Computing cliques and cavities in networks

AbstractComplex networks contain complete subgraphs such as nodes, edges, triangles, etc., referred to as simplices and cliques of different orders. Notably, cavities consisting of higher-order cliques play an important role in brain functions. Since searching for maximum cliques is an NP-complete problem, we use k-core decomposition to determine the computability of a given network. For a computable network, we design a search method with an implementable algorithm for finding cliques of different orders, obtaining also the Euler characteristic number. Then, we compute the Betti numbers by using the ranks of boundary matrices of adjacent cliques. Furthermore, we design an optimized algorithm for finding cavities of different orders. Finally, we apply the algorithm to the neuronal network of C. elegans with data from one typical dataset, and find all of its cliques and some cavities of different orders, providing a basis for further mathematical analysis and computation of its structure and function.

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Computing Cliques and Cavities in Networks

10.21203/rs.3.rs-576074/v1 ◽

2021 ◽

Author(s):

Dinghua Shi ◽

Zhifeng Chen ◽

Xiang Sun ◽

Qinghua Chen ◽

Chuang Ma ◽

...

Keyword(s):

Neuronal Network ◽

Search Algorithm ◽

Maximum Clique ◽

Characteristic Number ◽

Large Network ◽

C Elegans ◽

Brain Functions ◽

Complete Problem ◽

Np Complete ◽

And Function

Abstract Complex networks have complete subgraphs such as nodes, edges, triangles, etc., referred to as cliques of different orders. Notably, cavities consisting of higher-order cliques have been found playing an important role in brain functions. Since searching for the maximum clique in a large network is an NP-complete problem, we propose using k-core decomposition to determine the computability of a given network subject to limited computing resources. For a computable network, we design a search algorithm for finding cliques of different orders, which also provides the Euler characteristic number. Then, we compute the Betti number by using the ranks of the boundary matrices of adjacent cliques. Furthermore, we design an optimized algorithm for finding cavities of different orders. Finally, we apply the algorithm to the neuronal network of C. elegans in one dataset, and find all of its cliques and some cavities of different orders therein, providing a basis for further mathematical analysis and computation of the structure and function of the C. elegans neuronal network.

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Structure and function of a neocortical synapse

10.1101/2019.12.13.875971 ◽

2019 ◽

Cited By ~ 9

Author(s):

Simone Holler-Rickauer ◽

German Köstinger ◽

Kevan A.C. Martin ◽

Gregor F.P. Schuhknecht ◽

Ken J. Stratford

Keyword(s):

Pyramidal Neurons ◽

Structure And Function ◽

Excitatory Postsynaptic Potential ◽

Brain Volumes ◽

C Elegans ◽

Synaptic Release ◽

Hippocampal Synapses ◽

Large Brain ◽

And Function ◽

Whole Cell Recordings

Thirty-four years since the small nervous system of the nematode C. elegans was manually reconstructed in the electron microscope (EM)1, ‘high-throughput’ EM techniques now enable the dense reconstruction of neural circuits within increasingly large brain volumes at synaptic resolution2–6. As with C. elegans, however, a key limitation for inferring brain function from neuronal wiring diagrams is that it remains unknown how the structure of a synapse seen in EM relates to its physiological transmission strength. Here, we related structure and function of the same synapses to bridge this gap: we combined paired whole-cell recordings of synaptically connected pyramidal neurons in slices of mouse somatosensory cortex with correlated light microscopy and high-resolution EM of all putative synaptic contacts between the neurons. We discovered a linear relationship between synapse size (postsynaptic density area) and synapse strength (excitatory postsynaptic potential amplitude), which provides an experimental foundation for assigning the actual physiological weights to synaptic connections seen in the EM. Furthermore, quantal analysis revealed that the number of vesicle release sites exceeded the number of anatomical synapses formed by a connection by a factor of at least 2.6, which challenges the current understanding of synaptic release in neocortex and suggests that neocortical synapses operate with multivesicular release, like hippocampal synapses7–11. Thus, neocortical synapses are more complex computational devices and may modulate their strength more flexibly than previously thought, with the corollary that the canonical neocortical microcircuitry possesses significantly higher computational power than estimated by current models.

