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113-402: The claustrum is made up of various cell types differing in size, shape and neurochemical composition. Five cell types exist, and a majority of these cells resemble pyramidal neurons found in the cortex. Within the claustrum, there is no laminar organization of cell types as in the cortical layers , and the cell bodies can be a pyramidal, fusiform or circular. The principal cell type found in

226-1035: A hyperpolarizing afterpotential. The afterpotential increases in duration which creates spike frequency adaptation (SFA) in the neuron. RSna pyramidal neurons, or non-adapting regular spiking neurons, fire a train of action potentials after a pulse. These neurons show no signs of adaptation. IB pyramidal neurons, or intrinsically bursting neurons, respond to threshold pulses with a burst of two to five rapid action potentials. IB pyramidal neurons show no adaptation. There are several studies showing that morphological and electric pyramidal cells properties could be deduced from gene expression measured by single cell sequencing . Several studies are proposing that single cell classifications in mouse and human neurons based on gene expression could explain various neuronal properties . Neuronal types in these classifications are split into excitatory, inhibitory and hundreds of corresponding sub-types. For example, pyramidal cells of layer 2-3 in human are classified as FREM3 type and often have

339-416: A robot can be described by a manifold called configuration space . In the area of motion planning , one finds paths between two points in configuration space. These paths represent a motion of the robot's joints and other parts into the desired pose. Disentanglement puzzles are based on topological aspects of the puzzle's shapes and components. In order to create a continuous join of pieces in

452-497: A smooth structure on a manifold to be defined. Smooth manifolds are "softer" than manifolds with extra geometric structures, which can act as obstructions to certain types of equivalences and deformations that exist in differential topology. For instance, volume and Riemannian curvature are invariants that can distinguish different geometric structures on the same smooth manifold – that is, one can smoothly "flatten out" certain manifolds, but it might require distorting

565-486: A blank stare, and unresponsiveness. It has been reported that the claustrum has a basal frequency firing that is modulated to increase or decrease with directed attention. For example, projections to motor and oculomotor areas would assist with gaze movement to direct attention to new stimuli by increasing the firing frequency of claustral neurons. Salvinorin A , the active hallucinogenic compound found in Salvia divinorum ,

678-421: A circle from two non-intersecting circles. The ideas underlying topology go back to Gottfried Wilhelm Leibniz , who in the 17th century envisioned the geometria situs and analysis situs . Leonhard Euler 's Seven Bridges of Königsberg problem and polyhedron formula are arguably the field's first theorems. The term topology was introduced by Johann Benedict Listing in the 19th century, although, it

791-412: A convenient proof that any subgroup of a free group is again a free group. Differential topology is the field dealing with differentiable functions on differentiable manifolds . It is closely related to differential geometry and together they make up the geometric theory of differentiable manifolds. More specifically, differential topology considers the properties and structures that require only

904-426: A given space. Changing a topology consists of changing the collection of open sets. This changes which functions are continuous and which subsets are compact or connected. Metric spaces are an important class of topological spaces where the distance between any two points is defined by a function called a metric . In a metric space, an open set is a union of open disks, where an open disk of radius r centered at x

1017-408: A high amount of Ih-current generated by HCN-channel . Pyramidal neurons are the primary neural cell type in the corticospinal tract . Normal motor control depends on the development of connections between the axons in the corticospinal tract and the spinal cord. Pyramidal cell axons follow cues such as growth factors to make specific connections. With proper connections, pyramidal cells take part in

1130-420: A homeomorphism and the domain of the function is said to be homeomorphic to the range. Another way of saying this is that the function has a natural extension to the topology. If two spaces are homeomorphic, they have identical topological properties, and are considered topologically the same. The cube and the sphere are homeomorphic, as are the coffee cup and the doughnut. However, the sphere is not homeomorphic to

1243-402: A micrometer to several micrometers. The length of a single dendrite is usually several hundred micrometers. Due to branching, the total dendritic length of a pyramidal cell may reach several centimeters. The pyramidal cell's axon is often even longer and extensively branched, reaching many centimeters in total length. Dendritic spines receive most of the excitatory impulses ( EPSPs ) that enter

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1356-399: A pyramidal cell. Dendritic spines were first noted by Ramón y Cajal in 1888 by using Golgi's method . Ramón y Cajal was also the first person to propose the physiological role of increasing the receptive surface area of the neuron. The greater the pyramidal cell's surface area, the greater the neuron's ability to process and integrate large amounts of information. Dendritic spines are absent on

1469-534: A set (for instance, determining if a cloud of points is spherical or toroidal ). The main method used by topological data analysis is to: Several branches of programming language semantics , such as domain theory , are formalized using topology. In this context, Steve Vickers , building on work by Samson Abramsky and Michael B. Smyth , characterizes topological spaces as Boolean or Heyting algebras over open sets, which are characterized as semidecidable (equivalently, finitely observable) properties. Topology

1582-499: A similar (yet less complicated) manner to the retinotopic conservation within the lateral geniculate nucleus. Within the claustrum, local connectivity is dominated by feed-forward disynaptic inhibition wherein parvalbumin -expressing interneurons suppress the activity of nearby projection neurons. Local interneurons themselves are connected through both chemical and electrical synapses , allowing for widespread and synchronous inhibition of local claustrum circuitry. In recent studies of

