Chromatin morphologies in human breast cancer cells treated with an anti-cancer agent are analyzed at their early stage of programmed cell death or apoptosis. The gray-level images of nuclear chromatin are modelled as random fields. We used two-dimensional isotropic generalized Cauchy field to characterize local self-similarity and global long-range dependence behaviors in the image spatial data. Generalized Cauchy field allows the description of fractal behavior inferred from fractal dimension and the long-range dependence inferred from correlation exponent to be carried out independently. We demonstrated the usefulness of locally self-similar random fields with long-range dependence for modelling chromatin condensation.
We study some Gaussian models for anomalous diffusion, which include the time-rescaled Brownian motion, two types of fractional Brownian motion, and models associated with fractional Brownian motion based on the generalized Langevin equation. Gaussian processes associated with these models satisfy the anomalous diffusion relation which requires the mean-square displacement to vary with t(alpha), 0
Fractional Brownian motion (FBM) is widely used in the modeling of phenomena with power spectral density of power-law type. However, FBM has its limitation since it can only describe phenomena with monofractal structure or a uniform degree of irregularity characterized by the constant Holder exponent. For more realistic modeling, it is necessary to take into consideration the local variation of irregularity, with the Holder exponent allowed to vary with time (or space). One way to achieve such a generalization is to extend the standard FBM to multifractional Brownian motion (MBM) indexed by a Holder exponent that is a function of time. This paper proposes an alternative generalization to MBM based on the FBM defined by the Riemann-Liouville type of fractional integral. The local properties of the Riemann-Liouville MBM (RLMBM) are studied and they are found to be similar to that of the standard MBM. A numerical scheme to simulate the locally self-similar sample paths of the RLMBM for various types of time-varying Holder exponents is given. The local scaling exponents are estimated based on the local growth of the variance and the wavelet scalogram methods. Finally, an example of the possible applications of RLMBM in the modeling of multifractal time series is illustrated.
Background. Syngnathid fishes produce three kinds of sounds, named click, growl and purr. These sounds are generated by different mechanisms to give a consistent signal pattern or signature which is believed to play a role in intraspecific and interspecific communication. Commonly known sounds are produced when the fish feeds (click, purr) or is under duress (growl). While there are more acoustic studies on seahorses, pipefishes have not received much attention. Here we document the differences in feeding click signals between three species of pipefishes and relate them to cranial morphology and kinesis, or the sound-producing mechanism. Methods. The feeding clicks of two species of freshwater pipefishes, Doryichthys martensii and Doryichthys deokhathoides and one species of estuarine pipefish, Syngnathoides biaculeatus, were recorded by a hydrophone in acoustic dampened tanks. The acoustic signals were analysed using time-scale distribution (or scalogram) based on wavelet transform. A detailed time-varying analysis of the spectral contents of the localized acoustic signal was obtained by jointly interpreting the oscillogram, scalogram and power spectrum. The heads of both Doryichthys species were prepared for microtomographical scans which were analysed using a 3D imaging software. Additionally, the cranial bones of all three species were examined using a clearing and double-staining method for histological studies. Results. The sound characteristics of the feeding click of the pipefish is species-specific, appearing to be dependent on three bones: the supraoccipital, 1st postcranial plate and 2nd postcranial plate. The sounds are generated when the head of the Dorichthyes pipefishes flexes backward during the feeding strike, as the supraoccipital slides backwards, striking and pushing the 1st postcranial plate against (and striking) the 2nd postcranial plate. In the Syngnathoides pipefish, in the absence of the 1st postcranial plate, the supraoccipital rubs against the 2nd postcranial plate twice as it is pulled backward and released on the return. Cranial morphology and kinesis produce acoustic signals consistent with the bone strikes that produce sharp energy spikes (discrete or merged), or stridulations between bones that produce repeated or multimodal sinusoidal waveforms. Discussion. The variable structure of the sound-producing mechanism explains the unique acoustic signatures of the three species of pipefish. The differences in cranial bone morphology, cranial kinesis and acoustic signatures among pipefishes (and seahorses) could be attributed to independent evolution within the Syngnathidae, which warrants further investigation.
Acoustic signals of the tiger-tail seahorse (Hippocampus comes) during feeding were studied using wavelet transform analysis. The seahorse "click" appears to be a compounded sound, comprising three acoustic components that likely come from two sound producing mechanisms. The click sound begins with a low-frequency precursor signal, followed by a sudden high-frequency spike that decays quickly, and a final, low-frequency sinusoidal component. The first two components can, respectively, be traced to the sliding movement and forceful knock between the supraorbital bone and coronet bone of the cranium, while the third one (purr) although appearing to be initiated here is produced elsewhere. The seahorse also produces a growling sound when under duress. Growling is accompanied by the highest recorded vibration at the cheek indicating another sound producing mechanism here. The purr has the same low frequency as the growl; both are likely produced by the same structural mechanism. However, growl and purr are triggered and produced under different conditions, suggesting that such "vocalization" may have significance in communication between seahorses.
Microscopic models of reaction-diffusion processes on the cell membrane can link local spatiotemporal effects to macroscopic self-organized patterns often observed on the membrane. Simulation schemes based on the microscopic lattice method (MLM) can model these processes at the microscopic scale by tracking individual molecules, represented as hard spheres, on fine lattice voxels. Although MLM is simple to implement and is generally less computationally demanding than off-lattice approaches, its accuracy and consistency in modeling surface reactions have not been fully verified. Using the Spatiocyte scheme, we study the accuracy of MLM in diffusion-influenced surface reactions. We derive the lattice-based bimolecular association rates for two-dimensional (2D) surface-surface reaction and one-dimensional (1D) volume-surface adsorption according to the Smoluchowski-Collins-Kimball model and random walk theory. We match the time-dependent rates on lattice with off-lattice counterparts to obtain the correct expressions for MLM parameters in terms of physical constants. The expressions indicate that the voxel size needs to be at least 0.6% larger than the molecule to accurately simulate surface reactions on triangular lattice. On square lattice, the minimum voxel size should be even larger, at 5%. We also demonstrate the ability of MLM-based schemes such as Spatiocyte to simulate a reaction-diffusion model that involves all dimensions: three-dimensional (3D) diffusion in the cytoplasm, 2D diffusion on the cell membrane, and 1D cytoplasm-membrane adsorption. With the model, we examine the contribution of the 2D reaction pathway to the overall reaction rate at different reactant diffusivity, reactivity, and concentrations.