Stochastic models for aggregation processes

Three models are presented, which describe the aggregation of objects into groups and the distributions of groups sizes and group numbers within habitats. The processes regarded are pure accumulation processes which involve only formation and invasion of groups. Invasion represents the special case of fusion when only single objects - and not groups - join a group of certain size. The basic model is derived by a single parameter, the formation probability q, which represents the probability of an object to form a new group. A novel, discrete and finite distribution that results for the group sizes is deduced from this aggregation process and it is shown that it converges to a geometric distribution if the number of objects tends to infinity. Two extensions of this model, which both converge to the Waring distribution, are added: the model can be extended either with a beta distributed formation probability or with the assumption that the invasion probability depends on the group size. Relationships between the limiting distributions involved are discussed.     

Stochastic modelling of prey depletion processes

The modelling of prey-predator interactions is of major importance for the understanding of population dynamics. Classically, these interactions are modelled using ordinary differential equations, but this approach has the drawbacks of assuming continuous population variables and of being deterministic. We propose a general approach to stochastic modelling based on the concept of functional response for a prey depletion process with a constant number of predators. Our model could involve any kind of functional response, and permits a likelihood-based approach to statistical modelling and stable computation using matrix exponentials. To illustrate the method we use the Holling-Juliano functional response and compare the outcomes of our model with a deterministic counterpart considered by Schenk and Bacher [2002. Functional response of a generalist insect predator to one of its prey species in the field. Journal of Animal Ecology 71 (3), 524-531], who observed the depletion of Cassida rubiginosa due to its exclusive predator, Polistes dominulus. The predation was found to be Holling type III, reflecting the ability of the predator to regulate its prey. Our approach corroborates this result, but suggests that the prey depletion census should have been performed more often, and that predation features were significantly different between the two years for which data are available.     

Stochastic processes in neurophysiology: Transformation from point to continuous processes

The spike train activity of neurones is considered as a point process, and methods of analysing and interpreting recorded spike trains are considered. The generation of a continuous process (membrane noise) from interacting point processes is described.     

Stochastic model of template-directed elongation processes in biology

We present a novel modular, stochastic model for biological template-based linear chain elongation processes. In this model, elongation complexes (ECs; DNA polymerase, RNA polymerase, or ribosomes associated with nascent chains) that span a finite number of template units step along the template, one after another, with semaphore constructs preventing overtaking. The central elongation module is readily extended with modules that represent initiation and termination processes. The model was used to explore the effect of EC span on motor velocity and dispersion, and the effect of initiation activator and repressor binding kinetics on the overall elongation dynamics. The results demonstrate that (1) motors that move smoothly are able to travel at a greater velocity and closer together than motors that move more erratically, and (2) the rate at which completed chains are released is proportional to the occupancy or vacancy of activator or repressor binding sites only when initiation or activator/repressor dissociation is slow in comparison with elongation.     

Stochastic processes influence stationary-phase decisions in Bacillus subtilis

It has recently been proposed that phenotypic variation in clonal populations of bacterial species results from intracellular "noise," i.e., random fluctuations in levels of cellular molecules, which would be predicted to be insensitive to selective pressure. To test this notion, we propagated five populations of Bacillus subtilis for 5,000 generations with selection for one phenotype: the decision to sporulate. In support of the noise hypothesis, we report that none of the populations responded to selection by improving their efficiency of sporulation, indicating that intracellular noise is independent of heritable genotype.     

Cellular promiscuity: explaining cellular fidelity in vivo against unrestrained pluripotency in vitro

