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Interpreting cancer genetics through a two-step "evolutionary cascade hypothesis": bridging neutral and selective perspectives.

BACKGROUND: DNA mutations are the fundamental engines of cancer, driving its initiation and progression. The forces that fuel malignancy are also the architects of evolution, shaping life through genetic variations. Mutations, in fact, can emerge naturally from endogenous processes, such as oxidative DNA damage or errors in replication, as well as induced by external factors, including cosmic radiation and chemical carcinogens. MAIN BODY: A key question in cancer research is whether tumor evolution is primarily governed by selective bottlenecks, neutral evolution, or dynamic genetic plasticity. In this work, we examine cancer as a disease driven by evolutionary processes rooted in fundamental biological requirements, including sustained proliferation and nutrient utilization. We hypothesize that the accumulation of mutations activates an evolutionary switch, enabling tumor cells to acquire an enhanced capacity for survival, adaptation, and growth at rates far exceeding typical evolutionary timescales. We propose the "evolutionary cascade hypothesis," a unifying framework that integrates these models into a coherent sequence. At its core lies the failure of DNA repair mechanisms, representing a critical transition in cancer progression. This shift marks the transition from an initial non-Darwinian, neutral phase to a Darwinian, more deterministic phase. CONCLUSIONS: As predictive models of tumor evolution advance through genomic big data and artificial intelligence-driven analysis, the future of cancer treatment may extend beyond targeting individual mutations to disrupting the underlying evolutionary mechanisms that sustain malignancy. This paradigm shift could redefine therapeutic strategies and ultimately improve patient outcomes.

Humans↗

Analysis of neural spike trains with interspike interval reconstruction.

As a method for the analysis of neural spike trains, we examine fundamental characteristics of interspike interval (ISI) reconstruction theoretically with a leaky-integrator neuron model and experimentally with cricket wind receptor cells. Both the input to the leaky integrator and the stimulus to the wind receptor cells are the time series generated from the Rossler system. By numerical analysis of the leaky integrator, it is shown that, even if ISI reconstruction is possible, sometimes the entire structure of the Rössler attractor may not be reconstructed with ISI reconstruction. For analysis of the in vivo physiological responses of cricket wind receptor cells, we apply ISI reconstruction, nonlinear prediction and the surrogate data method to the experimental data. As a result of the analysis, it is found that there is a significant deterministic structure in the spike trains. By this analysis of physiological data, it is also shown that, even if ISI reconstruction is possible, the entire attractor may not be reconstructed.

Action Potentials↗

Modeling synaptic dynamics driven by receptor lateral diffusion.

The synaptic weight between a pre- and a postsynaptic neuron depends in part on the number of postsynaptic receptors. On the surface of neurons, receptors traffic by random motion in and out from a microstructure called the postsynaptic density (PSD). In the PSD, receptors can be stabilized at the membrane when they bind to scaffolding proteins. We propose a mathematical model to compute the postsynaptic counterpart of the synaptic weight based on receptor trafficking. We take into account the receptor fluxes at the PSD, which can be regulated by neuronal activity, and the interactions of receptors with the scaffolding molecules. Using a Markovian approach, we estimate the mean and the fluctuations of the number of bound receptors. When the number of receptors is large, a deterministic system is also derived. Moreover, these equations can be used, for example, to fit fluorescence-recovery-after-photobleaching experiments to determine, in living neurons, the chemical binding constants for the receptors/scaffolding molecules interaction at synapses.

Algorithms↗

EEG analysis with nonlinear deterministic and stochastic methods: a combined strategy.

We describe nonlinear deterministic versus stochastic methodology, their applications to EEG research and the neurophysiological background underlying both approaches. Nonlinear methods are based on the concept of attractors in phase space. This concept on the one hand incorporates the idea of an autonomous (stationary) system, on the other hand implicates the investigation of a long time evolution. It is an unresolved problem in nonlinear EEG research that nonlinear methods per se give no feedback about the stationarity aspect. Hence, we introduce a combined strategy utilizing both stochastic and nonlinear deterministic methods. We propose, in a first step to segment the EEG time series into piecewise quasi-stationary epochs by means of nonparametric change point analysis. Subsequently, nonlinear measures can be estimated with higher confidence for the segmented epochs fulfilling the stationarity condition.

Algorithms↗

Dose timing in tumor radiotherapy: considerations of cell number stochasticity.

