate designs. We found that the optimal design depends on the number of neurons, interneuronal connectivity, and axon diameter. In particular, the requirement to connect neurons with many fast axons drives the segregation of the brain into white and gray matter. These results provide a possible explanation for the structure of various regions of the vertebrate brain, such as the mammalian neocortex and neostriatum, the avian telencephalon, and the spinal cord.
Vertebrate brains generally contain two kinds of tissue: gray matter and white matter. Gray matter contains local networks of neurons that are wired by dendrites and mostly nonmyelinated local axons. White matter contains long-range axons that implement global communication via often myelinated axons. What is the evolutionary advantage of segregating the brain into white and gray matter rather than intermixing them? In this study, the authors postulate that brain functionality benefits from high synaptic connectivity and short conduction delays—the time required for a signal from one neuron soma to reach another. Using this postulate, they show quantitatively that the existence of many fast, long-range axons drives the segregation of the brain into gray and white matter. The theory not only provides a possible explanation for the structure of various brain regions such as cerebral cortex, neostriatum, and spinal cord, but also makes several testable predictions such as the scaling estimate of the cortical thickness.
PMCID: PMC1323466  PMID: 16389299
14.  A multi-compartment CNS neuron-glia co-culture microfluidic platform 
We present a novel multi-compartment neuron co-culture microsystem platform for in vitro CNS axon-glia interaction research, capable of conducting up to six independent experiments in parallel for higher-throughput. We developed a new fabrication method to create microfluidic devices having both micro and macro scale structures within the same device through a single soft-lithography process, enabling mass fabrication with good repeatability.
The multi-compartment microfluidic co-culture platform is composed of one soma compartment for neurons and six axon/glia compartments for oligodendrocytes (OLs). The soma compartment and axon/glia compartments are connected b y arrays of axon-guiding microchannels that function as physical barriers to confine neuronal soma in the soma compartment, while allowing axons to grow into axon/glia compartments. OLs loaded into axon/glia compartments can interact only with axons but not with neuronal soma or dendrites, enabling localized axon-glia interaction studies. The microchannels also enabled fluidic isolation between compartments, allowing six independent experiments to be conducted on a single device for higher throughput.
Soft-lithography using poly(dimethylsiloxane) (PDMS) is a commonly used technique in biomedical microdevices. Reservoirs on these devices are commonly defined by manual punching. Although simple, poor alignment and time consuming nature of the process makes this process not suitable when large numbers of reservoirs have to be repeatedly created. The newly developed method did not require manual punching of reservoirs, overcoming such limitations. First, seven reservoirs (depth: 3.5 mm) were made on a poly(methyl methacrylate) (PMMA) block using a micro-milling machine. Then, arrays of ridge microstructures, fabricated on a glass substrate, were hot-embossed against the PMMA block to define microchannels that connect the soma and axon/glia compartments. This process resulted in macro-scale reservoirs (3.5 mm) and micro-scale channels (2.5 µm) to coincide within a single PMMA master. A PDMS replica that served as a mold master was obtained using soft-lithography and the final PDMS device was replicated from this master.
Primary neurons from E16–18 rats were loaded to the soma compartment and cultured for two weeks. After one week of cell culture, axons crossed microchannels and formed axonal only network layer inside axon/glia compartments. Axons grew uniformly throughout six axon/glia compartments and OLs from P1–2 rats were added to axon/glia compartments at 14 days in vitro for co-culture.
PMCID: PMC2774404  PMID: 19745806
Neuron culture; neuron-glia interaction; microfluidics; cell culture microsystem
15.  Chemically Based Mathematical Model for Development of Cerebral Cortical Folding Patterns 
PLoS Computational Biology  2009;5(9):e1000524.
The mechanism for cortical folding pattern formation is not fully understood. Current models represent scenarios that describe pattern formation through local interactions, and one recent model is the intermediate progenitor model. The intermediate progenitor (IP) model describes a local chemically driven scenario, where an increase in intermediate progenitor cells in the subventricular zone correlates to gyral formation. Here we present a mathematical model that uses features of the IP model and further captures global characteristics of cortical pattern formation. A prolate spheroidal surface is used to approximate the ventricular zone. Prolate spheroidal harmonics are applied to a Turing reaction-diffusion system, providing a chemically based framework for cortical folding. Our model reveals a direct correlation between pattern formation and the size and shape of the lateral ventricle. Additionally, placement and directionality of sulci and the relationship between domain scaling and cortical pattern elaboration are explained. The significance of this model is that it elucidates the consistency of cortical patterns among individuals within a species and addresses inter-species variability based on global characteristics and provides a critical piece to the puzzle of cortical pattern formation.
