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PubMed2026

A step-wise, deterministic and fatal mouse model of myeloid neoplasm with spontaneous acquisition of patient-relevant RTK-RAS mutations.

Leukaemia arises through the stepwise transformation of healthy haematopoietic cells, yet the asymptomatic premalignant phase and its progression to overt disease remain poorly understood. To model this process, we engineered a patient-derived CEBPA mutation into Hoxb8-FL multipotent murine progenitors and transplanted them into syngeneic mice, capturing a clinically silent premalignant stage. All recipients developed overt disease after ~12 months with 100% penetrance and all acquired secondary RTK-RAS mutations, often with identical amino acid changes to those in patients. Single-cell transcriptomics and phenotypic profiling showed that premalignant mutant cells adopt a plasmacytoid dendritic progenitor-like state in vitro which generates both myeloid and B-lymphoid lineages during premalignancy in vivo, with individual tumours restricted to one lineage. The specificity for RTK-RAS mutations coupled with ongoing differentiation, reflects clinically relevant biological contexts thus providing a tractable model of myeloid neoplasm for mechanistic studies and drug discovery.

Journal Article↗
PubMed1995

Dynamical analysis of neuromuscular transmission jitter.

Utilizing prolonged axonal stimulation single fiber EMG, neuromuscular transmission becomes a time-series of interpotential intervals (IPIs). In this form, the underlying processes of neuromuscular transmission can be studied using standard numerical techniques to determine whether these processes can be described by a simple mathematical model. In particular, neuromuscular transmission jitter can be examined in this way. In this article, we attempt to determine whether healthy jitter is noise or deterministic chaos. The presence of deterministic chaos was assessed by analysis of the IPI time-series using visual inspection of both phase-space plots and their principal component dimensions, and using the Grassberger-Procaccia algorithm to determine the correlation dimension of the time-series dynamics. These graphical and mathematical techniques provided little evidence for the existence of deterministic chaos. Linear autoregression time-series prediction also failed to account for the variability of the data and IPI histograms exhibited simple gaussian distributions. These results suggest normal neuromuscular transmission jitter is the result of intrinsic noise.

Action Potentials↗
PubMed1991

A stochastic model for the development of an AIDS epidemic in a heterosexual population.

A non-age-dependent model, describing the evolution of a bisexual population, is developed in this paper and applied to projecting an AIDS epidemic in a heterosexual population. Included in the formulation are frequency- and non-frequency-dependent rules of partnership formation as well as five states of HIV disease, affecting the probability of infection per sexual contact. Results from computer experiments, designed to study the development of an AIDS epidemic in a heterosexual population fed by single males with a 50% prevalence of HIV infection prior to becoming active in heterosexual partnerships, are reported. In these experiments, the only source of HIV infection for females was sexual contacts with infected males within partnerships. Data on the probability of infection per sexual contact with an infected partner and the number of sexual contacts per month were incorporated into the model. However, the numbers used for the initial population of singles, couples, and those becoming sexually active per month were hypothetical. Even though the prevalence of HIV infection among males entering heterosexual partnerships was high, after 30 years the projected prevalence of HIV infection among females ranged from about 10 to 15% depending in part on the expected duration of partnerships and on whether the frequency- or non-frequency-dependent model was used. In these experiments, solutions of the embedded, nonlinear, deterministic equations for the incidence of HIV infection and the cumulative number of deaths due to AIDS proved to be good measures of central tendency for the sample functions of the stochastic population process.

Acquired Immunodeficiency Syndrome↗
PubMed1992

Quantal noise and decision rules in dynamic models of light adaptation.

To evaluate some of the consequences of including probabilistic processes (e.g. quantal noise) in a computable model of light-adaptation dynamics, we considered the behavior of a general class of models. These models contain four stages: (1) early noise; (2) a deterministic filtering and gain-changing stage; (3) late noise; (4) a decision rule that is either an ideal (signal-known-exactly) detector or a peak-trough detector. With the ideal detector and without late noise, the observer's sensitivity as a function of mean luminance and temporal frequency is not affected by the filtering and gain-changing stage. Consequently, if the early noise is entirely quantal fluctuations, sensitivity will always be a square-root function of mean luminance and a uniform (flat) function of temporal frequency. This latter prediction is contradicted by all known data; either the ideal-detector is the wrong decision rule or sensitivity is almost always limited by sources of noise other than quantal fluctuations. With the peak-trough detector, however, with or without late noise, the observer's sensitivity as a function of temporal frequency does reflect the sensitivity of the low-level filtering and gain-changing stage. Late noise is needed, however, if the observer's sensitivity as a function of mean luminance is to go through both a square-root and a Weber region. Comparing these conclusions to similar work on the spatial frequency dimension highlights differences between the spatial and temporal frequency domains. Finally, on the basis of these analyses and evidence from the literature, we question whether quantal fluctuations limit visual sensitivity under any condition.