The differentiation of pluripotent stem cells into various progeny is perplexing. In vivo, nature imposes strict fate constraints. In vitro, PSCs differentiate into almost any phenotype. Might the concept of ‘cellular promiscuity'' explain these surprising behaviours?John Gurdon''s [1] and Shinya Yamanaka''s [2] Nobel Prize involves discoveries that vex fundamental concepts about the stability of cellular identity [3,4], ageing as a rectified path and the differences between germ cells and somatic cells. The differentiation of pluripotent stem cells (PSCs) into progeny, including spermatids [5] and oocytes [6], is perplexing. In vivo, nature imposes strict fate constraints. Yet in vitro, reprogrammed PSCs liberated from the body government freely differentiate into any phenotype—except placenta—violating even somatic cell against germ cell segregations. Albeit that it is anthropomorphic, might the concept of ‘cellular promiscuity'' explain these surprising behaviours?Fidelity to one''s differentiated state is nearly universal in vivo—even cancers retain some allegiance. Appreciating the mechanisms in vitro that liberate reprogrammed cells from the numerous constraints governing development in vivo might provide new insights. Similarly to highway guiderails, a range of constraints preclude progeny cells within embryos and organisms from travelling too far away from the trajectory set by their ancestors. Restrictions are imposed externally—basement membranes and intercellular adhesions; internally—chromatin, cytoskeleton, endomembranes and mitochondria; and temporally by ageing.‘Cellular promiscuity'' was glimpsed previously during cloning; it was seen when somatic cells successfully ‘fertilized'' enucleated oocytes in amphibians [1] and later with ‘Dolly'' [7]. Embryonic stem cells (ESCs) corroborate this. The inner cell mass of the blastocyst cells develops faithfully, but liberation from the trophoectoderm generates pluripotent ESCs in vitro, which are freed from fate and polarity restrictions. These freedom-seeking ESCs still abide by three-dimensional rules as they conform to chimaera body patterning when injected into blastocysts. Yet if transplanted elsewhere, this results in chaotic teratomas or helter-skelter in vitro differentiation—that is, pluripotency.August Weismann''s germ plasm theory, 130 years ago, recognized that gametes produce somatic cells, never the reverse. Primordial germ cell migrations into fetal gonads, and parent-of-origin imprints, explain how germ cells are sequestered, retaining genomic and epigenomic purity. Left uncontaminated, these future gametes are held in pristine form to parent the next generation. However, the cracks separating germ and somatic lineages in vitro are widening [5,6]. Perhaps, they are restrained within gonads not for their purity but to prevent wild, uncontrolled misbehaviours resulting in germ cell tumours.The ‘cellular promiscuity'' concept regarding PSCs in vitro might explain why cells of nearly any desired lineage can be detected using monospecific markers. Are assays so sensitive that rare cells can be detected in heterogeneous cultures? Certainly population heterogeneity is considered for transplantable cells—dopaminergic neurons and islet cells—compared with applications needing few cells—sperm and oocytes. This dilemma of maintaining cellular identity in vitro after reprogramming is significant. If not addressed, the value of unrestrained induced PSCs (iPSCs) as reliable models for ‘diseases in a dish'', let alone for subsequent therapeutic transplantations, might be diminished. X-chromosome re-inactivation variants in differentiating human PSCs, epigenetic imprint errors and copy number variations are all indicators of in vitro infidelity. PSCs, which are held to be undifferentiated cells, are artefacts after all, as they undergo their programmed development in vivo.If correct, the hypothesis accounts for concerns raised about the inherent genomic and epigenomic unreliability of iPSCs; they are likely to be unfaithful to their in vivo differentiation trajectories due to both the freedom from in vivo developmental programmes, as well as poorly characterized modifications in culture conditions. ‘Memory'' of the PSC''s identity in vivo might need to be improved by using approaches that might not fully erase imprints. Regulatory authorities, including the Food & Drug Administration, require evidence that cultured PSCs do retain their original cellular identity. Notwithstanding fidelity lapses at the organismal level, the recognition that our cells have intrinsic freedom-loving tendencies in vitro might generate better approaches for only partly releasing somatic cells into probation, rather than full emancipation.     

Stochastic processes in particle-number fluctuations in an electron-photon shower

The paper is concerned with the existence and asymptotic character of the nonlinear boundary value problemdG/dt=F(t,G,F, ¦α?β¦) (1) ¦α?β¦dF/dt=g(t,G,F, ¦α?β¦)G(o,¦α?β¦)=k ₁,G(∞,¦α?β¦)=k ₂ (2) as ¦α?β¦→ o+ The discussion is related to the problem of particle-number fluctuations in the theory of cosmic radiation andG andF denote respectively the probability generating functions for the electron distribution in an electron-initiated and a photon-initiated shower. A solution of the system (1) satisfying the boundary conditions (2) is constructed so that specified limiting conditions are fulfilled.     

N-myristoyltransferase in the leukocytic development processes

The lipidic modification of proteins has recently been shown to be of immense importance, although many of the roles of these modifications remain as yet unidentified. One of such key modifications occurring on several proteins is the covalent addition of a 14-carbon long saturated fatty acid, a process termed myristoylation. Myristoylation can occur during both co-translational protein synthesis and posttranslationally, confers lipophilicity to protein molecules, and controls protein functions. The protein myristoylation process is catalyzed by the enzyme N-myristoyltransferase (NMT), which exists as two isoforms: NMT1 and NMT2. NMT1 is essential for growth and development, during which rapid cellular proliferation is required, in a variety of organisms. NMT1 is also reported to be elevated in many cancerous states, which also involve rapid cellular growth, albeit in an unwanted and uncontrolled manner. The delineation of myristoylation-dependent cellular functions is still in a state of infancy, and many of the roles of the myristoylated proteins remain to be established. The development of cells of the leukocytic lineage represents a phase of rapid growth and development, and we have observed that NMT1 plays a role in this process. The current review outlines the roles of NMT1 in the growth and differentiation of the cells of leukocytic origin. The described studies clearly demonstrate the roles of NMT1 in the regulation of the developmental processes of the leukocytes cells and provide a basis for further research with the aim of unraveling the roles of protein myristoylation in both cellular and physiological context.     