A typical tumor radiotherapy regimen using external beam X rays consists of doses on weekdays for 4-7 weeks. During the final weeks, the tumor may contain only a few cells capable of regenerating the tumor and may be growing exponentially between doses. Stochastic fluctuations of the cell number can influence the optimal time pattern of dose delivery. If the total dose is fixed, a deterministic model of exponential tumor growth, neglecting stochastic effects, predicts that the way the radiation dose is spread out in time does not affect the average number of tumor cells at the end. However, we here show, within the framework of a birth-death model, that when stochastics are taken into account, the earlier the dose is given (consistent with other constraints imposed by quite different considerations), the better. The proof uses a transformation that simplifies the characteristic equation of the partial differential equation governing the probability generating function for a birth-death process with time-dependent rates. The theorem that earlier is better holds for any statistical distribution of cell number from patient to patient at the start of the exponential growth phase and for virtually any cell-killing model. Numerical results indicate the stochastic effects, although not dominant, are not negligible.

Cell Count↗

Stochastic models for subpopulation emergence in heterogeneous tumors.

A stochastic analog to a deterministic model describing subpopulation emergence in heterogeneous tumors is developed. The resulting system is described by the Fokker-Planck or forward Kolmogorov equation. A finite element approach for the numerical solution to this equation is described. Four biological and clinical scenarios are simulated (emergence of heterogeneity, exclusion of a subpopulation, and induction of drug resistance in both pure and heterogeneous tumors). The results of the simulations show that the stochastic model describes the same basic dynamics as its deterministic counterpart via a convective component, but that for each simulation a distribution of tumor sizes and mixes can also be derived from a diffusive component in the model. These distributions yield estimates for subpopulation extinction probabilities. The biological and clinical relevance of these results are discussed.

Drug Resistance↗

Cell orientation induced by extracellular signals.

Cells like fibroblasts and osteoblasts are oriented by different extracellular guiding signals like an electric field, a bent surface, and a periodically stretched surface. An automatic controller is responsible for the cell alignment. The controller contains both a deterministic and a stochastic signal. The following machine properties were determined: (1) The angle dependence of the cellular signal transformer is cos 2(psi 0 - psi). (2) The set point of the automatic controller is psi 0 = +/- 90 degrees. The cells like to orient their long axis perpendicular to the direction of the applied guiding signal. (3) The signal transformer measures the extracellular signal in a quadratic fashion. The cells cannot register the sign of the guiding field. (4) The stochastic signal in the automatic controller can be quantified by a characteristic time (approximately 130 min for fibroblasts). (5) The extracellular signal is registered in cell-made standards (ratio of the deterministic and stochastic signal equals one): 0.3 +/- 0.05 V/mm for human fibroblasts (electric field) and 85 +/- 3 microns for human fibroblasts and osteoblasts (cyclindrically bent surface). (6) The lag-time in the signal transduction system of fibroblasts is approximately 4 min.

Cell Polarity↗

Nonlinear multivariable modeling and analysis of sleep apnea time series.

This paper investigates the modeling and analysis of physiological data recorded from a 49-year-old male and are composed of three time series: blood oxygen saturation, heart rate and respiration. In particular, it is desired to verify if the models estimated from data can distinguish between the dynamics underlying two different breathing patterns (normal breathing and apnea). The estimated models are nonlinear autoregressive, moving average with exogenous inputs (NARMAX) and the regressors used to compose such models are carefully chosen, among hundreds of candidates, by an automatic procedure. The results discussed in this paper suggest that the dynamics underlying the data are nonlinear and basically deterministic. Using estimated models it seems to be possible to quantify the stability of the fixed point in phase space reconstructed using the blood oxygen time series. This, as discussed, could be the basis of an algorithmic monitoring system.

Algorithms↗

Control of blast cell proliferation and differentiation in acute myelogenous leukemia by soluble polypeptide growth factors.

Proliferation of acute myelogenous leukemia (AML) derived blast cells requires the presence in culture of one or more growth factors. In the majority of cases Interleukin-3 (IL-3) and granulocyte-macrophage colony-stimulating factor (GM-CSF) stimulate clonogenicity of AML blasts, which can be synergised by Interleukin-6 (IL-6), Interleukin-1 (IL-1) and granulocyte colony-stimulating factor (G-CSF). In contrast, macrophage colony-stimulating factor (M-CSF) favors deterministic divisions. A substantial part of AML samples have clonogenic cells which, however, proliferate autonomously in vitro. The production by leukemic cells of a variety of growth or synergizing factors including GM-CSF, G-CSF, IL-1, IL-6, and Tumor Necrosis Factor (TNF) has been demonstrated and a fraction of cases will use these molecules to support clonogenic growth in an autocrine or paracrine fashion. However, unlike the situation with retrovirus-induced murine or avian leukemias, the role of production of CSFs and other cytokines by human leukemic cells in the transformational process remains uncertain.

Biological Factors↗

Comparison of a finite-element multigroup discrete-ordinates code with Monte Carlo for radiotherapy calculations.

