Arata Y et al. (2014) Front Physiol "Power law relationship between cell cycle duration and cell volume in the early embryonic development of Caenorhabditis elegans."

Sawa H, Takagi H, Sako Y, Arata Y

[Front Physiol, 2014]

Cell size is a critical factor for cell cycle regulation. In Xenopus embryos after midblastula transition (MBT), the cell cycle duration elongates in a power law relationship with the cell radius squared. This correlation has been explained by the model that cell surface area is a candidate to determine cell cycle duration. However, it remains unknown whether this second power law is conserved in other animal embryos. Here, we found that the relationship between cell cycle duration and cell size in Caenorhabditis elegans embryos exhibited a power law distribution. Interestingly, the powers of the time-size relationship could be grouped into at least three classes: highly size-correlated, moderately size-correlated, and potentially a size-non-correlated class according to C. elegans founder cell lineages (1.2, 0.81, and <0.39 in radius, respectively). Thus, the power law relationship is conserved in Xenopus and C. elegans, while the absolute powers in C. elegans were different from that in Xenopus. Furthermore, we found that the volume ratio between the nucleus and cell exhibited a power law relationship in the size-correlated classes. The power of the volume relationship was closest to that of the time-size relationship in the highly size-correlated class. This correlation raised the possibility that the time-size relationship, at least in the highly size-correlated class, is explained by the volume ratio of nuclear size and cell size. Thus, our quantitative measurements shed a light on the possibility that early embryonic C. elegans cell cycle duration is coordinated with cell size as a result of geometric constraints between intracellular structures.

Yadav A et al. (2015) Chaos "Origin and implications of zero degeneracy in networks spectra."

Yadav A, Jalan S

[Chaos, 2015]

The spectra of many real world networks exhibit properties which are different from those of random networks generated using various models. One such property is the existence of a very high degeneracy at the zero eigenvalue. In this work, we provide all the possible reasons behind the occurrence of the zero degeneracy in the network spectra, namely, the complete and partial duplications, as well as their implications. The power-law degree sequence and the preferential attachment are the properties which enhances the occurrence of such duplications and hence leading to the zero degeneracy. A comparison of the zero degeneracy in protein-protein interaction networks of six different species and in their corresponding model networks indicates importance of the degree sequences and the power-law exponent for the occurrence of zero degeneracy.

Ciftci K (2018) Network "Synaptic noise facilitates the emergence of self-organized criticality in the Caenorhabditis elegans neuronal network."

Ciftci K

[Network, 2018]

Avalanches with power-law distributed size parameters have been observed in neuronal networks. This observation might be a manifestation of self-organized criticality (SOC). Yet, the physiological mechanisms of this behaviour are currently unknown. Describing synaptic noise as transmission failures mainly originating from the probabilistic nature of neurotransmitter release, this study investigates the potential of this noise as a mechanism for driving the functional architecture of the neuronal networks towards SOC. To this end, a simple finite state neuron model, with activity dependent and synapse specific failure probabilities, was built based on the known anatomical connectivity data of the nematode Ceanorhabditis elegans. Beginning from random values, it was observed that synaptic noise levels picked out a set of synapses and consequently an active subnetwork that generates power-law distributed neuronal avalanches. The findings of this study bring up the possibility that synaptic failures might be a component of physiological processes underlying SOC in neuronal networks.

Arata Y et al. (2022) Sci Rep "Insulin signaling shapes fractal scaling of C. elegans behavior."

Kiyono K, Jurica P, Sako Y, Arata Y, Shiga I, Kimura H, Ikeda Y

[Sci Rep, 2022]