1695-454: A single map, which includes V1 and three other visual areas. Cells in the V1 are part of layer 6, and are different to cells that go to the lateral geniculate nucleus ; these cells use glutamate as their neurotransmitter . The cat claustrum has 3 defined zones: (1) the anterior dorsal zone, which connects to the motor and somatosensory cortex, (2) the posterior dorsal zone that has connections to

1808-461: A single-case study, consciousness was shown to be disrupted when there was stimulation to the extreme capsule of the brain – which is in close proximity to the claustrum – such that upon termination of stimulation, consciousness was regained. Another study looking at the symptomology of schizophrenia established that the severity of delusions was associated with decreased grey matter volume of the left claustrum; postulating that correlations exist between

1921-437: A topology. The deformations that are considered in topology are homeomorphisms and homotopies . A property that is invariant under such deformations is a topological property . The following are basic examples of topological properties: the dimension , which allows distinguishing between a line and a surface ; compactness , which allows distinguishing between a line and a circle; connectedness , which allows distinguishing

2034-457: Is a π -system . The members of τ are called open sets in X . A subset of X is said to be closed if its complement is in τ (that is, its complement is open). A subset of X may be open, closed, both (a clopen set ), or neither. The empty set and X itself are always both closed and open. An open subset of X which contains a point x is called an open neighborhood of x . A function or map from one topological space to another

2147-661: Is a quantum field theory that computes topological invariants . Although TQFTs were invented by physicists, they are also of mathematical interest, being related to, among other things, knot theory , the theory of four-manifolds in algebraic topology, and to the theory of moduli spaces in algebraic geometry. Donaldson , Jones , Witten , and Kontsevich have all won Fields Medals for work related to topological field theory. The topological classification of Calabi–Yau manifolds has important implications in string theory , as different manifolds can sustain different kinds of strings. In cosmology, topology can be used to describe

2260-461: Is an abundance of Na , Ca , and K channels in the dendrites, and some channels in the soma. Ion channels within pyramidal cell dendrites have different properties from the same ion channel type within the pyramidal cell soma. Voltage-gated Ca channels in pyramidal cell dendrites are activated by subthreshold EPSPs and by back-propagating action potentials. The extent of back-propagation of action potentials within pyramidal dendrites depends upon

2373-464: Is arousal and alertness; (ii) content of consciousness, which is the processing of content. A study of traumatic brain injuries in war veterans was undertaken to better understand the functional role of the claustrum. Damage to the claustrum was associated with the duration of one's loss of consciousness, but not its frequency. Lesion size was correlated with a longer duration of LOC events. No consequences were shown to attenuate cognitive processing. In

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2486-438: Is because of widespread connectivity to fronto-parietal areas, cingulate cortex, and thalami. Sustained attention is from the connections to the cingulate cortex, temporal cortex, and thalamus. Crick and Koch suggest that the claustrum has a role similar to that of a conductor within an orchestra as it attempts to co-ordinate the function of all connections. This “conductor” analogy can also be supported through connections between

2599-406: Is called continuous if the inverse image of any open set is open. If the function maps the real numbers to the real numbers (both spaces with the standard topology), then this definition of continuous is equivalent to the definition of continuous in calculus . If a continuous function is one-to-one and onto , and if the inverse of the function is also continuous, then the function is called

2712-462: Is capable of inducing loss of awareness. Consumption of salvinorin A can induce synesthesia, in which different sensory modalities are interpreted by different sensory cortices. (For example: seeing sounds, tasting colours.) This supports the idea of intrathalamic segregation and conduction (attention). The claustrum has kappa opioid receptors to which Salvinorin A binds, eliciting this effect. High frequency stimulation (HFS) in cat claustrum(s) has

2825-431: Is connected with the contralateral hemisphere's claustrum with strong, functional connections. Connections with MD thalamus, mPFC, and surrounding and distant cortical areas also exist. Electrical stimulation in the dorsal claustrum of cats elicits excitatory responses within the visual cortex. The claustrum is situated anatomically at the confluence of a large number of white-matter tracts used to connect different parts of

2938-419: Is decreased. The claustrum is also seen to play a role in epilepsy; MRIs have found increased claustral signal intensity in people who have been diagnosed with epilepsy. In certain cases, seizures tend to appear to originate from the claustrum when they are involved in early kainic acid induced seizures . A single case-study showed that consciousness was disrupted when the area between the insula and claustrum

3051-509: Is important for memory formation. By enabling dynamic control of the sensitivity of CA3 pyramidal cells, this clustering of mossy fiber synapses on pyramidal cells may facilitate the initiation of somatic spikes. The interactions between pyramidal cells and an estimated 41 mossy fiber boutons, each originating from a unique granule cell, highlight the role of these boutons in information processing and synaptic connectivity, which are essential for memory and learning. Fundamentally, mossy fiber input

3164-408: Is observed in the claustrum structurally and functionally, supporting the notion that interactions occur with high-order sensory areas involved in encoding objects and features. Input from the prefrontal cortex, for example, will define attention based upon higher-cognitive task-driven behaviour. Moreover, induction of electrical stimulation to the claustrum has been shown to cause inhibition of reading,