Radiotherapy calculations often involve complex geometries such as interfaces between materials of vastly differing atomic number, such as lung, bone and/or air interfaces. Monte Carlo methods have been used to calculate accurately the perturbation effects of the interfaces. However, these methods can be computationally expensive for routine clinical calculations. An alternative approach is to solve the Boltzmann equation deterministically. We present one such deterministic code, Attila. Further, we computed a brachytherapy example and an external beam benchmark to compare the results with data previously calculated by MCNPX and EGS4. Our data suggest that the presented deterministic code is as accurate as EGS4 and MCNPX for the transport geometries examined in this study.

Body Burden↗

Predicting future trends in the number of patients on renal replacement therapy in Denmark.

OBJECTIVES: To predict the future prevalence of patients on renal replacement therapy due to chronic renal failure in Denmark. SUBJECTS AND METHODS: Four thousand and nine terminal uraemic patients (median age 50.0 years, 15.2% diabetic) were treated in Denmark with renal replacement therapy in the period 1 January 1991 to 31 December 1995. Incidence rates and rates of transition between the treatment modalities (haemodialysis, peritoneal dialysis, and renal transplantation) were calculated. The prediction was made using a Markov model in three ways: (1) using the average rates (deterministic model), (2) using rates simulated with pseudorandom numbers based on the average rates (stochastic model), and (3) using increasing incidence rates in a deterministic model. RESULTS: Using present rates both model types predicted a significant increase in the prevalence of renal transplant recipients < 60 years (from 1003 in 1995 to about 1465 in 2006) and the prevalence of haemodialysis patients > or = 60 years (from 456 in 1995 to about 903 in 2006) while the prevalence of other treatment modalities would change less dramatically. The overall prevalence proportion would increase from 539 patients per million population (p.m.p.) in 1995 to about 777 p.m.p. in 2006. The stochastic model clearly demonstrated the uncertainties linked to the prognosis in contrast to the deterministic model. The deterministic model with increasing rates predicted a prevalence proportion of 1162 p.m.p. in 2006. CONCLUSION: Even with present rates the prevalence of haemodialysis patients in Denmark will continue to increase. Mathematical models offers a good tool to study future trends and to plan future capacity.

Adult↗

Heart rate dynamics during accentuated sympathovagal interaction.

Concomitant sympathetic and vagal activation can occur in various physiological conditions, but there is limited information on heart rate (HR) behavior during the accentuated sympathovagal antagonism. Beat-to-beat HR and blood pressure were recorded during intravenous infusion of incremental doses of norepinephrine in 18 healthy male volunteers (mean age 23 +/- 5 yr). HR and blood pressure spectra and two-dimensional Poincaré plots were generated from the baseline recordings and from the recordings at different doses of norepinephrine. The mean blood pressure increased (from 90 +/- 7 to 120 +/- 9 mmHg, P < 0.001), HR decreased (from 60 +/- 9 to 48 +/- 7 beats/min, P < 0.001), and the high-frequency spectral component of HR variability increased (P < 0.001) during the norepinephrine infusion as evidence of accentuated sympathovagal interaction. Abrupt aperiodic changes in sinus intervals that were not related to respiratory cycles or changes in blood pressure occurred in 14 of 18 subjects during the norepinephrine infusions. These fluctuations in sinus intervals resulted in a complex or parabola-shaped structure of the Poincaré plots of successive R-R intervals and a widening of the high-frequency spectral peak. In four subjects, the abrupt fluctuations in sinus intervals were followed by a sudden onset of fixed R-R interval dynamics with a loss of respiratory modulation of HR, resulting in a torpedo-shaped structure of the Poincaré plots. These data show that HR behavior becomes remarkably unstable during accentuated sympathovagal interaction, resembling stochastic dynamics or deterministic chaotic behavior. These features of HR dynamics can be better identified by dynamic analysis of beat-to-beat behavior of R-R intervals than by traditional analysis techniques of HR variability.

Adult↗

Stochastic models for the spread of HIV in a mobile heterosexual population.

An important factor in the dynamic transmission of HIV is the mobility of the population. We formulate various stochastic models for the spread of HIV in a heterosexual mobile population, under the assumptions of constant and varying population sizes. We also derive deterministic and diffusion analogues for these models, using a convenient rescaling technique, and analyze their stability conditions and equilibrium behavior. We illustrate the dynamic behavior of the models and their approximations via a range of numerical experiments.

Algorithms↗

Quantitative diffusion tensor MRI fiber tractography of sensorimotor white matter development in premature infants.