Stochastic and deterministic assembly processes in subsurface microbial communities

A major goal of microbial community ecology is to understand the forces that structure community composition. Deterministic selection by specific environmental factors is sometimes important, but in other cases stochastic or ecologically neutral processes dominate. Lacking is a unified conceptual framework aiming to understand why deterministic processes dominate in some contexts but not others. Here we work toward such a framework. By testing predictions derived from general ecological theory we aim to uncover factors that govern the relative influences of deterministic and stochastic processes. We couple spatiotemporal data on subsurface microbial communities and environmental parameters with metrics and null models of within and between community phylogenetic composition. Testing for phylogenetic signal in organismal niches showed that more closely related taxa have more similar habitat associations. Community phylogenetic analyses further showed that ecologically similar taxa coexist to a greater degree than expected by chance. Environmental filtering thus deterministically governs subsurface microbial community composition. More importantly, the influence of deterministic environmental filtering relative to stochastic factors was maximized at both ends of an environmental variation gradient. A stronger role of stochastic factors was, however, supported through analyses of phylogenetic temporal turnover. Although phylogenetic turnover was on average faster than expected, most pairwise comparisons were not themselves significantly non-random. The relative influence of deterministic environmental filtering over community dynamics was elevated, however, in the most temporally and spatially variable environments. Our results point to general rules governing the relative influences of stochastic and deterministic processes across micro- and macro-organisms.     

Stochastic processes in nano-biomachines revealed by single molecule detection

Proteins and their assemblies are in the size of nanometers and are exposed to thermal disturbances. Many molecular processes in these nano-biomachines are stochastic, reflecting the fact that the input energy level is comparable to that of thermal energy. These stochastic properties have been revealed by recently developed single molecule detection techniques. The movement of molecular motors, myosin, and kinesin, has been suggested to be thermally driven. Random thermal movement is biased using the energy of the ATP hydrolysis. Thus, the molecular motors may harness thermal energy. This unique mechanism may be important in understanding the operation of the biosystems.     

A secreted luciferase for ex vivo monitoring of in vivo processes

Luciferases are widely used to monitor biological processes. Here we describe the naturally secreted Gaussia princeps luciferase (Gluc) as a highly sensitive reporter for quantitative assessment of cells in vivo by measuring its concentration in blood. The Gluc blood assay complements in vivo bioluminescence imaging, which has the ability to localize the signal and provides a multifaceted assessment of cell viability, proliferation and location in experimental disease and therapy models.     

Stochastic modeling in toxicokinetics. Application to the in vivo micronucleus assay

A stochastic model for the in vivo micronucleus assay is presented. This model describes the kinetic of the rate of micronucleated polychromatic erythrocytes induced by the administration of a mutagenic compound. For this, biological assumptions are made both on the erythropoietic system and on the mechanisms of action of the compound. Its pharmacokinetic profile is also taken into account and it is linked to the induced toxicological effect. This model has been evaluated by analyzing the induction of micronuclei is mice bone marrow by a mutagenic compound, 6-mercaptopurine (6-mp). This analysis enabled to make interesting remarks about the induction of micronuclei by 6-mp and to put to light an unsuspected wavy kinetic by optimizing the experimental design of the in vivo micronucleus assay.     

Pressure effects on in vivo microbial processes

Pressures between 10 and 100 MPa can exert powerful effects on the growth and viability of organisms. Here I describe the effects of elevated pressure in this range on mesophilic (atmospheric pressure adapted) and piezophilic (high-pressure adapted) microorganisms. Examination of pressure effects on mesophiles makes use of this unique physical parameter to aid in the characterization of fundamental cellular processes, while in the case of piezophiles it provides information on the essence of the adaptation of life to high-pressure environments, which comprise the bulk of our biosphere. Research is presented on the isolation of pressure-resistant mutants, high-pressure regulation of gene expression, the role of membrane lipids and proteins in determining growth ability at high pressure, pressure effects on DNA replication and topology as well as on cell division, and the role of extrinsic factors in modulating enzyme activity at high pressure.     

Stochastic P systems and the simulation of biochemical processes with dynamic compartments

We introduce a sequential rewriting strategy for P systems based on Gillespie's stochastic simulation algorithm, and show that the resulting formalism of stochastic P systems makes it possible to simulate biochemical processes in dynamically changing, nested compartments. Stochastic P systems have been implemented using the spatially explicit programming language MGS. Implementation examples include models of the Lotka-Volterra auto-catalytic system, and the life cycle of the Semliki Forest virus.