3277-776: Is point-set topology. The basic object of study is topological spaces , which are sets equipped with a topology , that is, a family of subsets , called open sets , which is closed under finite intersections and (finite or infinite) unions . The fundamental concepts of topology, such as continuity , compactness , and connectedness , can be defined in terms of open sets. Intuitively, continuous functions take nearby points to nearby points. Compact sets are those that can be covered by finitely many sets of arbitrarily small size. Connected sets are sets that cannot be divided into two pieces that are far apart. The words nearby , arbitrarily small , and far apart can all be made precise by using open sets. Several topologies can be defined on

3390-472: Is received by pyramidal cells in the hippocampus which integrate synaptic voltages within their dendritic architecture. The location of prickly protrusions and the clustering of synapses influence sensitivity and contribute to the processing of information pertaining to memory and learning. Topology Topology (from the Greek words τόπος , 'place, location', and λόγος , 'study')

3503-453: Is relevant to physics in areas such as condensed matter physics , quantum field theory and physical cosmology . The topological dependence of mechanical properties in solids is of interest in disciplines of mechanical engineering and materials science . Electrical and mechanical properties depend on the arrangement and network structures of molecules and elementary units in materials. The compressive strength of crumpled topologies

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3616-411: Is so exciting that we are getting closer to linking specific brain connections and actions with the ultimate puzzle of consciousness.' However, cognitive scientist Stevan Harnad does not consider the claustrum to be a "switch" for consciousness, but merely for wakefulness. He claims that if the claustrum were truly a switch for consciousness, artificial activation of the claustrum would not result in

3729-464: Is studied in attempts to understand the high strength to weight of such structures that are mostly empty space. Topology is of further significance in Contact mechanics where the dependence of stiffness and friction on the dimensionality of surface structures is the subject of interest with applications in multi-body physics. A topological quantum field theory (or topological field theory or TQFT)

3842-605: Is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations , such as stretching , twisting , crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a set endowed with a structure, called a topology , which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity . Euclidean spaces , and, more generally, metric spaces are examples of topological spaces, as any distance or metric defines

3955-428: Is the set of all points whose distance to x is less than r . Many common spaces are topological spaces whose topology can be defined by a metric. This is the case of the real line , the complex plane , real and complex vector spaces and Euclidean spaces . Having a metric simplifies many proofs. Algebraic topology is a branch of mathematics that uses tools from algebra to study topological spaces. The basic goal

4068-437: Is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence. The most important of these invariants are homotopy groups , homology, and cohomology . Although algebraic topology primarily uses algebra to study topological problems, using topology to solve algebraic problems is sometimes also possible. Algebraic topology, for example, allows for

4181-603: The Bridges of Königsberg , the result does not depend on the shape of the sphere; it applies to any kind of smooth blob, as long as it has no holes. To deal with these problems that do not rely on the exact shape of the objects, one must be clear about just what properties these problems do rely on. From this need arises the notion of homeomorphism . The impossibility of crossing each bridge just once applies to any arrangement of bridges homeomorphic to those in Königsberg, and

4294-543: The Rexed laminae of the spinal cord is indicative of function, the visual, auditory and somatomotor regions within the claustrum share similar neurons with specific functional characteristics. For example, the portion of the claustrum that processes visual information ( primarily synthesizing afferent fibers concerned with our peripheral visual field ) is comprised by a majority of binocular cells that have "elongated receptive fields and no orientation selectivity". This focus on

4407-429: The geometrization conjecture (now theorem) in 3 dimensions – every 3-manifold can be cut into pieces, each of which has one of eight possible geometries. 2-dimensional topology can be studied as complex geometry in one variable ( Riemann surfaces are complex curves) – by the uniformization theorem every conformal class of metrics is equivalent to a unique complex one, and 4-dimensional topology can be studied from

4520-599: The plane , the sphere, and the torus, which can all be realized without self-intersection in three dimensions, and the Klein bottle and real projective plane , which cannot (that is, all their realizations are surfaces that are not manifolds). General topology is the branch of topology dealing with the basic set-theoretic definitions and constructions used in topology. It is the foundation of most other branches of topology, including differential topology, geometric topology, and algebraic topology. Another name for general topology

4633-505: The real line , the complex plane , and the Cantor set can be thought of as the same set with different topologies. Formally, let X be a set and let τ be a family of subsets of X . Then τ is called a topology on X if: If τ is a topology on X , then the pair ( X , τ ) is called a topological space. The notation X τ may be used to denote a set X endowed with the particular topology τ . By definition, every topology

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4746-457: The 20th century emphasized cortical inputs and outputs. However, later work has suggested the claustrum has extensive connections to cortical and subcortical regions. More specifically, electrophysiological studies show extensive connections to thalamic nuclei and the basal ganglia , while isotopological reports have linked the claustrum with the prefrontal, frontal, parietal, temporal and occipital cortices. Additional studies have also looked at

4859-418: The K channels. K channels in pyramidal cell dendrites provide a mechanism for controlling the amplitude of action potentials. The ability of pyramidal neurons to integrate information depends on the number and distribution of the synaptic inputs they receive. A single pyramidal cell receives about 30,000 excitatory inputs and 1700 inhibitory ( IPSPs ) inputs. Excitatory (EPSPs) inputs terminate exclusively on