Diffusion tensor MRI (DTI) fiber tracking is the first non-invasive and in vivo technique for the delineation and quantitation of specific white matter pathways. In this study, quantitative fiber tracking was used to assess the structural development of the motor tract and somatosensory radiation in premature human newborns. These pathways are unmyelinated in the youngest premature infants and begin to myelinate during late preterm maturation. Previous studies have only been able to delineate parts of these pathways that could be manually outlined in 2D based on anatomical landmarks. Furthermore, these previous studies could not separate motor and sensory regions. A high-sensitivity neonatal head coil was employed in conjunction with an MR-compatible incubator to perform high-resolution imaging of the premature infant brain. The motor and somatosensory tracts were successfully delineated with 3D DTI fiber tracking in 37 exams of preterm newborns between 28 and 43 weeks gestational age. Both streamline deterministic and probabilistic methods were employed to perform quantitative fiber tractography. Tract-specific measurements of diffusion parameters including fractional anisotropy, directionally averaged diffusivity, and eigenvalues were obtained from the motor and sensory pathways. Using both deterministic and probabilistic fiber tracking, all tract-specific diffusion parameters were found to be significantly correlated with age and the motor tracts were found to have higher anisotropy and lower diffusivity than the sensory pathway. By segmenting the 3D fiber tracks by slice, measurements from different axial levels of the brain were found to vary with region and age. In summary, deterministic and probabilistic DTI fiber tracking methods were used to quantify the developmental changes of motor and somatosensory pathways in premature infants.

Adult↗

Multistep navigation of leukocytes: a stochastic model with memory effects.

We present a model for the chemotactically directed migration of neutrophil leukocytes. It reproduces the multistep navigation by memory effects investigated experimentally by E. F. Foxman, J. J. Campbell and E. C. Butcher in 1997. The model consists of a system of stochastic differential equations. The long time behaviour of the corresponding deterministic system is analysed and two approaches for the numerical solution of the full stochastic system are compared. One of them consists in performing direct simulations, the other one is based on a moment approximation of the Fokker-Planck equation and numerical methods for convection-dominated partial differential equations.

Chemotaxis, Leukocyte↗

The evolution of self-fertilization in density-regulated populations.

The evolution of selfing in hermaphrodites has been studied to reveal the demographic conditions that lead to intermediate selfing rates. Using a demographic model based on Ricker-type density regulation, we assume first that, independent of population density, inbred individuals survive less well than outbred individuals and second, that inbred and outbred individuals differ in their competitive abilities in density-regulated populations. The evolution of selfing, driven by inbreeding depression and the cost of outcrossing, is then analysed for three fundamentally different demographic scenarios: stable population densities, deterministically varying population densities (resulting from cyclical or chaotic population dynamics) and stochastic fluctuations of carrying capacities (resulting from environmental noise). We show that even under stable demographic conditions evolutionary outcomes are not confined to either complete selfing or full outcrossing. Instead, intermediate selfing rates arise under a wide range of conditions, depending on the nature of competitive interactions between inbred and outbred individuals. We also explore the evolution of selfing under deterministic and stochastic density fluctuations to demonstrate that such environmental conditions can evolutionarily stabilize intermediate selfing rates. This is the first study, to our knowledge, to consider in detail the effect of density regulation on the evolution of selfing rates.

Adaptation, Physiological↗

Cavity solitons in semiconductor microresonators: existence, stability, and dynamical properties

We apply a versatile numerical technique to establishing the existence of cavity solitons (CS) in a semiconductor microresonator with bulk GaAs or multiple quantum well GaAs/AlGaAs as its active layer. Based on a Newton method, our approach implies the evaluation of the linearized operator describing deviations from the exact stationary state. The eigenvalues of this operator determine the dynamical stability of the CS. A typical eigenspectrum contains a zero eigenvalue with which a "neutral mode" of the CS is associated. Such neutral modes are characteristic of models with translational symmetry. All other eigenvalues typically have negative real parts large enough to cause any excitations to die out in a few medium response times. The neutral mode thus dominates the response to external random or deterministic perturbations, and its excitation induces a simple translation of the CS, which are thus stable and robust. We show how to relate the speed with which a CS moves under external perturbations to the projection of the perturbations on to the neutral mode, and give some examples, including weak gradients on the driving field and interaction with other CS. Finally, we show that the separatrix between two stable coexisting solutions: the homogeneous solution and the CS is the intervening unstable CS solution. Our results are important with a view to future applications of CS to optical information processing.

Journal Article↗

Stochastic epidemics: the probability of extinction of an infectious disease at the end of a major outbreak.

The aim of this study is to derive an asymptotic expression for the probability that an infectious disease will disappear from a population at the end of a major outbreak ('fade-out'). The study deals with a stochastic SIR-model. Local asymptotic expansions are constructed for the deterministic trajectories of the corresponding deterministic system, in particular for the deterministic trajectory starting in the saddle point. The analytical expression for the probability of extinction is derived by asymptotically solving a boundary value problem based on the Fokker-Planck equation for the stochastic system. The asymptotic results are compared with results obtained by random walk simulations.

Communicable Disease Control↗