Author Summary
The size and shape of the cerebral cortex varies across species. The cortical folding pattern also varies from a smooth surface where no pattern is visible, as observed in the common treeshrew (Tupaia glis) and Eastern mole (Scalopus aquaticus), to an intricate labyrinthine pattern, as observed in humans. One current model, the intermediate progenitor model, describes the creation of a fold through local interactions in the ventricular zone which surrounds the lateral ventricle. Here we extend the local scenario described in the intermediate progenitor model to include global characteristics that differ between species. We approximate the lateral ventricle with a prolate spheroid and examine how patterns on a spheroidal surface change based on size and eccentricity. Our model reveals a direct correlation between pattern formation and lateral ventricular size and shape. This model's significance is that it elucidates the consistency of cortical patterns among individuals within a species and addresses inter-species variability based on global characteristics, such as size and shape of the lateral ventricle, and provides a critical piece to the puzzle of cortical pattern formation.
PMCID: PMC2740831  PMID: 19779554
16.  Dendritic Branch Intersections Are Structurally Regulated Targets for Efficient Axonal Wiring and Synaptic Clustering 
PLoS ONE  2013;8(12):e82083.
Synaptic clustering on dendritic branches enhances plasticity, input integration and neuronal firing. However, the mechanisms guiding axons to cluster synapses at appropriate sites along dendritic branches are poorly understood. We searched for such a mechanism by investigating the structural overlap between dendritic branches and axons in a simplified model of neuronal networks - the hippocampal cell culture. Using newly developed software, we converted images of meshes of overlapping axonal and dendrites into topological maps of intersections, enabling quantitative study of overlapping neuritic geometry at the resolution of single dendritic branch-to-branch and axon-to-branch crossings. Among dendro-dendritic crossing configurations, it was revealed that the orientations through which dendritic branches cross is a regulated attribute. While crossing angle distribution among branches thinner than 1 µm appeared to be random, dendritic branches 1 µm or wider showed a preference for crossing each other at angle ranges of either 50°–70° or 80°–90°. It was then found that the dendro-dendritic crossings themselves, as well as their selective angles, both affected the path of axonal growth. Axons displayed 4 fold stronger tendency to traverse within 2 µm of dendro-dendritic intersections than at farther distances, probably to minimize wiring length. Moreover, almost 70% of the 50°–70° dendro-denritic crossings were traversed by axons from the obtuse angle’s zone, whereas only 15% traversed through the acute angle’s zone. By contrast, axons showed no orientation restriction when traversing 80°–90° crossings. When such traverse behavior was repeated by many axons, they converged in the vicinity of dendro-dendritic intersections, thereby clustering their synaptic connections. Thus, the vicinity of dendritic branch-to-branch crossings appears to be a regulated structure used by axons as a target for efficient wiring and as a preferred site for synaptic clustering. This synaptic clustering mechanism may enhance synaptic co-activity and plasticity.
PMCID: PMC3862581  PMID: 24349189
17.  Mutual inhibition among postmitotic neurons regulates robustness of brain wiring in Drosophila 
eLife  2013;2:e00337.
Brain connectivity maps display a delicate balance between individual variation and stereotypy, suggesting the existence of dedicated mechanisms that simultaneously permit and limit individual variation. We show that during the development of the Drosophila central nervous system, mutual inhibition among groups of neighboring postmitotic neurons during development regulates the robustness of axon target choice in a nondeterministic neuronal circuit. Specifically, neighboring postmitotic neurons communicate through Notch signaling during axonal targeting, to ensure balanced alternative axon target choices without a corresponding change in cell fate. Loss of Notch in postmitotic neurons modulates an axon's target choice. However, because neighboring axons respond by choosing the complementary target, the stereotyped connectivity pattern is preserved. In contrast, loss of Notch in clones of neighboring postmitotic neurons results in erroneous coinnervation by multiple axons. Our observations establish mutual inhibition of axonal target choice as a robustness mechanism for brain wiring and unveil a novel cell fate independent function for canonical Notch signaling.
eLife digest
The brains of all members of a species are similar, but not identical, and these differences are partly responsible for the range of behaviors displayed by individuals. The development of the nervous system is known to depend on the Notch signaling pathway, but the mechanisms that regulate the balance between fixed patterns of neuronal connectivity vs individual variability are largely unknown.