4972-421: The brain – revealed that connectivity to the claustrum was the single most sensitive and specific marker of lesion-induced parkinsonism. In mice, suppression of claustrum appears to attenuate anxiety / stress and increase chronic stress-resistance. In animals, through tract tracing, findings have shown that the claustrum has extensive connections throughout the cortex with sensory and motor regions along with

5085-476: The brain. The claustrum is made up of various cell types that differ in size, shape and neurochemical composition. Excitatory cell types in the claustrum consist of two main classes which differentially project to cortical and subcortical brain regions. Inhibitory neurons represent only 10%-15% of the neurons within the claustrum and consist of three types, expressing parvalbumin , somatostatin or vasoactive intestinal peptide , similar to inhibitory neurons in

5198-411: The brainstem and spinal cord. In summary, the cortical and subcortical connectivity of the claustrum implies that it is most involved with processing sensory information, as well as the physical and emotional state of an animal. Inputs to the claustrum are organized by modality, which include prefrontal, visual, auditory and somatomotor processing areas. In the same way that the morphology of neurons in

5311-416: The branch of mathematics known as graph theory . Similarly, the hairy ball theorem of algebraic topology says that "one cannot comb the hair flat on a hairy ball without creating a cowlick ." This fact is immediately convincing to most people, even though they might not recognize the more formal statement of the theorem, that there is no nonvanishing continuous tangent vector field on the sphere. As with

5424-437: The capability to induce autonomic changes and induce “inactivation syndrome”. This syndrome is described as a decrease in awareness, indicating the relationship between the claustrum and consciousness. In humans this same effect can be observed. Stimulation of the left claustrum in humans has produced "a complete arrest of volitional behavior, unresponsiveness, and amnesia without negative motor symptoms, or mere aphasia" suggesting

5537-466: The circuitry responsible for vision guided motor function. Pyramidal neurons in the prefrontal cortex are implicated in cognitive ability. In mammals, the complexity of pyramidal cells increases from posterior to anterior brain regions. The degree of complexity of pyramidal neurons is likely linked to the cognitive capabilities of different anthropoid species. Pyramidal cells within the prefrontal cortex appear to be responsible for processing input from

5650-475: The claustral, sensory, and frontal regions. The claustrum has been confirmed to be reciprocally connected to the prefrontal cortex, visual, auditory, sensory, and motor regions respectively. Connections to these modalities provide insight into the functionality of the claustrum. Here it is proposed that the claustrum functions in the gating of selective attention. Through this gating process the claustrum can selectively control input from these modalities to facilitate

5763-420: The claustrocortical neurons. Experiments in mice monitoring claustrocortical axonal activity to changing visual stimuli suggest the claustrum signals stimulus changes. Although claustrocortical input to visual cortical areas were engaged, the strongest responses measured were in higher-order regions of the cortex, this included the anterior cingulate cortex which is densely innervated by claustral projection. In

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5876-439: The claustrum as the likely origin of parkinsonism across different conditions. The team used a novel methodology called lesion network mapping to discover the origins of parkinsonism in 29 patients whose symptoms were not the result of Parkinson's disease but rather attributed to a brain lesion – an abnormality or injury to the brain visible on brain imaging. The mapping of the 29 lesions – which were located in different regions of

5989-402: The claustrum as the most highly connected structure per regional volume in the brain and suggest that it may serve as a hub to coordinate activity of cerebral circuits. Even with this extensive connectivity, most projections to and from the claustrum are ipsilateral (although there are still contralateral projections), and little evidence exists to describe its afferent or efferent connections with

6102-445: The claustrum have been observed using diffusion tensor imaging (DTI). A functional magnetic resonance imaging (fMRI) scan looks at oxygenated blood levels in the brain as a way of observing the activity of specific cortical areas. fMRI scans show dampened activity when anesthetized versus awake in rats, specifically claustrum connections to the medial prefrontal cortex (mPFC) and the mediodorsal thalamus (MD thalamus). The claustrum

6215-441: The claustrum in mice and bats , cortically-projecting excitatory claustrum neurons were found to form synapses across the anteroposterior axis and were biased toward neurons that do not share projection targets, with the possible function of joining the activity of different afferent modules. Combined, these two circuits suggest that the claustrum is capable of performing local transformations of diverse input information from across

6328-559: The claustrum is the Golgi type I neuron, which is a large cell with dendrites covered in spines . Through interhemispheric connections, the claustrum is believed to play a role in synchronizing activity in widely separated, but functionally related, parts of the brain such as between frontal eye fields and the visual cortex . As such, the claustrum is thought to play a role in combining different information modalities, potentially to support consciousness itself. Another proposed function of

6441-448: The claustrum is to differentiate between relevant and irrelevant information so that the latter can be ignored. Cortical components of consciousness include the fronto-parietal cortex, cingulate and precuneus . Due to the claustrum's widespread connectivity to these areas, it is suggested that it may play a role in both attention and consciousness . The neural networks that mediate sustained attention and consciousness send inputs to

