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PubMed2006

Scale invariant correlations between genes and SNPs on Human chromosome 1 reveal potential evolutionary mechanisms.

The local density of gene structures and single nucleotide polymorphisms (SNPs) along human chromosomes appears inhomogeneous. In chromosome 1, the density patterns from both these elements are shown here to exhibit similar scale invariant clustering, as well as long-ranged and scale invariant auto- and cross-correlations. The local densities of these elements sites can be accurately represented by the scale invariant exponential dispersion models, a group of stochastic models that act as limiting distributions for a wide range of generalized linear models. The scale invariant Poisson-gamma (PG) distribution is the most applicable of these models, since it describes the above findings and it lends itself to a stochastic mechanism for the accumulation of segmental chromosomal changes. This PG model describes the summation of neutral chromosomal mutations, deletions, rearrangements and recombinations, within chromosomal segments that are distinguished by their evolutionary genealogies. Scale invariance is a necessary property if such a description is to remain valid at different measurement scales. The observed density patterns, and proposed model, presumably represent the convergent summation of multiple stochastic processes within the evolutionary history of the chromosome.

Chromosomes, Human, Pair 1↗

PubMed2006

Use of IGHJ and IGHD gene mutations in analysis of immunoglobulin sequences for the prognosis of chronic lymphocytic leukemia.

The level of somatic point mutation in immunoglobulin genes is an important prognostic indicator for patients with chronic lymphocytic leukemia (CLL). Mutation analysis presently focuses solely upon the heavy chain IGHV gene, however mutation is a stochastic process that also targets IGHD and IGHJ genes. Here, we evaluate the completeness and reliability of the reported IGHJ gene repertoire, and demonstrate the likely consequences of the inclusion of IGHD and IGHJ mutations in CLL analysis, using a dataset of 607 sequences. Inclusion of these mutations would lead to the re-classification of many sequences, which should significantly improve the prognostic value of mutation analysis.

Computational Biology↗

PubMed2026

Functional convergence of rTCA-related carbon-fixation potential and biochemical residue accumulation in seagrass sediments.

Seagrass meadows are globally significant blue carbon ecosystems, yet the microbial and biochemical mechanisms driving sediment organic carbon (SOC) accumulation remain poorly understood. To address this, we employed an integrated approach combining metagenomic sequencing, biochemical assays, and structural equation modeling to investigate carbon cycling in the seagrass and adjacent unvegetated sediments of Swan Lake, China. A total of 115,179 carbon fixation genes and 119,615 decomposition genes were identified, revealing distinct microbial community structures among the habitats. Seagrass sediments harbored more diverse carbon-fixing (CFMs) and decomposing microorganisms (CDMs), with 83 medium-to high-quality metagenome-assembled genomes (MAGs) recovered. While neutral community model analysis indicated that stochastic processes predominantly governed community assembly, functional analyses highlighted specific drivers of sequestration. The reductive tricarboxylic acid (rTCA) cycle emerged as the dominant carbon fixation pathway, with key genes (e.g., aclA, korA) showing strong positive correlations with SOC. Conversely, decomposition pathways for starch and lignin were negatively associated with SOC. Furthermore, seagrass sediments exhibited elevated concentrations of total amino sugars (TAS) and lignin phenols (TLP), which linked significantly to carbon fixation rather than decomposition. PLS-SEM revealed statistically significant associations among seagrass traits, environmental variables, microbial carbon-fixation potential, biochemical residue pools, and SOC, supporting a mechanistic pathway in which enhanced microbial functional potential drives the accumulation of recalcitrant biochemical residues, thereby facilitating long-term carbon retention in sediments. These findings emphasize the pivotal role of microbial anabolism and the accumulation of biosynthetic residues in sediment carbon storage, suggesting a functional convergence in seagrass-driven carbon sinks.

Metagenomics↗

PubMed2005

A comprehensive continuous-time model for the appearance of CGH signal due to chromosomal missegregations during mitosis.