Notch proteins are transmembrane proteins, which means that they have one part inside the cell membrane and another outside the cell. When a ligand protein—such as a Delta ligand—binds to the part that is outside the cell, the Notch protein breaks in two and the part inside the cell travels to the nucleus, where it can influence the expression of genes.
Cells are selected to become neurons through a process known as mutual, or lateral, inhibition. When a Delta ligand belonging to one cell binds to the Notch receptor on a neighboring cell, the production of Delta ligands in the second cell is reduced. This amplifies any initial differences in the amount of Delta produced by each cell, and leads ultimately to them becoming distinct cell types.
Now, Langen et al. show that this same mechanism is reactivated at a later stage of development during wiring up of the visual system. They used the fruit fly (Drosophila)—a model organism with a fully sequenced genome and short intergeneration time—to study a group of brain cells known as dorsal cluster neurons. At the end of the fruit fly larval stage, these neurons extend long axons across the brain to the opposite hemisphere: however, it is unclear how the neurons decide which cells to form connections with.
Using genetically modified flies, Langen et al. showed that inhibiting Notch in a single dorsal cluster neuron caused that neuron to target a different cell: however, other neurons adjusted their choices accordingly so that the overall pattern of connections remained unchanged. Inhibiting Notch in a cluster of dorsal cluster neurons, on the other hand, disrupted the entire network, suggesting that Notch-mediated communication between neurons (via mutual inhibition) is needed to establish a robust wiring map.
Langen et al. suggest that evolution has favored a mechanism that ensures that the overall pattern of connections within a circuit is preserved, while individual connections differ from one species member to the next.
PMCID: PMC3589824  PMID: 23471010
Neurobiology; Neural Circuit; Robustness; Variability; Notch Signaling; Axonal targeting; D. melanogaster
18.  Communication and wiring in the cortical connectome 
In cerebral cortex, the huge mass of axonal wiring that carries information between near and distant neurons is thought to provide the neural substrate for cognitive and perceptual function. The goal of mapping the connectivity of cortical axons at different spatial scales, the cortical connectome, is to trace the paths of information flow in cerebral cortex. To appreciate the relationship between the connectome and cortical function, we need to discover the nature and purpose of the wiring principles underlying cortical connectivity. A popular explanation has been that axonal length is strictly minimized both within and between cortical regions. In contrast, we have hypothesized the existence of a multi-scale principle of cortical wiring where to optimize communication there is a trade-off between spatial (construction) and temporal (routing) costs. Here, using recent evidence concerning cortical spatial networks we critically evaluate this hypothesis at neuron, local circuit, and pathway scales. We report three main conclusions. First, the axonal and dendritic arbor morphology of single neocortical neurons may be governed by a similar wiring principle, one that balances the conservation of cellular material and conduction delay. Second, the same principle may be observed for fiber tracts connecting cortical regions. Third, the absence of sufficient local circuit data currently prohibits any meaningful assessment of the hypothesis at this scale of cortical organization. To avoid neglecting neuron and microcircuit levels of cortical organization, the connectome framework should incorporate more morphological description. In addition, structural analyses of temporal cost for cortical circuits should take account of both axonal conduction and neuronal integration delays, which appear mostly of the same order of magnitude. We conclude the hypothesized trade-off between spatial and temporal costs may potentially offer a powerful explanation for cortical wiring patterns.