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UNDERSTANDING AGING IN TERMS OF PHYSIOLOGICAL STATES

Innovation in Aging ◽

10.1093/geroni/igz038.2297 ◽

2019 ◽

Vol 3 (Supplement_1) ◽

pp. S616-S617

Author(s):

Alexander Mendenhall ◽

Nikolay Burnaevskiy ◽

Soo Yun ◽

Bryan Sands

Keyword(s):

Aging Process ◽

Physiological State ◽

Structure And Function ◽

High Expression ◽

Initial System ◽

System Failure ◽

C Elegans ◽

Process Work ◽

Acidification Capacity ◽

And Function

Abstract The “network” of homeostatic systems fails in distinct ways in individual isogenic animals during the aging process. We believe that understanding these distinct physiological states, the transitions between them, and how they relate to homeostatic system functions will allow us to better affect change in the aging process. Work in yeast showed that fixing an initial system failure, loss of vacuole acidification capacity, could increase cellular lifespan. Here we showed how the long-lived physiological state conferred by high expression of the hsp-16.2 promoter based lifespan/penetrance biomarker correlates with differences in the expression of other genes, and the structure and function of lysosomes. We found that vacuole acidification failure is not a major initial proximal cause of aging in C. elegans – at least not in their intestine cells.

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Him-10 Is Required for Kinetochore Structure and Function on Caenorhabditis elegans Holocentric Chromosomes

The Journal of Cell Biology ◽

10.1083/jcb.153.6.1227 ◽

2001 ◽

Vol 153 (6) ◽

pp. 1227-1238 ◽

Cited By ~ 77

Author(s):

Mary Howe ◽

Kent L. McDonald ◽

Donna G. Albertson ◽

Barbara J. Meyer

Keyword(s):

Caenorhabditis Elegans ◽

Structure And Function ◽

Holocentric Chromosomes ◽

Molecular Architecture ◽

Mitotic Chromosomes ◽

C Elegans ◽

Meiotic Chromosomes ◽

Evolutionarily Conserved ◽

And Function ◽

Chromosome Nondisjunction

Macromolecular structures called kinetochores attach and move chromosomes within the spindle during chromosome segregation. Using electron microscopy, we identified a structure on the holocentric mitotic and meiotic chromosomes of Caenorhabditis elegans that resembles the mammalian kinetochore. This structure faces the poles on mitotic chromosomes but encircles meiotic chromosomes. Worm kinetochores require the evolutionarily conserved HIM-10 protein for their structure and function. HIM-10 localizes to the kinetochores and mediates attachment of chromosomes to the spindle. Depletion of HIM-10 disrupts kinetochore structure, causes a failure of bipolar spindle attachment, and results in chromosome nondisjunction. HIM-10 is related to the Nuf2 kinetochore proteins conserved from yeast to humans. Thus, the extended kinetochores characteristic of C. elegans holocentric chromosomes provide a guide to the structure, molecular architecture, and function of conventional kinetochores.

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A short history of studies on intelligence and brain in honeybees

Apidologie ◽

10.1007/s13592-020-00794-x ◽

2020 ◽

Cited By ~ 1

Author(s):

Randolf Menzel

Keyword(s):

Structure And Function ◽

Behavioral Biology ◽

Short History ◽

Brain Functions ◽

Scientific Approach ◽

History Of ◽

Methodological Approaches ◽

Future Outcomes ◽

And Function ◽

The Brain

AbstractReflections about the historical roots of our current scientific endeavors are useful from time to time as they help us to acknowledge the ideas, concepts, methodological approaches, and idiosyncrasies of the researchers that paved the ground we stand on right now. The 50-year anniversary of Apidologie offers the opportunity to refresh our knowledge about the history of bee research. I take the liberty of putting the founding year of Apidologie in the middle of the period I cover here. The nascent period of behavioral biology around the late 19th to the early twentieth century was intimately connected with a loss of concepts related to the mental functions of the brain, concepts that were rooted in Darwin’s theory of gradualism in the living world including cognition in animals. This loss was celebrated both in ethology and behaviorism as the gateway to scientific impartiality. Using this apparently strict scientific approach, impressive discoveries were made by observing and strictly quantifying the behavior of bees. The first forays into the brain, however, uncovered a richness of structure and function that reached far beyond stereotypical input/output connections and opened the way to compensating the conceptual restrictions imposed on us by traditional ethology. Honeybee research provides us with a particularly exciting story in this context. The cognitive turn in behavioral biology is intimately connected to the increasing knowledge of how the brain works, also in honeybee research. What has been achieved so far is just the beginning, but it gives us a glimpse of a promising future. Teamwork between neuroscientists and behavioral biologists is needed to elucidate brain functions such as the expectation of future outcomes and intentionality as an entry to animal intelligence reflecting the flexibility and adaptability in behavior also seen in honeybees.