Aneuploidy, the gain or loss of large regions of the genome, is a common feature in cancer cells. Irregularities in chromosomal copy number caused by missegregations of chromosomes during mitosis can be visualized by cytogenetic techniques including fluorescence in situ hybridization (FISH), spectral karyotyping (SKY) and comparative genomic hybridization (CGH). In the current work, we consider the propagation of irregular copy numbers throughout a cell population as the individual cells progress through ordinary mitotic cell cycles. We use an algebraic model to track the different copy numbers as states in a stochastic process, based on the model of chromosome instability of Gusev, Kagansky, and Dooley, and consider the average copy number of a particular chromosome within a cell population as a function of the cell division rate. We review a number of mathematical models for determining the length of the cell cycle, including the Smith-Martin transition probability model and the 'sloppy size' model of Wheals, Tyson and Diekmann. The program MITOSIM simulates the growth of a population of cells using the aforementioned models of the cell cycle. MITOSIM allows the cell population to grow, with occasional resampling, until the average copy number of a given chromosome in the population reaches a preset threshold signifying a positive copy number alteration in this region. MITOSIM calculates the relationship between the missegregation rate and the growth rate of the cell population. This allows the user to test hypotheses regarding the effect chromosomal aberrations have upon the cell cycle, cell growth rates, and time to population dominance.

Aneuploidy↗

PubMed2026

Multi-omics reveal microbial functional traits and antifungal metabolites associated with lower Pseudogymnoascus destructans loads in bat cave soils.

White-nose syndrome, caused by Pseudogymnoascus destructans (Pd), is a major fungal disease threatening hibernating bats. Cave soils can serve as environmental reservoirs for Pd, yet the microbial and biochemical mechanisms underlying naturally low Pd burdens in some cave environments remain poorly understood. Here, we integrated soil microbiome profiling, metagenomics, metabolomics, multi-omics network analysis, and in vitro validation to investigate the ecological and functional basis of differential Pd loads in hibernating bat caves in Northeast China. The three caves shared cold, humid, and weakly acidic microenvironments, but differed significantly in electrical conductivity, soil water content, nutrient availability, and extracellular enzyme activities. Soil microbial communities showed significant inter-cave variation in composition, diversity, and niche breadth, with stochastic processes contributing substantially to community assembly. Environmental variables, particularly pH and Pd load, were important predictors of microbial community structure. Functional analyses revealed that the low-Pd Gezi Cave was enriched in genes associated with organic carbon degradation, nitrogen input and retention, and secondary metabolism. Metabolomic profiling further identified cave-specific metabolite signatures, among which Biochanin A, 4-Hydroxybenzaldehyde, Vanillin, and Arachidonic acid were negatively correlated with Pd loads. Integrated pathway and network analyses showed that differential genes and metabolites jointly mapped to secondary metabolite biosynthesis, aminobenzoate degradation, and flavonoid degradation pathways, forming a microbe-metabolite-functional gene coupling network involving key taxa such as Rhodococcus, Pseudorhodoplanes, and Rhodoplanes. In vitro assays confirmed that 4-Hydroxybenzaldehyde, Coumarin, and Vanillin inhibited Pd growth. Structural equation modelling further indicated that environmental heterogeneity was associated with variation in Pd loads through microbial functional attributes and metabolite profiles. These findings suggest that naturally low-Pd cave soils are associated with coordinated environmental filtering, microbial functional specialization, and antifungal metabolite production, providing mechanistic insight into microbial and biochemical constraints on Pd persistence in cave reservoirs.

Animals↗

PubMed2006

The VESPA: a method for the rapid estimation of a visual evoked potential.

Faster and less obtrusive means for measuring a Visual Evoked Potential would be valuable in clinical testing and basic neuroscience research. This study presents a method for accomplishing this by smoothly modulating the luminance of a visual stimulus using a stochastic process. Despite its visually unobtrusive nature, the rich statistical structure of the stimulus enables rapid estimation of the visual system's impulse response. The profile of these responses, which we call VESPAs, correlates with standard VEPs, with r=0.91, p<10(-28) for the group average. The time taken to obtain a VESPA with a given signal-to-noise ratio compares favorably to that required to obtain a VEP with a similar level of certainty. Additionally, we show that VESPA responses to two independent stimuli can be obtained simultaneously, which could drastically reduce the time required to collect responses to multiple stimuli. The new method appears to provide a useful alternative to standard VEP methods, and to have potential application both in clinical practice and to the study of sensory and perceptual functions.

Adult↗

PubMed2005

Optical recording from respiratory pattern generator of fetal mouse brainstem reveals a distributed network.