PMCID: PMC3472565  PMID: 23087619
axon; cerebral cortex; communication; connectome; dendrite; networks; optimization; Ramón y Cajal
19.  Distribution of neurons in functional areas of the mouse cerebral cortex reveals quantitatively different cortical zones 
How are neurons distributed along the cortical surface and across functional areas? Here we use the isotropic fractionator (Herculano-Houzel and Lent, 2005) to analyze the distribution of neurons across the entire isocortex of the mouse, divided into 18 functional areas defined anatomically. We find that the number of neurons underneath a surface area (the N/A ratio) varies 4.5-fold across functional areas and neuronal density varies 3.2-fold. The face area of S1 contains the most neurons, followed by motor cortex and the primary visual cortex. Remarkably, while the distribution of neurons across functional areas does not accompany the distribution of surface area, it mirrors closely the distribution of cortical volumes—with the exception of the visual areas, which hold more neurons than expected for their volume. Across the non-visual cortex, the volume of individual functional areas is a shared linear function of their number of neurons, while in the visual areas, neuronal densities are much higher than in all other areas. In contrast, the 18 functional areas cluster into three different zones according to the relationship between the N/A ratio and cortical thickness and neuronal density: these three clusters can be called visual, sensory, and, possibly, associative. These findings are remarkably similar to those in the human cerebral cortex (Ribeiro et al., 2013) and suggest that, like the human cerebral cortex, the mouse cerebral cortex comprises two zones that differ in how neurons form the cortical volume, and three zones that differ in how neurons are distributed underneath the cortical surface, possibly in relation to local differences in connectivity through the white matter. Our results suggest that beyond the developmental divide into visual and non-visual cortex, functional areas initially share a common distribution of neurons along the parenchyma that become delimited into functional areas according to the pattern of connectivity established later.
PMCID: PMC3800983  PMID: 24155697
mouse; visual cortex; occipital cortex; cortical development; neuronal density; numbers of neurons
20.  Kinase/phosphatase overexpression reveals pathways regulating hippocampal neuron morphology 
Kinases and phosphatases that regulate neurite number versus branching versus extension are weakly correlated.The kinase family that most strongly enhances neurite growth is a family of non-protein kinases; sugar kinases related to NADK.Pathway analysis revealed that genes in several cancer pathways were highly active in enhancing neurite growth.
In neural development, neuronal precursors differentiate, migrate, extend long axons and dendrites, and finally establish connections with their targets. Clinical conditions such as spinal cord injury, traumatic brain injury, stroke, multiple sclerosis, Parkinson's disease, Huntington's disease, and Alzheimer's disease are often associated with a loss of axon and/or dendrite connectivity and treatment strategies would be enhanced by new therapies targeting cell intrinsic mechanisms of axon elongation and regeneration.
Phosphorylation controls most cellular processes, including the cell cycle, proliferation, metabolism, and apoptosis. Neuronal differentiation, including axon formation and elongation, is also regulated by a wide range of kinases and phosphatases. For example, the non-receptor tyrosine kinase Src is required for cell adhesion molecule-dependent neurite outgrowth. In addition to individual kinases and phosphatases, signaling pathways like the MAPK, growth factor signaling, PIP3, cytoskeletal, and calcium-dependent pathways have been shown to impinge on or control neuronal process development. Recent results have implicated GSK3 and PTEN as therapeutically relevant targets in axonal regeneration after injury. However, these and other experiments have studied only a small fraction of the total kinases and phosphatases in the genome. Because of recent advances in genomic knowledge, large-scale cDNA production, and high-throughput phenotypic analysis, it is now possible to take a more comprehensive approach to understanding the functions of kinases and phosphatases in neurons.
We performed a large, unbiased set of experiments to answer the question ‘what effect does the overexpression of genes encoding kinases, phosphatases, and related proteins have on neuronal morphology?' We used ‘high-content analysis' to obtain detailed results about the specific phenotypes of neurons. We studied embryonic rat hippocampal neurons because of their stereotypical development in vitro (Dotti et al, 1988) and their widespread use in studies of neuronal differentiation and signaling. We transfected over 700 clones encoding kinases and phosphatases into hippocampal neurons and analyzed the resulting changes in neuronal morphology.
Many known genes, including PP1a, ERK1, ErbB2, atypical PKC, Calcineurin, CaMK2, IGF1R, FGFR, GSK3, and PIK3 were observed to have significant effects on neurite outgrowth in our system, consistent with earlier findings in the literature.
We obtained quantitative data for many cellular and neuronal morphological parameters from each neuron imaged. These included nuclear morphology (nuclear area and Hoechst dye intensity), soma morphology (tubulin intensity, area, and shape), and numerous parameters of neurite morphology (e.g. tubulin intensity along the neurites, number of primary neurites, neurite length, number of branches, distance from the cell body to the branches, number of crossing points, width and area of the neurites, and longest neurite; Supplementary Figure 1). Other parameters were reported on a ‘per well' basis, including the percentage of transfected neurons in a condition, as well as the percentage of neurons initiating neurite growth. Data for each treatment were normalized to a control (pSport CAT) within the same experiment, then aggregated across replicate experiments.