6554-436: The claustrum with the default mode network (DMN), and the fronto-parietal task control network (FPTC). Psilocybin was found to significantly decrease functional connectivity of the right claustrum with the default mode network, and increase right claustrum connectivity with the fronto-parietal task control network. A team of investigators led by neuroscientists at Beth Israel Deaconess Medical Center has identified lesions in

6667-427: The claustrum's ability to disrupt consciousness when stimulated electrically. A 2020 study involving artificial activation of the claustrum by optogenetic light stimulation silenced brain activity across the cortex, a phenomenon known as a "Down state," which can be seen when mice are sleeping or resting awake (quiet wakefulness). The authors state that 'The claustrum is a coordinator of global slow-wave activity, and it

6780-416: The claustrum's ability to disrupt consciousness when stimulated electrically. Damage to the claustrum may mimic various common diseases or mental disorders; delayed development of the structure appears to be linked to autism . The claustrum may be involved in schizophrenia as findings show an increase in positive symptoms, such as delusions, when the grey matter volume of the left claustrum and right insula

6893-414: The claustrum, and one case report in humans suggests that electrical stimulation near the claustrum reversibly disrupted the patient's conscious state. The claustrum is a small bilateral gray matter structure (comprising roughly 0.25% of the cerebral cortex) located deep to the insular cortex and extreme capsule, and superficial to the external capsule and basal ganglia. Its name means “hidden away”, and

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7006-446: The claustrum, lesions to both claustrums on each hemisphere would need to occur. However, a study in 2019, consisting of electrical stimulation of the claustrum, found no disruption of consciousness in any of the five patients that were subjected to the analysis. The tested patients reported subjective experiences in various sensory domains and exhibited reflexive movement, but none of them displayed loss of consciousness, thus questioning

7119-453: The claustrum. Additionally, large or small types of aspiny neurons are reported in the monkey brain, which are classified as “local circuit neurons". The dorsal claustrum has bi-directional connections with motor structures in the cortex. The relationship between the animal's movement and how neurons in the dorsocaudal claustrum behave are as follows: 70% of movement neurons are non-selective and can fire to do any push, pull or turn movements in

7232-741: The claustrum. Studies therefore indicate distinct patterning of connectivity of claustrum with different cortical areas. These suggest, rather than a diffuse role, they play specialized roles in cortical processing. In mice, parvalbumin fibres are highly interconnected by chemical and electrical synapses. They are additionally also highly interconnected with claustrocortical neurons – suggesting that these inhibitory interneurons strongly modulate their activity. These local networks suggest to synchronize activity of claustrocortical projections to therefore influence brain rhythms and co-ordinated activity of different cortical brain regions. There are additional classes of inhibitory interneurons with local connections within

7345-509: The concepts now known as homotopy and homology , which are now considered part of algebraic topology . Unifying the work on function spaces of Georg Cantor , Vito Volterra , Cesare Arzelà , Jacques Hadamard , Giulio Ascoli and others, Maurice Fréchet introduced the metric space in 1906. A metric space is now considered a special case of a general topological space, with any given topological space potentially giving rise to many distinct metric spaces. In 1914, Felix Hausdorff coined

7458-602: The cortex. Finally, many studies show that the claustrum is best distinguished structurally by its prominent plexus of parvalbumin-positive fibers formed by parvalbumin-expressing inhibitory cell types. In recent studies, the use of myelin basic protein (MBP) and retrogradely traveling cholera toxin have additionally been used as effective methods of identifying the claustrum. Several approaches in mice have been used to assess claustrum cell types, including electrophysiological, morphological, genetic, and connectomic approaches. While no clear consensus has yet been reached regarding

7571-432: The cortex. This further suggests an integration center role for these different modalities, such as sensory and motor. Gap junctions have been shown to exist between aspiny (lacking dendrite projections) interneurons of the claustrum – suggesting a role in its ability to synchronize these modalities as input is received. Additional studies point to involvement in spatial navigation and slow-wave sleep . The claustrum has

7684-458: The definition of sheaves on those categories, and with that the definition of general cohomology theories. Topology has been used to study various biological systems including molecules and nanostructure (e.g., membraneous objects). In particular, circuit topology and knot theory have been extensively applied to classify and compare the topology of folded proteins and nucleic acids. Circuit topology classifies folded molecular chains based on

7797-563: The dendritic spines, while inhibitory (IPSPs) inputs terminate on dendritic shafts, the soma, and even the axon. Pyramidal neurons can be excited by the neurotransmitter glutamate , and inhibited by the neurotransmitter GABA . Pyramidal neurons have been classified into different subclasses based upon their firing responses to 400-1000 millisecond current pulses. These classification are RSad, RSna, and IB neurons. RSad pyramidal neurons, or adapting regular spiking neurons , fire with individual action potentials (APs), which are followed by

7910-500: The dentate gyrus. These have associative roles in spatial memory, suggesting that some form of memory consolidation takes place in these areas. Functionally, the claustrum will integrate various cortical inputs through its connections into consciousness. Based upon its structure and connectivity, its function is suggested to be related to coordination of different brain functions; i.e. the conductor analogy. Consciousness functionally can be divided into two components: (i) wakefulness, which

8023-446: The differential ability to select between task-relevant information and task-irrelevant information to provide directed attention. It contains the highest density of connecting white matter tracts in the cortex. This supports the notion of networking and coordination among different regions of the brain. The claustrum has regional specificity to it; information coming in from visual centers project to specific areas of grey matter neurons in