Fractal scaling in animal behavioral activity, where similar temporal patterns appear repeatedly over a series of magnifications among time scales, governs the complex behavior of various animal species and, in humans, can be altered by neurodegenerative diseases and aging. However, the mechanism underlying fractal scaling remains unknown. Here, we cultured C. elegans in a microfluidic device for 3days and analyzed temporal patterns of C. elegans activity by fractal analyses. The residence-time distribution of C. elegans behaviors shared a common feature with those of human and mice. Specifically, the residence-time power-law distribution of the active state changed to an exponential-like decline at a longer time scale, whereas the inactive state followed a power-law distribution. An exponential-like decline appeared with nutrient supply in wild-type animals, whereas this decline disappeared in insulin-signaling-defective daf-2 and daf-16 mutants. The absolute value of the power-law exponent of the inactive state distribution increased with nutrient supply in wild-type animals, whereas the value decreased in daf-2 and daf-16 mutants. We conclude that insulin signaling differentially affects mechanisms that determine the residence time in active and inactive states in C. elegans behavior. In humans, diabetes mellitus, which is caused by defects in insulin signaling, is associated with mood disorders that affect daily behavioral activities. We hypothesize that comorbid behavioral defects in patients with diabetes may be attributed to altered fractal scaling of human behavior.

Tiraihi A et al. (2011) Theor Biol Med Model "Self-organization of developing embryo using scale-invariant approach."

Tiraihi A, Tiraihi M, Tiraihi T

[Theor Biol Med Model, 2011]

BACKGROUND: Self-organization is a fundamental feature of living organisms at all hierarchical levels from molecule to organ. It has also been documented in developing embryos. METHODS: In this study, a scale-invariant power law (SIPL) method has been used to study self-organization in developing embryos. The SIPL coefficient was calculated using a centro-axial skew symmetrical matrix (CSSM) generated by entering the components of the Cartesian coordinates; for each component, one CSSM was generated. A basic square matrix (BSM) was constructed and the determinant was calculated in order to estimate the SIPL coefficient. This was applied to developing C. elegans during early stages of embryogenesis. The power law property of the method was evaluated using the straight line and Koch curve and the results were consistent with fractal dimensions (fd). Diffusion-limited aggregation (DLA) was used to validate the SIPL method. RESULTS AND CONCLUSION: The fractal dimensions of both the straight line and Koch curve showed consistency with the SIPL coefficients, which indicated the power law behavior of the SIPL method. The results showed that the ABp sublineage had a higher SIPL coefficient than EMS, indicating that ABp is more organized than EMS. The fd determined using DLA was higher in ABp than in EMS and its value was consistent with type 1 cluster formation, while that in EMS was consistent with type 2.

Zhao H et al. (2023) IEEE/ACM Trans Comput Biol Bioinform "The Intrinsic Similarity of Topological Structure in Biological Neural Networks."

Shi Z, He S, Shao C, Zhao H, Gong Z

[IEEE/ACM Trans Comput Biol Bioinform, 2023]

Most previous studies mainly have focused on the analysis of structural properties of individual neuronal networks from C. elegans. In recent years, an increasing number of synapse-level neural maps, also known as biological neural networks, have been reconstructed. However, it is not clear whether there are intrinsic similarities of structural properties of biological neural networks from different brain compartments or species. To explore this issue, we collected nine connectomes at synaptic resolution including C. elegans, and analyzed their structural properties. We found that these biological neural networks possess small-world properties and modules. Excluding the Drosophila larval visual system, these networks have rich clubs. The distributions of synaptic connection strength for these networks can be fitted by the truncated pow-law distributions. Additionally, compared with the power-law model, a log-normal distribution is a better model to fit the complementary cumulative distribution function (CCDF) of degree for these neuronal networks. Moreover, we also observed that these neural networks belong to the same superfamily based on the significance profile (SP) of small subgraphs in the network. Taken together, these findings suggest that biological neural networks share intrinsic similarities in their topological structure, revealing some principles underlying the formation of biological neural networks within and across species.

Singh SS et al. (2017) J Theor Biol "Fractal rules in brain networks: signatures of self-organization."