Correlations among the 19 normalized parameters were analyzed for neurons transfected with all kinase and phosphatase clones (Figure 2). On the basis of this analysis, the primary variables that define the neurite morphology are primary neurite count, neurite average length, and average branches. Interestingly, primary neurite count was not well correlated with neurite length or branching. The Pearson correlation coefficient (r2) between the number of primary neurites and the average length of the neurites was 0.3, and between the number of primary neurites and average branching was 0.2. In contrast, the correlation coefficient of average branching with neurite average length was 0.7. The most likely explanation is that signaling mechanisms underlying the neurite number determination are different than those controlling length/branching of the neurites.
Related proteins are often involved in similar neuronal functions. For example, families of receptor protein tyrosine phosphatases are involved in motor axon extension and guidance in both Drosophila and in vertebrates, and a large family of Eph receptor tyrosine kinases regulates guidance of retinotectal projections, motor axons, and axons in the corpus callosum. We therefore asked whether families of related genes produced similar phenotypes when overexpressed in hippocampal neurons. Our set of genes covered 40% of the known protein kinases, and many of the non-protein kinases and phosphatases.
Gene families commonly exhibit redundant function. Redundant gene function has often been identified when two or more knockouts are required to produce a phenotype. Our technique allowed us to measure whether different members of gene families had similar (potentially redundant) or distinct effects on neuronal phenotype.
To determine whether groups of related genes affect neuronal morphology in similar ways, we used sequence alignment information to construct gene clusters (Figure 6). Genes were clustered at nine different thresholds of similarity (called ‘tiers'). The functional effect for a particular parameter was then averaged within each cluster of a given tier, and statistics were performed to determine the significance of the effect. We analyzed the results for three key neurite parameters (average neurite length, primary neurite count, and average branching). Genes that perturbed each of these phenotypes are grouped in Figure 6. Eight families, most with only a few genes, produced significant changes for one or two parameters. A diverse family of non-protein kinases had a positive effect on neurite outgrowth in three of the four parameters analyzed. This family of kinases consisted of a variety of enzymes, mostly sugar and lipid kinases. A similar analysis was performed using pathway cluster analysis with pathways from the KEGG database, rather than sequence homology. Interestingly, pathways involved in cancer cell proliferation potentiated neurite extension and branching.
Our studies have identified a large number of kinases and phosphatases, as well as structurally and functionally defined families of these proteins, that affect neuronal process formation in specific ways. We have provided an analytical methodology and new tools to analyze functional data, and have implicated genes with novel functions in neuronal development. Our studies are an important step towards the goal of a molecular description of the intrinsic control of axodendritic growth.
Development and regeneration of the nervous system requires the precise formation of axons and dendrites. Kinases and phosphatases are pervasive regulators of cellular function and have been implicated in controlling axodendritic development and regeneration. We undertook a gain-of-function analysis to determine the functions of kinases and phosphatases in the regulation of neuron morphology. Over 300 kinases and 124 esterases and phosphatases were studied by high-content analysis of rat hippocampal neurons. Proteins previously implicated in neurite growth, such as ERK1, GSK3, EphA8, FGFR, PI3K, PKC, p38, and PP1a, were confirmed to have effects in our functional assays. We also identified novel positive and negative neurite growth regulators. These include neuronal-developmentally regulated kinases such as the activin receptor, interferon regulatory factor 6 (IRF6) and neural leucine-rich repeat 1 (LRRN1). The protein kinase N2 (PKN2) and choline kinase α (CHKA) kinases, and the phosphatases PPEF2 and SMPD1, have little or no established functions in neuronal function, but were sufficient to promote neurite growth. In addition, pathway analysis revealed that members of signaling pathways involved in cancer progression and axis formation enhanced neurite outgrowth, whereas cytokine-related pathways significantly inhibited neurite formation.
PMCID: PMC2925531  PMID: 20664637
bioinformatics; development; functional genomics; metabolic and regulatory networks; neuroscience
21.  A Phenomenological Theory of Spatially Structured Local Synaptic Connectivity 
PLoS Computational Biology  2005;1(1):e11.