8136-402: The direction in which pyramidal neurons direct their axons. Pyramidal cells in rats have been shown to undergo many rapid changes during early postnatal life. Between postnatal days 3 and 21, pyramidal cells have been shown to double the size of the soma, increase the length of the apical dendrite fivefold, and increase basal dendrite length thirteen-fold. Other changes include the lowering of

8249-643: The doughnut. While topological spaces can be extremely varied and exotic, many areas of topology focus on the more familiar class of spaces known as manifolds. A manifold is a topological space that resembles Euclidean space near each point. More precisely, each point of an n -dimensional manifold has a neighborhood that is homeomorphic to the Euclidean space of dimension n . Lines and circles , but not figure eights , are one-dimensional manifolds. Two-dimensional manifolds are also called surfaces , although not all surfaces are manifolds. Examples include

8362-455: The electrode was removed, the patient resumed reading and could not remember the events of being dazed. A 2019 study consisting of electrical stimulation of the claustrum found no disruption of consciousness in any of the five patients that were subjected to the analysis. The tested patients reported subjective experiences in various sensory domains and exhibited reflexive movement, but none of them displayed loss of consciousness, thus questioning

8475-447: The evolution of human cognition. The hippocampus's pyramidal cells are essential for certain types of memory and learning. They form synapses that aid in the integration of synaptic voltages throughout their complex dendritic trees through interactions with mossy fibers from granule cells . Since it affects the postsynaptic voltages produced by mossy fiber activation, the placement of thorny excrescences on basal and apical dendrites

8588-491: The exact number of excitatory cell types, recent studies have suggested that cortically- and subcortically-projecting claustrum neurons are likely distinct and vary along several metrics, such as their intrinsic electrophysiological profiles, afferent projections, and neuromodulatory profiles. The claustrum has been shown to have widespread activity to numerous cortical components, all of which have been associated with having components of consciousness and sustained attention. This

8701-430: The forelimb; the rest were more discerning and did only one of the three movements listed above. Pyramidal neurons Pyramidal cells , or pyramidal neurons , are a type of multipolar neuron found in areas of the brain including the cerebral cortex , the hippocampus , and the amygdala . Pyramidal cells are the primary excitation units of the mammalian prefrontal cortex and the corticospinal tract . One of

8814-402: The forepaw representations of both). Rodent claustrum does not receive input from S1 or S2, and is primarily driven by motor cortex. In rats, motor whisker areas receive input from the ipsilateral claustrum but will then project to the contralateral claustrum. The sensory barrel cortex and primary visual cortex also receive input from the ipsilateral claustrum but send very few projection back to

8927-407: The hairy ball theorem applies to any space homeomorphic to a sphere. Intuitively, two spaces are homeomorphic if one can be deformed into the other without cutting or gluing. A traditional joke is that a topologist cannot distinguish a coffee mug from a doughnut, since a sufficiently pliable doughnut could be reshaped to a coffee cup by creating a dimple and progressively enlarging it, while shrinking

9040-488: The hippocampus. A variety of animal models have been used such as cats, rodents and monkeys. In cats, high-frequency stimulation (HFS) of the claustrum can alter motor activity, induce autonomic changes, and precipitate an “inactivation syndrome” described as “decreased awareness". Recordings, primarily in cats and primates, show that claustral neurons respond to sensory stimuli and also respond during voluntary movements. Mapping from visual cortex to claustrum includes just

9153-402: The hole into a handle. Homeomorphism can be considered the most basic topological equivalence . Another is homotopy equivalence . This is harder to describe without getting technical, but the essential notion is that two objects are homotopy equivalent if they both result from "squishing" some larger object. Topology, as a well-defined mathematical discipline, originates in the early part of

9266-516: The involvement in consciousness. Furthermore, MRI studies have shown that increased signal intensity within the claustrum has been associated with status epilepticus – a condition in which epileptic seizures follow one another without recovery of consciousness between events. As well, increased signal intensity is associated with focal dyscognitive seizures, which are seizures that elicit impairment of awareness or consciousness without convulsions. The individual becomes unaware of his or her environment, and

9379-650: The main structural features of the pyramidal neuron is the conic shaped soma , or cell body, after which the neuron is named. Other key structural features of the pyramidal cell are a single axon , a large apical dendrite , multiple basal dendrites , and the presence of dendritic spines . Pyramidal neurons are also one of two cell types where the characteristic sign , Negri bodies , are found in post-mortem rabies infection. Pyramidal neurons were first discovered and studied by Santiago Ramón y Cajal . Since then, studies on pyramidal neurons have focused on topics ranging from neuroplasticity to cognition . One of

9492-469: The main structural features of the pyramidal neuron is the conic shaped soma , or cell body, after which the neuron is named. Other key structural features of the pyramidal cell are a single axon , a large apical dendrite , multiple basal dendrites , and the presence of dendritic spines . The apical dendrite rises from the apex of the pyramidal cell's soma. The apical dendrite is a single, long, thick dendrite that branches several times as distance from