Adaptation, Ocular↗
PubMed1993

Statistical moments in pharmacokinetics: models and assumptions.

The modelling basis of statistical moments in pharmacokinetics is considered and the associated assumptions and restrictions highlighted. Both deterministic and statistical models are described and they are seen to give identical results on the basis of equivalent assumptions. It is shown that it is not necessary to assume that all kinetic processes are first order and that some of the pharmacokinetic parameters may be dependent on the dose of administered drug and on the route of administration.

Models, Statistical↗
PubMed1977

Mutation-selection balance with stochastic selection.

Diffusion theory has been used to analyze a model of mutation-selection balance in which the selection process is assumed to be stochastic in time. The limiting outcome of the mutation-stochastic selection process is determined qualitatively by the geometric mean fitnesses of the genotypes, and the conditions for fixation or polymorphism are similar to those that determine the outcome of the mutation-selection process when selection is constant. However, in the case of a completely recessive allele, detailed numerical study of the polymorphism associated with stochastic selection has shown that the average allele frequency maintained is greater than the equilibrium frequency expected when selection is constant, even when the geometric mean fitness of the recessive homozygotes is identical in the stochastic and deterministic models. Thus, allele frequencies in natural populations that are too high to be plausibly explained by a balance between mutation and constant selection can be accounted for if selection is stochastic.

Alleles↗
PubMed1991

Radiobiological fundamentals in radioepidemiology and radiation protection.

Radiation is a convenient tool to study fundamental processes of life. Biological effects of irradiation may result from indirect actions which are mediated by free radicals (e.g. OH-radicals) or from direct actions which involve ionizations in the DNA and other biomolecules. Damage to the DNA is the principal, but not exclusive target for cell death, loss of reproductive integrity, mutation, cancer, developmental anomalies and other radiobiological effects. Repair of damaged DNA and cellular recovery processes play an essential role in affecting the survival of cells. Dose, dose rate, radiation quality, biological and chemical modifiers also have a pronounced effect upon the extent of radiation responses. The biological effects of ionizing radiation are somatic or hereditary and can further be classified into stochastic and deterministic effects. For radiation epidemiology and protection the stochastic action is more relevant because the probability of an effect is a function of dose, without a threshold. Induction of cancer, hereditary diseases and probably also mental retardation are regarded as stochastic effects.

Cell Survival↗
PubMed1983

Theoretical framework for spectrum analysis in ultrasonic tissue characterization.

An analytic model is described for application in ultrasonic tissue characterization. The model is applicable to clinical broadband pulse echo systems. It treats spectra derived from received echo signals and relates them to physical tissue properties. The model can be applied to deterministic tissue structures (e.g., retinal detachments, larger blood vessels, and surface layers of the kidney) and to stochastic tissue structures (e.g., various tumors). The beam patterns included in the model are those generated by focused transducers typically used in high-resolution clinical ultrasound. Appropriate calibration procedures are also treated; these are needed for interpretation of absolute spectral parameters. The results obtained with the analytic model have been used to design a digital processing system and the associated techniques which are now being applied during examinations of the eye and abdominal organs. The results have proven useful in interpreting data from various types of tissues. To illustrate the application of these results, representative clinical data, obtained from the digital system, are presented for two types of tissue architectures. The first case is a detached retina representing a deterministic structure characterized by well-defined thickness and reflection coefficients. The second case is asteroid hyalosis and represents a stochastic entity in which the positions of small scattering particles are best described in statistical terms, and characterization is accompanied by means of normalized power spectra.

Eye Diseases↗
PubMed1994

Chaos and physiology: deterministic chaos in excitable cell assemblies.