The structure of local synaptic circuits is the key to understanding cortical function and how neuronal functional modules such as cortical columns are formed. The central problem in deciphering cortical microcircuits is the quantification of synaptic connectivity between neuron pairs. I present a theoretical model that accounts for the axon and dendrite morphologies of pre- and postsynaptic cells and provides the average number of synaptic contacts formed between them as a function of their relative locations in three-dimensional space. An important aspect of the current approach is the representation of a complex structure of an axonal/dendritic arbor as a superposition of basic structures—synaptic clouds. Each cloud has three structural parameters that can be directly estimated from two-dimensional drawings of the underlying arbor. Using empirical data available in literature, I applied this theory to three morphologically different types of cell pairs. I found that, within a wide range of cell separations, the theory is in very good agreement with empirical data on (i) axonal–dendritic contacts of pyramidal cells and (ii) somatic synapses formed by the axons of inhibitory interneurons. Since for many types of neurons plane arborization drawings are available from literature, this theory can provide a practical means for quantitatively deriving local synaptic circuits based on the actual observed densities of specific types of neurons and their morphologies. It can also have significant implications for computational models of cortical networks by making it possible to wire up simulated neural networks in a realistic fashion.
Each neuron communicates signals via synaptic connections simultaneously to several hundreds of neighboring neurons forming a synaptic circuit. Determining the pattern of synaptic connections between local neurons is crucial for understanding a specific cortical function implemented by a synaptic circuit. The connectivity between a pair of neurons is affected by their axonal/dendritic morphologies and relative spatial locations. Although neuroscientists have precise tools to measure neuronal activity caused by the flow of signals between circuit neurons, there are still considerable difficulties in the direct experimental measurement of local synaptic connectivity, which actually determines the underlying activity. This paper presents a theoretical approach to synaptic connectivity accounting for the morphologies of pre- and postsynaptic neurons and providing the average number of synaptic contacts formed between them as a function of their relative locations. An important aspect is the decomposition of the complex structure of an axonal/dendritic arbor into a small number of basic structures. The theory is in very good agreement, within a wide range of cell separations, with empirical data on axonal–dendritic contacts of pyramidal cells and somatic synapses formed by the axons of inhibitory interneurons. The current approach can provide a practical means for quantitatively deriving local synaptic circuits based on the actual observed densities of specific types of neurons and their morphologies.
PMCID: PMC1183517  PMID: 16103900
22.  A cytomechanical investigation of neurite growth on different culture surfaces 
The Journal of Cell Biology  1992;118(3):655-661.
We have examined the relationship between tension, an intrinsic stimulator of axonal elongation, and the culture substrate, an extrinsic regulator of axonal elongation. Chick sensory neurons were cultured on three substrata: (a) plain tissue culture plastic; (b) plastic treated with collagen type IV; and (c) plastic treated with laminin. Calibrated glass needles were used to increase the tension loads on growing neurites. We found that growth cones on all substrata failed to detach when subjected to two to threefold and in some cases 5- 10-fold greater tensions than their self-imposed rest tension. We conclude that adhesion to the substrate does not limit the tension exerted by growth cones. These data argue against a "tug-of-war" model for substrate-mediated guidance of growth cones. Neurite elongation was experimentally induced by towing neurites with a force-calibrated glass needle. On all substrata, towed elongation rate was proportional to applied tension above a threshold tension. The proportionality between elongation rate and tension can be regarded as the growth sensitivity of the neurite to tension, i.e., its growth rate per unit tension. On this basis, towed growth on all substrata can be described by the simple linear equation: elongation rate = sensitivity x (applied tension - tension threshold) The numerical values of tension thresholds and neurite sensitivities varied widely among different neurites. On all substrata, thresholds varied from near zero to greater than 200 mudynes, with some tendency for thresholds to cluster between 100 and 150 mudynes. Similarly, the tension sensitivity of neurites varied between 0.5 and 5.0 microns/h/mudyne. The lack of significant differences among sensitivity or threshold values on the various substrata suggest to use that the substratum does not affect the internal "set points" of the neurite for its response to tension. The growth cone of chick sensory neurons is known to pull on its neurite. The simplest cytomechanical model would assume that both growth cone- mediated elongation and towed growth are identical as far as tension input and elongation rate are concerned. We used the equation above and mean values for thresholds and sensitivity from towing experiments to predict the mean growth cone-mediated elongation rate based on mean rest tensions. These predictions are consistent with the observed mean values.