9605-536: The membrane's resting potential , reduction of membrane resistance, and an increase in the peak values of action potentials . Like dendrites in most other neurons, the dendrites are generally the input areas of the neuron, while the axon is the neuron's output. Both axons and dendrites are highly branched. The large amount of branching allows the neuron to send and receive signals to and from many different neurons. Pyramidal neurons, like other neurons, have numerous voltage-gated ion channels . In pyramidal cells, there

9718-433: The monkey, there are widespread connections of the claustrum with allocortical and neocortical regions. These connections project towards the frontal lobe, visual cortical regions, temporal cortex, parieto-occipital cortex and somatosensory areas amongst others. The subcortical areas receiving projections are the amygdala, caudate nucleus and hippocampus. It is unknown if there are cortical regions that do not receive input from

9831-435: The neuronal lineage in the subcortical proliferative ventricular zone (VZ) and the subventricular zone (SVZ). Immature pyramidal cells undergo migration to occupy the cortical plate , where they further diversify. Endocannabinoids (eCBs) are one class of molecules that have been shown to direct pyramidal cell development and axonal pathfinding. Transcription factors such as Ctip2 and Sox5 have been shown to contribute to

9944-482: The number of vertices, edges, and faces of the polyhedron). Some authorities regard this analysis as the first theorem, signaling the birth of topology. Further contributions were made by Augustin-Louis Cauchy , Ludwig Schläfli , Johann Benedict Listing , Bernhard Riemann and Enrico Betti . Listing introduced the term "Topologie" in Vorstudien zur Topologie , written in his native German, in 1847, having used

10057-475: The overall shape of the universe . This area of research is commonly known as spacetime topology . In condensed matter a relevant application to topological physics comes from the possibility to obtain one-way current, which is a current protected from backscattering. It was first discovered in electronics with the famous quantum Hall effect , and then generalized in other areas of physics, for instance in photonics by F.D.M Haldane . The possible positions of

10170-465: The pairwise arrangement of their intra-chain contacts and chain crossings. Knot theory , a branch of topology, is used in biology to study the effects of certain enzymes on DNA. These enzymes cut, twist, and reconnect the DNA, causing knotting with observable effects such as slower electrophoresis . Topological data analysis uses techniques from algebraic topology to determine the large scale structure of

10283-414: The patient passing out, but instead the patient would continue behaving normally, and later report that they experienced no sensations during the period of time when their claustrum was being stimulated. The claustrum expresses a high density of 5HT2A receptors, meaning it is significantly affected by serotonergic psychedelics like psilocybin . Psilocybin appears to affect the functional connectivity of

10396-472: The peripheral sensory system is not an isolated occurrence, as most sensory afferents entering the claustrum bring peripheral sensory information. Moreover, the claustrum possesses a distinct topological organization for each sensory modality as well as the dense connectivity it shares with frontal cortices. For example, there is a retinotopic organization within the visual processing area of the claustrum that mirrors that of visual association cortices and V1, in

10509-481: The planar and higher-dimensional Schönflies theorem . In high-dimensional topology, characteristic classes are a basic invariant, and surgery theory is a key theory. Low-dimensional topology is strongly geometric, as reflected in the uniformization theorem in 2 dimensions – every surface admits a constant curvature metric; geometrically, it has one of 3 possible geometries: positive curvature /spherical, zero curvature/flat, and negative curvature/hyperbolic – and

10622-519: The plane into two parts, the part inside and the part outside. In one of the first papers in topology, Leonhard Euler demonstrated that it was impossible to find a route through the town of Königsberg (now Kaliningrad ) that would cross each of its seven bridges exactly once. This result did not depend on the lengths of the bridges or on their distance from one another, but only on connectivity properties: which bridges connect to which islands or riverbanks. This Seven Bridges of Königsberg problem led to

10735-426: The point of view of complex geometry in two variables (complex surfaces), though not every 4-manifold admits a complex structure. Occasionally, one needs to use the tools of topology but a "set of points" is not available. In pointless topology one considers instead the lattice of open sets as the basic notion of the theory, while Grothendieck topologies are structures defined on arbitrary categories that allow

10848-420: The primary auditory cortex, primary somatosensory cortex, and primary visual cortex, all of which process sensory modalities. These cells might also play a critical role in complex object recognition within the visual processing areas of the cortex. Relative to other species, the larger cell size and complexity of pyramidal neurons, along with certain patterns of cellular organization and function, correlates with

10961-404: The process of “focusing”. It has also been suggested that it operates in the opposite context; that through divisive normalization the claustrum may implement resistance to certain input modalities to prevent “distraction”. The claustrum, in order to facilitate consciousness, would need to integrate various sensory and motor modalities from various parts of the cortex. The anatomical connections of

11074-400: The relationship of the claustrum to well-described subcortical white matter tracts. Structures such as the corona radiata , occipitofrontal fasciculus and uncinate fasciculus project to the claustrum from frontal, pericentral, parietal and occipital regions. Reciprocal connections also exist with motor, somatosensory , auditory and visual cortical regions. Altogether, these findings leave

11187-521: The same region in the visual field as the area of the cortex that projects to the claustrum. The visual claustrum is a single map of the contralateral visual hemifield, receiving information based on motion in the visual field's periphery and has no real selectivity. In terms of somatosensation, cat claustrum receives dense inputs from primary somatosensory cortex (S1), but weaker inputs from secondary somatosensory cortex (S2). The inputs from S1 overlap with inputs from primary motor cortex (at least those from