Ishrat R, Singh RKB, Malik MZ, Singh SS, Haobijam D

[J Theor Biol, 2017]

We study brain network data of three species, namely, C. elegans, cat and macaque monkey within the framework of network theory and Potts Hamiltonian model, and explore rich fractal nature in it, which could be an important signature of self-organization, and a simple rule to be obeyed in complex patterns of brain networks. Further, this fractal behaviors in topological parameters of brain networks at various network levels could be an indicator of systems level organization in complicated brain functionality. Again, Rich-club formation of leading hubs in brain networks becomes unpredictable as one goes down to different levels of organization. The popularity of these leading hubs in main modules or sub-modules also gets changed at different network levels, with varied attitudes at each level. Moreover, distribution of edges, which involves intra- and inter-modular/sub-modular interactions, inherited from one level of organization to another level follows fractal law. In addition to this, the Hamiltonian function at each network level, which may correspond to the energy cost in network organization at that level, shows fractal nature. Significant motifs, which are building blocks of networks and related to basic functionalities, in brain networks is found to be triangular motif, and its probability distribution at various levels as a function of size of modules or sub-modules follows fractal law.

Dong KJ et al. (2004) Biochem Biophys Res Commun "Quantum algorithm for programmed cell death of Caenorhabditis elegans."

Dong KJ, Qian JX

[Biochem Biophys Res Commun, 2004]

During the development of Caenorhabditis elegans, through cell divisions, a total of exactly 1090 cells are generated, 131 of which undergo programmed cell death (PCD) to result in an adult organism comprising 959 cells. Of those 131, exactly 113 undergo PCD during embryogenesis. subdivided across the cell lineages in the following fashion: 98 for AB lineage; 14 for MS lineage; and 1 for C lineage. Is there a law underlying these numbers, and if there is, what Could it be? Here we wish to show that the count of the cells undergoing PCD complies with the cipher laws related to the algorithms of Shor and of Grover.

Backholm M et al. (2015) Eur Phys J E Soft Matter "The nematode C. elegans as a complex viscoelastic fluid."

Backholm M, Dalnoki-Veress K, Ryu WS

[Eur Phys J E Soft Matter, 2015]

The viscoelastic material properties of the model organism C. elegans were probed with a micropipette deflection technique and modelled with the standard linear solid model. Dynamic relaxation measurements were performed on the millimetric nematode to investigate its viscous characteristics in detail. We show that the internal properties of C. elegans can not be fully described by a simple Newtonian fluid. Instead, a power-law fluid model was implemented and shown to be in excellent agreement with experimental results. The nematode exhibits shear thinning properties and its complex fluid characteristics were quantified. The bending-rate dependence of the internal damping coefficient of C. elegans could affect its gait modulation in different external environments.

Padawer T et al. (2012) Nucleic Acids Res "Duplicate gene enrichment and expression pattern diversification in multicellularity."

Wang D, Leighty RE, Padawer T

[Nucleic Acids Res, 2012]

The enrichment of duplicate genes, and therefore paralogs (proteins coded by duplicate genes), in multicellular versus unicellular organisms enhances genomic functional innovation. This study quantitatively examined relationships among paralog enrichment, expression pattern diversification and multicellularity, aiming to better understand genomic basis of multicellularity. Paralog abundance in specific cells was compared with those in unicellular proteomes and the whole proteomes of multicellular organisms. The budding yeast, Saccharomyces cerevisiae and the nematode, Caenorhabditis elegans, for which the gene sets expressed in specific cells are available, were used as uni and multicellular models, respectively. Paralog count (K) distributions [P((k))] follow a power-law relationship [Formula in text] in the whole proteomes of both species and in specific C. elegans cells. The value of the constant can be used as a gauge of paralog abundance; the higher the value, the lower the paralog abundance. The -value is indeed lower in the whole proteome of C. elegans (1.74) than in S. cerevisiae (2.34), quantifying the enrichment of paralogs in multicellular species. We also found that the power-law relationship applies to the proteomes of specific C. elegans cells. Strikingly, values of in specific cells are higher and comparable to that in S. cerevisiae. Thus, paralog abundance in specific cells is lower and comparable to that in unicellular species. Furthermore, how much the expression level of a gene fluctuates across different C. elegans cells correlates positively with its paralog count, which is further confirmed by human gene-expression patterns across different tissues. Taken together, these results quantitatively and mechanistically establish enrichment of paralogs with diversifying expression patterns as genomic and evolutionary basis of multicellularity.