Unfailing respiration depends on neural mechanisms already present in mammals before birth. Experiments were made to determine how inspiratory and expiratory neurons are grouped in the brainstem of fetal mice. A further aim was to assess whether rhythmicity arises from a single pacemaker or is generated by multiple sites in the brainstem. To measure neuronal firing, a fluorescent calcium indicator dye was applied to embryonic central nervous systems isolated from mice. While respiratory commands were monitored electrically from third to fifth cervical ventral roots, activity was measured optically over areas containing groups of respiratory neurones, or single neurones, along the medulla from the facial nucleus to the pre-Bötzinger complex. Large optical signals allowed recordings to be made during individual respiratory cycles. Inspiratory and expiratory neurones were intermingled. A novel finding was that bursts of activity arose in a discrete area intermittently, occurring during some breaths, but failing in others. Raised CO2 partial pressure or lowered pH increased the frequency of respiration; neurons then fired reliably with every cycle. Movies of activity revealed patterns of activation of inspiratory and expiratory neurones during successive respiratory cycles; there was no evidence for waves spreading systematically from region to region. Our results suggest that firing of neurons in immature respiratory circuits is a stochastic process, and that the rhythm does not depend on a single pacemaker. Respiratory circuits in fetal mouse brainstem appear to possess a high safety factor for generating rhythmicity, which may or may not persist as development proceeds.

Animals↗

PubMed2005

Line shapes in CP/MAS (13)C NMR spectra of cellulose I.

The CP/MAS (13)C NMR line shape of cellulose I has been qualitatively analyzed by direct simulations using the Ornstein-Uhlenbeck stochastic process and the Kubo model. Both approaches describe a anhydroglucose C4 carbon as a oscillator with fluctuating Larmor frequency. The NMR resonance frequency is written omega=omega +omega(t), where the fluctuating part with zero mean was modelled as a stationary Markov diffusion process. The simulation results both motivates the use of multiple line shapes when fitting CP/MAS (13)C NMR spectra recorded on cellulose I and gives some insights into why signals from crystalline cellulose I give rise to Lorentzian line shapes.

Carbohydrate Conformation↗

PubMed2004

Rad23 and Rpn10: perennial wallflowers join the melee.

Substrate ubiquitination is highly regulated; by contrast, substrate targeting to the proteasome has been considered a stochastic process that is mediated primarily by high-affinity interaction with multi-ubiquitin chains. However, recent findings have shown that substrate recognition by the proteasome is also regulated, and requires Rad23, Dsk2 and Rpn10. These studies suggest that the engagement of protein ubiquitination and translocation with degradation by the proteasome is coordinated by a series of regulated events.

Carrier Proteins↗

PubMed2004

Asymptotic behavior of joint distributions of characteristics of a pair of randomly chosen individuals in discrete-time Fisher-Wright models with mutations and drift.

This is a continuation of the series of articles (C.R. Rao, D.N. Shanbhag (Eds.), Handbook of Statistics 19: Stochastic Processes: Theory and Methods, Elsevier Science, Amsterdam, 2001 (Chapter 8); Math. Biosci. 175 (2002) 83; Math. Meth. Appl. Sci. 26 (2003) 1587; Adv. Appl. Probab. 36 (2004) 57) devoted to a study of the interplay between two of the main forces of population genetics, mutations and drift, in the Fisher-Wright model. We provide discrete-time versions of theorems describing asymptotic behavior of joint distributions of characteristics of a pair of individuals in this model; their continuous-time counterparts were presented in the previous papers. Furthermore, we show that imbalance index, introduced in Kimmel et al. (Genetics 148 (1998) 1921) and King et al. (Mol. Biol. Evol. 17(12) (2000) 1895) in the context of continuous-time models, may also be used in discrete-time models to detect past population growth.

Genetic Drift↗

PubMed2006

Double-labelled HIV-1 particles for study of virus-cell interaction.

Human immunodeficiency virus (HIV) delivers its genome to a host cell through fusion of the viral envelope with a cellular membrane. While the viral and cellular proteins involved in entry have been analyzed in detail, the dynamics of virus-cell fusion are largely unknown. Single virus tracing (SVT) provides the unique opportunity to visualize viral particles in real time allowing direct observation of the dynamics of this stochastic process. For this purpose, we developed a double-coloured HIV derivative carrying a green fluorescent label attached to the viral matrix protein combined with a red label fused to the viral Vpr protein designed to distinguish between complete virions and subviral particles lacking MA after membrane fusion. We present here a detailed characterization of this novel tool together with exemplary live cell imaging studies, demonstrating its suitability for real-time analyses of HIV-cell interaction.