In this review we examined the emerging science of deterministic chaos (nonlinear systems theory) and its application to selected physiological systems. Although many of the popular images of fractals represent fascination and beauty that by analogy corresponds to nature as we see it, the question remains as to its ultimate meaning for physiological processes. It was our intent to help clarify this somewhat popular, somewhat obscure area of nonlinear dynamics in the context of an ever-changing procedural base. We examined not only the basic concepts of chaos, but also its applications ranging from observations in single cells to the complexity of the EEG. We have not suggested that nonlinear dynamics will answer all of our questions; however, we did attempt to illustrate ways in which this approach may help us to answer new questions and to rearticulate old ones. Chaos is revolutionary in that the overall approach requires us to adopt a different frame of reference which, at times, may move us away from previous concerns and methods of data analysis. In sections I-IV, we summarized the nonlinear dynamics approach and described its application to physiology and neural systems. First, we presented a general overview of the application of nonlinear dynamical techniques to neural systems. We discussed the manner in which even apparently simple deterministic systems can behave in an unpredictable manner. Second, we described the principles of nonlinear dynamical systems including the derived analytical techniques. We now see a variety of procedures for delineating whether frenetic chaotic behavior results from a nonlinear dynamical system with a few degrees of freedom, or whether it is caused by an infinite number of variables, i.e., noise. Third, we approached the applications of nonlinear procedures to the cardiovascular systems and to the neurosciences. In terms of time series, we described initial studies which applied the now "traditional" measures of dimensionality (e.g., based on the algorithm by Grassberger and Procaccia) and information change (e.g., Lyapunov exponents). Examples include our own work and that of Pritchard et al., demonstrating that the dynamics of neural mass activity reflect psychopathological states. Today, however, the trend has expanded to include the use of surrogate data and statistical null hypotheses testing to examine whether a given time series can be considered different from that of white or colored noise (cf. Ref. 262). One of the most important potential applications is that of quantifying changes in nonlinear dynamics to predict future states of the system.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals↗
PubMed1991

The use of operational modeling of HIV/AIDS in a systems approach to public health decision making.

Compartmental models of infectious diseases readily represent known biological and epidemiological processes, are easily understood in flow-chart form by administrators, are simple to adjust to new information, and lend themselves to routine statistical analysis such as parameter estimation and model fitting. Technical results are immediately interpretable in epidemiological and public health terms. Deterministic models are easily stochasticized where this is important for practical purposes. With HIV/AIDS, serial data on both HIV prevalence and AIDS morbidity have been available from San Francisco. Assuming the distribution of the incubation period to be biologically stable, statistical analysis is quite feasible in other regions, even those with no reliable HIV data. Transmission rates must be estimated locally. It is also often possible to estimate the effective size of a population subgroup at risk, from population data on AIDS morbidity only. Computer simulation provides estimates of the evolving pattern of both HIV prevalence and AIDS morbidity. Some public health questions can be answered only by appropriately formulated stochastic models.

Decision Making↗
PubMed1992

Deterministic nonlinear chaos in brain function and borderline psychopathological phenomena.

There exists a fundamental overall property of the brain which monitors, modulates, and ensures a smoothness of function and which further determines elegance and grace in functioning. This property also imparts a quality of, or a sense of proportion among all other faculties of the brain. It is postulated in this paper that such a property/function, up to now almost taken for granted, is maintained/exercised by a nonlinear deterministic chaotic mode of brain function. If this is the case, borderline psychopathological phenomena, when they flare up, can be explained as resulting from sudden reduction of such a deterministic chaotic mode and the emergence of a pathological order, as the system becomes an oscillating one.

Borderline Personality Disorder↗
PubMed1992

Trefoil knotting revealed by molecular dynamics simulations of supercoiled DNA.

Computer simulations of the supercoiling of DNA, largely limited to stochastic search techniques, can offer important information to complement analytical models and experimental data. Through association of an energy function, minimum-energy supercoiled conformations, fluctuations about these states, and interconversions among forms may be sought. In theory, the observation of such large-scale conformational changes is possible, but modeling and numerical considerations limit the picture obtained in practice. A new computational approach is reported that combines an idealized elastic energy model, a compact B-spline representation of circular duplex DNA, and deterministic minimization and molecular dynamics algorithms. A trefoil knotting result, made possible by a large time-step dynamics scheme, is described. The simulated strand passage supports and details a supercoiled-directed knotting mechanism. This process may be associated with collective bending and twisting motions involved in supercoiling propagation and interwound branching. The results also demonstrate the potential effectiveness of the Langevin/implicit-Euler dynamics scheme for studying biomolecular folding and reactions over biologically interesting time scales.