PMCID: PMC2289549  PMID: 1639849
23.  Topography of Thalamic Projections Requires Attractive and Repulsive Functions of Netrin-1 in the Ventral Telencephalon 
PLoS Biology  2008;6(5):e116.
Recent studies have demonstrated that the topography of thalamocortical (TC) axon projections is initiated before they reach the cortex, in the ventral telencephalon (VTel). However, at this point, the molecular mechanisms patterning the topography of TC projections in the VTel remains poorly understood. Here, we show that a long-range, high-rostral to low-caudal gradient of Netrin-1 in the VTel is required in vivo for the topographic sorting of TC axons to distinct cortical domains. We demonstrate that Netrin-1 is a chemoattractant for rostral thalamic axons but functions as a chemorepulsive cue for caudal thalamic axons. In accordance with this model, DCC is expressed in a high-rostromedial to low-caudolateral gradient in the dorsal thalamus (DTh), whereas three Unc5 receptors (Unc5A–C) show graded expression in the reverse orientation. Finally, we show that DCC is required for the attraction of rostromedial thalamic axons to the Netrin-1–rich, anterior part of the VTel, whereas DCC and Unc5A/C receptors are required for the repulsion of caudolateral TC axons from the same Netrin-1–rich region of the VTel. Our results demonstrate that a long-range gradient of Netrin-1 acts as a counteracting force from ephrin-A5 to control the topography of TC projections before they enter the cortex.
Author Summary
The functional properties of each structure in the central nervous system are critically dependent on the precision of neuronal connectivity. The cerebral cortex in particular is a highly organized structure divided into many distinct cortical areas underlying important sensory, motor, and cognitive functions in the brain. Each primary cortical area receives its synaptic inputs from the periphery via the dorsal thalamus. The main relay station for sensory information to the cortex, the thalamus, can be divided into specific nuclei projecting topographically to individual cortical areas. How is the complex topography of thalamic axon projection to individual cortical areas specified during development? Recent evidence demonstrated that thalamic axons are routed to different cortical domains before they enter the cortex, by putative axon guidance cues present in the ventral forebrain. In the present study, we provide evidence that a secreted axon guidance cue, Netrin-1, expressed in a long-range gradient in the ventral forebrain, plays a critical role in the establishment of the topography of thalamic projections by directing different subsets of axons to specific cortical domains. These results provide important insights into the molecular mechanisms responsible for shaping the topographical patterns of thalamocortical axon projections in mammals.
A long-range gradient of Netrin-1 plays a critical role in the specification of the topography of thalamocortical projections in the ventral telencephalon. The function of Netrin-1 requires both its attractive and repulsive functions to guide different subsets of thalamic axons to specific cortical domains.
PMCID: PMC2584572  PMID: 18479186
24.  The cortical microstructural basis of lateralized cognition: a review 
The presence of asymmetry in the human cerebral hemispheres is detectable at both the macroscopic and microscopic scales. The horizontal expansion of cortical surface during development (within individual brains), and across evolutionary time (between species), is largely due to the proliferation and spacing of the microscopic vertical columns of cells that form the cortex. In the asymmetric planum temporale (PT), minicolumn width asymmetry is associated with surface area asymmetry. Although the human minicolumn asymmetry is not large, it is estimated to account for a surface area asymmetry of approximately 9% of the region’s size. Critically, this asymmetry of minicolumns is absent in the equivalent areas of the brains of other apes. The left-hemisphere dominance for processing speech is thought to depend, partly, on a bias for higher resolution processing across widely spaced minicolumns with less overlapping dendritic fields, whereas dense minicolumn spacing in the right hemisphere is associated with more overlapping, lower resolution, holistic processing. This concept refines the simple notion that a larger brain area is associated with dominance for a function and offers an alternative explanation associated with “processing type.” This account is mechanistic in the sense that it offers a mechanism whereby asymmetrical components of structure are related to specific functional biases yielding testable predictions, rather than the generalization that “bigger is better” for any given function. Face processing provides a test case – it is the opposite of language, being dominant in the right hemisphere. Consistent with the bias for holistic, configural processing of faces, the minicolumns in the right-hemisphere fusiform gyrus are thinner than in the left hemisphere, which is associated with featural