Biological Transport↗

PubMed2002

Thermodynamically irreversible gating of ryanodine receptors in situ revealed by stereotyped duration of release in Ca(2+) sparks.

For a single or a group of Markov channels gating reversibly, distributions of open and closed times should be the sum of positively weighted decaying exponentials. Violation of this microscopic reversibility has been demonstrated previously on a number of occasions at the single channel level, and has been attributed to possible channel coupling to external sources of free energy. Here we show that distribution of durations of Ca(2+) release underlying Ca(2+) sparks in intact cardiac myocytes exhibits a prominent mode at approximately 8 ms. Analysis of the cycle time for repetitive sparks at hyperactive sites revealed no intervals briefer than approximately 35 ms and a mode at approximately 90 ms. These results indicate that, regardless of whether Ca(2+) sparks are single-channel or multi-channel in origin, they are generated by thermodynamically irreversible stochastic processes. In contrast, data from planar lipid bilayer experiments were consistent with reversible gating of RyR under asymmetric cis (4 microM) and trans Ca(2+) (10 mM), suggesting that the irreversibility for Ca(2+) spark genesis may reside at a supramolecular level. Modeling suggests that Ca(2+)-induced Ca(2+) release among adjacent RyRs may couple the external energy derived from Ca(2+) gradients across the SR to RyR gating in situ, and drive the irreversible generation of Ca(2+) sparks.

Animals↗

PubMed1966

State vector description of the proliferation of mammalian cells in tissue culture. I. Exponential growth.

Proliferation of mammalian cells, even under conditions of unlimited growth, presents a complex problem because of the interaction of deterministic and stochastic processes. Division of the cell cycle into a finite number of parts establishes a multidimensional vector space. In this space an arbitrary culture can be represented by a vector called the state vector. The culture's subsequent growth is represented mathematically as a series of transformations of the state vector. The operators effecting these transformations are presented in matrix form and their relationship to the distribution of cell generation times is described. As an application of the model, the growth of an initially synchronized culture is considered and an unambiguous measure of the degree of synchrony is proposed. Results of a computer simulation of such a culture show the behavior with time of the degree of synchrony, the total cell number, and the mitotic index. In particular the importance of the magnitude of the coefficient of variation of the generation time distribution is illustrated.

Animals↗

PubMed1986

Morphological responses to calcium-induced interaction of phosphatidylserine-containing vesicles.

Structural changes in phospholipid vesicles made of dioleylphosphatidylethanolamine (DOPE)/bovine phosphatidylserine (PS) (1/1, 3/1, 10/1) or of egg phosphatidylcholine (PC)/PS (3/1) and exposed to calcium chloride for various times have been observed by means of video-enhanced light microscopy and freeze-fracture electron microscopy. Calcium induces the formation of large, smooth double-bilayer diaphragms as the spherical vesicles adhere to and deform each other. No subsequent changes are seen with PC/PS vesicles. DOPE/PS vesicles respond to the resultant stress, with about equal probability, by either fusing, through diaphragm rupture, or deflating, by way of volume loss through intact bilayers, even when they contain up to 400 mM sucrose. The diaphragm areas only rarely show the structural destabilization necessary for fusion. The final state is lipid segregated into DOPE hexagonal and Ca-PS lamellar bulk phases with the exclusion of most of the vesicle contents. Results with these and pure PS vesicles studied earlier indicate that the early response of vesicles to calcium chloride is determined by the competing rates at which mechanical stress (bilayer tension and intravesicular pressure) builds up as the vesicles adhere and flatten against each other, and is relieved by vesicle fusion or by volume loss. We attribute the qualitatively different responses of these three lipid systems to their measured differences in adhesion energies and consequent rate of build-up of mechanical stress. Yield to that stress for any one of these lipid systems is not a unique sequence of morphological changes, and so it remains obscure how such a stochastic process could be used in the controlled process of cellular fusion.