Chemical Phenomena↗
PubMed1979

A time series approach to forecasting Australian total live-births.

The relationship between classical demographic deterministic forecasting models, stochastic structural econometric models and time series models is discussed. Final equation autoregressive moving average (ARMA) models for Australian total live-births are constructed. Particular attention is given to the problem of transforming the time series to stationarity (and Gaussianity) and the properties of the forecasts are analyzed. Final form transfer function models linking births to females in the reproductive age groups are also constructed and a comparison of actual forecast performance using the various models is made. Long-run future forecasts are generated and compared with available projections based on the deterministic cohort model after which some policy implications of the analysis are considered.

Australia↗
PubMed1994

A clarification of the phi mixing model.

The authors review a deterministic model proposed for the analysis of two-way contingency tables that arise in counts of pairwise interactions. This model decomposes the table into the sum of two matrices with special forms: in one the contacts are distributed selectively, in the other they are distributed at random. We show that this model has several inherent problems. The decomposition is not unique, which compromises estimation and interpretation of the parameters; the deterministic framework provides no basis for estimation or hypothesis testing; and the assumption of decomposibility is supported by neither empirical evidence nor theoretical considerations. We show that generalized linear models provide a suitable alternative once the probability process is specified and the overparameterization is removed.

Animals↗
PubMed1995

Measuring "chaos" in the brain: a tutorial review of EEG dimension estimation.

The technique of dimension estimation is currently a leading application of nonlinear dynamics (popularly termed "chaos theory") to EEG analysis. A tutorial review of this technique is presented along with some elementary background concepts from nonlinear dynamics. Practical aspects of applying dimension estimation to EEG data are also reviewed, and the possible role of deterministic chaos in brain function is discussed.

Brain↗
PubMed1985

Possible forms for dwell-time histograms from single-channel current records.

Certain macromolecules embedded in the cell membranes of a variety of cells behave as gated ion-selective pores or channels. The length of time that a channel remains open or closed is not deterministic in nature and must be described in terms of relative probabilities. If channels act independently of each other and appropriate experimental conditions can be maintained, the behavior of a channel can be described by a homogeneous Markov process. Using this representation, the relative probability of observing openings (or closings) of various durations can be described by a sum of discrete components which are related to the underlying model of the kinetic behavior of the channel. Generally, these discrete components are taken to be simple decaying exponentials; however, exponentially decaying oscillatory components (as well as certain others which are discussed) are consistent with the Markov process representation. The presence of components other than simple decaying exponentials is shown to imply the violation of detailed balance in the steady-state (which requires energy), and thus, the presence of cyclic pathways in models which accurately represent the kinetic behavior of the channel. Oscillatory components, if present, will in general decay at a faster rate than the slowest decaying component, which, except under a very restricted set of conditions, will be a simple exponential.

Cell Membrane Permeability↗
PubMed1996

Computing marginal expectations for large compartmentalized models with application to AIDS evolution in a prison system.

The customary models for the AIDS epidemic are compartmentalized according to criteria such as risk factors, sexual habits, gender, race, age, and HIV status and stage. Hitherto, with very few exceptions, investigators have resorted to deterministic approximations or to simulation for the computational investigation of such models, which do not yield to purely analytic methods. The present paper describes a numerical technique, not dependent on Monte Carlo simulations, for such compartmentalized Markov population processes. Analytic error bounds and computational evidence suggest that this technique is quite accurate. The study is motivated and illustrated by a model for a prison system, with ten interrelated prisons, twenty compartments, and thousands of individuals. This model is of increasing interest in itself because the HIV/AIDS epidemic is particularly virulent among prison populations, where the environment offers special opportunities to investigate various prevention and educational programmes quantitatively. Our computational techniques are shown to be effective for the analysis of such a prison system, even though the resulting Markov process is an order of magnitude more complicated than other stochastic epidemic models currently being investigated. The modelling approach and numerical device appear to be applicable to a wide variety of population processes involving migration between population patches.

Acquired Immunodeficiency Syndrome↗