processing. Again, this asymmetry is not found in chimpanzees. The difference between hemispheres may also be seen in terms of processing speed, facilitated by asymmetric myelination of white matter tracts (Anderson et al., 1999 found that axons of the left posterior superior temporal lobe were more thickly myelinated). By cross-referencing the differences between the active fields of the two hemispheres, via tracts such as the corpus callosum, the relationship of local features to global features may be encoded. The emergent hierarchy of features within features is a recursive structure that may functionally contribute to generativity – the ability to perceive and express layers of structure and their relations to each other. The inference is that recursive generativity, an essential component of language, reflects an interaction between processing biases that may be traceable in the microstructure of the cerebral cortex. Minicolumn organization in the PT and the prefrontal cortex has been found to correlate with cognitive scores in humans. Altered minicolumn organization is also observed in neuropsychiatric disorders including autism and schizophrenia. Indeed, altered interhemispheric connections correlated with minicolumn asymmetry in schizophrenia may relate to language-processing anomalies that occur in the disorder. Schizophrenia is associated with over-interpretation of word meaning at the semantic level and over-interpretation of relevance at the level of pragmatic competence, whereas autism is associated with overly literal interpretation of word meaning and under-interpretation of social relevance at the pragmatic level. Both appear to emerge from a disruption of the ability to interpret layers of meaning and their relations to each other. This may be a consequence of disequilibrium in the processing of local and global features related to disorganization of minicolumnar units of processing.
PMCID: PMC4115615  PMID: 25126082
minicolumn; cytoarchitecture; lateralization; asymmetry; face-processing; language; schizophrenia; autism
25.  Specificity and Plasticity of Thalamocortical Connections in Sema6A Mutant Mice 
PLoS Biology  2009;7(4):e1000098.
The establishment of connectivity between specific thalamic nuclei and cortical areas involves a dynamic interplay between the guidance of thalamocortical axons and the elaboration of cortical areas in response to appropriate innervation. We show here that Sema6A mutants provide a unique model to test current ideas on the interactions between subcortical and cortical guidance mechanisms and cortical regionalization. In these mutants, axons from the dorsal lateral geniculate nucleus (dLGN) are misrouted in the ventral telencephalon. This leads to invasion of presumptive visual cortex by somatosensory thalamic axons at embryonic stages. Remarkably, the misrouted dLGN axons are able to find their way to the visual cortex via alternate routes at postnatal stages and reestablish a normal pattern of thalamocortical connectivity. These findings emphasize the importance and specificity of cortical cues in establishing thalamocortical connectivity and the spectacular capacity of the early postnatal cortex for remapping initial sensory representations.
Author Summary
During brain development, the emergence of distinct areas in the cerebral cortex involves an interplay between patterning of the cortical sheet in the early embryo and later influences of incoming connections made from other brain areas, namely the thalamus. Connectivity between the thalamus and the cortex is initially smooth and graded, and a prominent model for how thalamocortical connectivity is established proposes thalamic axons are topographically sorted as they course through subcortical regions and then passively delivered to appropriate areas of the cortical sheet. We have used mutant mice lacking the guidance molecule Semaphorin-6A to test this model. In these mutants, Semaphorin-6A axons from the visual part of the thalamus are subcortically misrouted and fail to innervate the presumptive visual cortex, which is instead invaded by somatosensory thalamic axons. Despite this major disruption in initial connectivity, many visual thalamic axons find their way specifically to visual cortex, arriving several days later than usual. These late-arriving axons often follow alternate routes, and upon arrival are able to out-compete earlier-arriving somatosensory axons to reestablish grossly normal thalamocortical connectivity. These results argue strongly against an essential role for early subcortical targeting in the establishment of thalamocortical connectivity patterns and suggest instead the existence of highly specific target-selection mechanisms that match thalamic axons with appropriate cortical areas.
Initial misrouting and subsequent recovery of thalamocortical axon projections in Semaphorin-6A mutant mice highlights the importance of specific target-selection mechanisms that match thalamic axons with appropriate cortical areas.
PMCID: PMC2672616  PMID: 19402755

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