Animals↗

PubMed1994

Dynamics of neutrophil rolling over stimulated endothelium in vitro.

Prior to extravasation at sites of acute inflammation, neutrophils roll over activated endothelium. Neutrophil rolling is often characterized by the average rolling velocity. An additional dynamic feature of rolling that has been identified but not extensively studied is the fluctuation in the rolling velocity about the average. To analyze this characteristic further, we have measured the instantaneous velocity of bovine neutrophils interacting with lipopolysaccharide-stimulated bovine aortic endothelium at shear stresses of 1, 2, 3, and 4 dynes/cm2. The average velocities are quantitatively similar to those reported for human neutrophils rolling over reconstituted P-selectin at a surface density of 400 sites/microns 2. At all shear stresses tested, the population average variance in the instantaneous velocity is at least 2 orders of magnitude higher than the theoretical variance generated from experimental error, indicating that the neutrophils translate with a nonconstant velocity. Possible sources of the variance are discussed. These include "macroscopic" sources such as topological heterogeneity in the endothelium and microscopic sources, such as inherent stochastic formation and breakage of the receptor-ligand bonds that mediate the rolling. Regardless of the ultimate source of the variance, these results justify the use of mathematical models that incorporate stochastic processes to describe bond formation and breakage between the neutrophil and the endothelium and hence are able to generate variable velocity trajectories.

Animals↗

PubMed1995

Force production by depolymerizing microtubules: load-velocity curves and run-pause statistics.

Experiments indicate that depolymerization of microtubules generates sufficient force to produce the minus-end-directed transport of chromosomes during mitosis (Koshland et al., 1988). In vitro, analogous transport of kinesin-coated microspheres exhibits a paradoxical effect. Minus-end-directed transport of the microspheres driven by depolymerization is enhanced by the presence of ATP, which fuels the motor action of kinesin driving the microspheres in the opposite direction, toward the plus end of the microtubule. Here we present a mathematical model to explain this behavior. We postulate that a microsphere at the plus end of the microtubule facilitates depolymerization and hence enhances minus-end-directed transport. The force-velocity curve of the model is derived; it has the peculiar feature that velocity is maximal at some positive load (opposing the motion) rather than at zero load. The model is used to simulate the stochastic process of microsphere-facilitated depolymerization-driven transport. Simulated trajectories at low load show distinctive runs and pauses, the statistics of which are calculated from the model. The statistics of the process provide sufficient information to determine all of the model's parameters.

Adenosine Triphosphate↗

PubMed1983

Cost containment in the concentrated care center: a study of nursing, bed and patient assignment policies.

In an effort to deliver the best possible care to seriously ill patients in the most cost-effective manner, Georgetown University has developed the Concentrated Care Center (CCC) as an essential component of the medical center complex. The design of the CCC, together with the application of controlled variable staffing procedures, permits considerable flexibility in the assignment of nurses (as well as patients) to individual units. This report outlines certain research hypotheses regarding policies designed to increase the cost-effectiveness of patient care in the CCC environment. Statistical techniques based on the theory of stochastic processes are developed to test these hypotheses and a FORTRAN IV computer program is developed to analyze one year of operational data from the CCC.

Computers↗

PubMed2003

Ice nucleation in nature: supercooling point (SCP) measurements and the role of heterogeneous nucleation.

In biological systems, nucleation of ice from a supercooled aqueous solution is a stochastic process and always heterogeneous. The average time any solution may remain supercooled is determined only by the degree of supercooling and heterogeneous nucleation sites it encounters. Here we summarize the many and varied definitions of the so-called "supercooling point," also called the "temperature of crystallization" and the "nucleation temperature," and exhibit the natural, inherent width associated with this quantity. We describe a new method for accurate determination of the supercooling point, which takes into account the inherent statistical fluctuations of the value. We show further that many measurements on a single unchanging sample are required to make a statistically valid measure of the supercooling point. This raises an interesting difference in circumstances where such repeat measurements are inconvenient, or impossible, for example for live organism experiments. We also discuss the effect of solutes on this temperature of nucleation. Existing data appear to show that various solute species decrease the nucleation temperature somewhat more than the equivalent melting point depression. For non-ionic solutes the species appears not to be a significant factor whereas for ions the species does affect the level of decrease of the nucleation temperature.

Crystallization↗