11300-399: The seizure will manifest as a blank or empty stare for a window of time. Using an operant conditioning task combined with HFS of the claustrum resulted in significant behavioural changes of rats; this included modulated motor responses, inactivity and decreased responsiveness. Beyond this, studies have also shown that the claustrum is active during REM sleep, alongside other structures such as

11413-473: The soma increases and extends towards the cortical surface. Basal dendrites arise from the base of the soma. The basal dendritic tree consists of three to five primary dendrites. As distance increases from the soma, the basal dendrites branch profusely. Pyramidal cells are among the largest neurons in the brain. Both in humans and rodents, pyramidal cell bodies (somas) average around 20 μm in length. Pyramidal dendrites typically range in diameter from half

11526-413: The soma, while the number increases away from it. The typical apical dendrite in a rat has at least 3,000 dendritic spines. The average human apical dendrite is approximately twice the length of a rat's, so the number of dendritic spines present on a human apical dendrite could be as high as 6,000. Pyramidal specification occurs during early development of the cerebrum. Progenitor cells are committed to

11639-408: The space and affecting the curvature or volume. Geometric topology is a branch of topology that primarily focuses on low-dimensional manifolds (that is, spaces of dimensions 2, 3, and 4) and their interaction with geometry, but it also includes some higher-dimensional topology. Some examples of topics in geometric topology are orientability , handle decompositions , local flatness , crumpling and

11752-426: The structure and positive symptoms seen in this psychiatric disorder. Further supporting this correlation between schizophrenia and the claustrum is that there is an increase in white matter volume entering the claustrum. Inverse correlations between grey matter volume and severity of hallucinations in the context of auditory hallucinations of schizophrenia has been supported. As well, to see the total loss of function of

11865-549: The structure and the auditory cortex. Unexpected stimuli also activate the claustrum, effecting an immediate focusing or allocation of function. In lower mammals (e.g. rats), claustral regions receive input from somatosensory modalities, such as whiskers' motor control perspective because of its sensory and discriminatory use in these mammals. Functionally, it is proposed that it segregates attention between these modalities. Attention itself has been considered as top-down processing or bottom-up processing; both fit contextually with what

11978-651: The term "topological space" and gave the definition for what is now called a Hausdorff space . Currently, a topological space is a slight generalization of Hausdorff spaces, given in 1922 by Kazimierz Kuratowski . Modern topology depends strongly on the ideas of set theory, developed by Georg Cantor in the later part of the 19th century. In addition to establishing the basic ideas of set theory, Cantor considered point sets in Euclidean space as part of his study of Fourier series . For further developments, see point-set topology and algebraic topology. The 2022 Abel Prize

12091-572: The twentieth century, but some isolated results can be traced back several centuries. Among these are certain questions in geometry investigated by Leonhard Euler . His 1736 paper on the Seven Bridges of Königsberg is regarded as one of the first practical applications of topology. On 14 November 1750, Euler wrote to a friend that he had realized the importance of the edges of a polyhedron . This led to his polyhedron formula , V − E + F = 2 (where V , E , and F respectively indicate

12204-414: The visual cortex and (3) a third zone that is ventral to the visual one and connects to the auditory areas. Sensory input is segregated based on modalities and there is a high preference for peripheral sensory information. In the cat, input is received from various visual cortical areas and projects back to the area. These loops are retinotopical, meaning that regions getting visual input are responsible for

12317-517: The word for ten years in correspondence before its first appearance in print. The English form "topology" was used in 1883 in Listing's obituary in the journal Nature to distinguish "qualitative geometry from the ordinary geometry in which quantitative relations chiefly are treated". Their work was corrected, consolidated and greatly extended by Henri Poincaré . In 1895, he published his ground-breaking paper on Analysis Situs , which introduced

12430-436: Was awarded to Dennis Sullivan "for his groundbreaking contributions to topology in its broadest sense, and in particular its algebraic, geometric and dynamical aspects". The term topology also refers to a specific mathematical idea central to the area of mathematics called topology. Informally, a topology describes how elements of a set relate spatially to each other. The same set can have different topologies. For instance,

12543-402: Was electrically stimulated; consciousness was regained when stimulation stopped. Patients that had a lesion in their left claustrum were more likely to experience a loss of consciousness compared to those that presented with lesions outside of the claustrum. For example, a patient that was subjected to electrode stimulation at the claustrum stopped reading, stared blankly and was unresponsive. Once

12656-421: Was first identified in 1672, with more detailed descriptions coming later on during the 19th century. Although the regional neuroanatomical boundaries of the claustrum have been defined, there remains a lack of consensus in the literature when defining its precise margins, though a meeting in 2019 of experts has posited a framework by which to refer to the structures across species. An early summary of reports from

12769-438: Was not until the first decades of the 20th century that the idea of a topological space was developed. The motivating insight behind topology is that some geometric problems depend not on the exact shape of the objects involved, but rather on the way they are put together. For example, the square and the circle have many properties in common: they are both one dimensional objects (from a topological point of view) and both separate

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