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A microfluidic platform for lifelong high-resolution and high throughput imaging of subtle aging phenotypes in C. elegans

Lab on a Chip ◽

10.1039/c8lc00655e ◽

2018 ◽

Vol 18 (20) ◽

pp. 3090-3100 ◽

Cited By ~ 10

Author(s):

Sahand Saberi-Bosari ◽

Javier Huayta ◽

Adriana San-Miguel

Keyword(s):

High Resolution ◽

High Throughput ◽

Structure And Function ◽

Neuronal Structure ◽

Microfluidic Platform ◽

C Elegans ◽

And Function ◽

High Throughput Imaging

Aging produces a number of changes in the neuronal structure and function throughout a variety of organisms.

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Caenorhabditis elegans male sensory-motor neurons and dopaminergic support cells couple ejaculation and post-ejaculatory behaviors

eLife ◽

10.7554/elife.02938 ◽

2014 ◽

Vol 3 ◽

Cited By ~ 22

Author(s):

Brigitte LeBoeuf ◽

Paola Correa ◽

Changhoon Jee ◽

L René García

Keyword(s):

Motor Neurons ◽

Structure And Function ◽

Intrauterine Environment ◽

C Elegans ◽

Cellular Events ◽

Sensory Motor ◽

Circuit Structure ◽

Circuit Components ◽

And Function ◽

Sperm Movement

The circuit structure and function underlying post-coital male behaviors remain poorly understood. Using mutant analysis, laser ablation, optogenetics, and Ca2+ imaging, we observed that following C. elegans male copulation, the duration of post-coital lethargy is coupled to cellular events involved in ejaculation. We show that the SPV and SPD spicule-associated sensory neurons and the spicule socket neuronal support cells function with intromission circuit components, including the cholinergic SPC and PCB and the glutamatergic PCA sensory-motor neurons, to coordinate sex muscle contractions with initiation and continuation of sperm movement. Our observations suggest that the SPV and SPD and their associated dopamine-containing socket cells sense the intrauterine environment through cellular endings exposed at the spicule tips and regulate both sperm release into the hermaphrodite and the recovery from post-coital lethargy.

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C. ELEGANS unc-105 MUTATIONS AFFECT MUSCLE AND ARE SUPPRESSED BY OTHER MUTATIONS THAT AFFECT MUSCLE

Genetics ◽

10.1093/genetics/113.4.853 ◽

1986 ◽

Vol 113 (4) ◽

pp. 853-867

Author(s):

Eun-Chung Park ◽

H Robert Horvitz

Keyword(s):

Structure And Function ◽

Loss Of Function ◽

Wild Type ◽

Nematode Caenorhabditis Elegans ◽

High Frequencies ◽

C Elegans ◽

Wild Type Phenotype ◽

Extragenic Suppressor ◽

And Function ◽

And Behavior

ABSTRACT Certain mutations in the unc-105 II gene of the nematode Caenorhabditis elegans have dominant effects on morphology and behavior: animals become small, severely hypercontracted and paralyzed. These unc-105 mutants revert both spontaneously and with mutagens at high frequencies to a wild-type phenotype. Most of the reversion events are intragenic, apparently because the null (loss-of-function) phenotype of unc-105 is wild type. One revertant defined an extragenic suppressor locus, sup-20 X. Such suppressor alleles of sup-20 are rare, and the apparent null phenotype of sup-20 is embryonic lethality. By constructing animals genetically mosaic for sup-20, we have shown that the primary effect of sup-20 is in muscle cells. In addition to mutations in sup-20, other mutations causing muscle defects, such as unc-54 and unc-22 mutations, suppress the hypercontracted phenotype of unc-105. The ease of identifying nonhypercontracted revertants of unc-105 mutants greatly facilitates the isolation of new mutants defective in muscle structure and function.

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A VISIBLE ALLELE OF THE MUSCLE GENE sup-10 X OF C. ELEGANS

Genetics ◽

10.1093/genetics/113.1.63 ◽

1986 ◽

Vol 113 (1) ◽

pp. 63-72

Author(s):

Iva Greenwald ◽

H Robert Horvitz

Keyword(s):

Caenorhabditis Elegans ◽

Protein Complex ◽

Structure And Function ◽

The Other ◽

Wild Type ◽

C Elegans ◽

Muscle Structure ◽

New Gene ◽

Muscle Gene ◽

And Function

ABSTRACT In this paper, we extend our previous analyses of a set of genes in Caenorhabditis elegans that are involved in muscle structure and function: unc-93 III, sup-9 II, sup-10 X and sup-11 I. We describe an unusual, visible allele of sup-10, examine how this allele interacts genetically with mutations in other genes of this set and propose that the wild-type products of the unc-93 and sup-10 loci may be components of a protein complex. We also describe a new gene of this set, sup-18 III, and the interaction of sup-18 alleles with mutations in the other genes.

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