A stochastic parabolic model of MEMS driven by fractional Brownian motion.

In this paper, we study a stochastic parabolic problem that emerges in the modeling and control of an electrically actuated MEMS (micro-electro-mechanical system) device. The dynamics under consideration are driven by an one dimensional fractional Brownian motion with Hurst index [Formula: see text]. We derive conditions under which the resulting SPDE has a global in time solution, and we provide analytic estimates for certain statistics of interest, such as quenching times and the corresponding quenching probabilities. Our results demonstrate the non-trivial impact of the fractional noise on the dynamics of the system. Given the significance of MEMS devices in biomedical applications, such as drug delivery and diagnostics, our results provide valuable insights into the reliability of these devices in the presence of positively correlated noise.

A Bayesian Framework to Estimate Fluid and Material Parameters in Micro-swimmer Models.

To advance our understanding of the movement of elastic microstructures in a viscous fluid, techniques that utilize available data to estimate model parameters are necessary. Here, we describe a Bayesian uncertainty quantification framework that is highly parallelizable, making parameter estimation tractable for complex fluid-structure interaction models. Using noisy in silico data for swimmers, we demonstrate the methodology's robustness in estimating fluid and elastic swimmer parameters, along with their uncertainties. We identify correlations between model parameters and gain insight into emergent swimming trajectories of a single swimmer or a pair of swimmers. Our proposed framework can handle data with a spatiotemporal resolution representative of experiments, showing that this framework can be used to aid in the development of artificial micro-swimmers for biomedical applications, as well as gain a fundamental understanding of the range of parameters that allow for certain motility patterns.

Data-driven selection and parameter estimation for DNA methylation mathematical models.

Epigenetics is coming to the fore as a key process which underpins health. In particular emerging experimental evidence has associated alterations to DNA methylation status with healthspan and aging. Mammalian DNA methylation status is maintained by an intricate array of biochemical and molecular processes. It can be argued changes to these fundamental cellular processes ultimately drive the formation of aberrant DNA methylation patterns, which are a hallmark of diseases, such as cancer, Alzheimer's disease and cardiovascular disease. In recent years mathematical models have been used as effective tools to help advance our understanding of the dynamics which underpin DNA methylation. In this paper we present linear and nonlinear models which encapsulate the dynamics of the molecular mechanisms which define DNA methylation. Applying a recently developed Bayesian algorithm for parameter estimation and model selection, we are able to estimate distributions of parameters which include nominal parameter values. Using limited noisy observations, the method also identified which methylation model the observations originated from, signaling that our method has practical applications in identifying what models best match the biological data for DNA methylation.

Limit theorem for the Robin Hood game.

In its simplest form, the Robin Hood game is described by the following urn scheme: every day the Sheriff of Nottingham puts s balls in an urn. Then Robin chooses r (r < s) balls to remove from the urn. Robin's goal is to remove balls in such a way that none of them are left in the urn indefinitely. Let T n be the random time that is required for Robin to take out all s · n balls put in the urn during the first n days. Our main result is a limit theorem for T n if Robin selects the balls uniformly at random. Namely, we show that the random variable T n · n -s/r converges in law to a Fréchet distribution as n goes to infinity.

Moran-type bounds for the fixation probability in a frequency-dependent Wright-Fisher model.

We study stochastic evolutionary game dynamics in a population of finite size. Individuals in the population are divided into two dynamically evolving groups. The structure of the population is formally described by a Wright-Fisher type Markov chain with a frequency dependent fitness. In a strong selection regime that favors one of the two groups, we obtain qualitatively matching lower and upper bounds for the fixation probability of the advantageous population. In the infinite population limit we obtain an exact result showing that a single advantageous mutant can invade an infinite population with a positive probability. We also give asymptotically sharp bounds for the fixation time distribution.

Giant Acceleration of DNA Diffusion in an Array of Entropic Barriers.

We investigate with experiments and computer simulations the nonequilibrium dynamics of DNA polymers crossing arrays of entropic barriers in nanofluidic devices in a pressure-driven flow. With increasing driving pressure, the effective diffusivity of DNA rises and then peaks at a value that is many times higher than the equilibrium diffusivity. This is an entropic manifestation of "giant acceleration of diffusion." The phenomenon is sensitive to the effective energy landscape; thus, it offers a unique probe of entropic barriers in a system driven away from equilibrium.

Stochastic modelling of chromosomal segregation: errors can introduce correction.

Cell division is a complex process requiring the cell to have many internal checks so that division may proceed and be completed correctly. Failure to divide correctly can have serious consequences, including progression to cancer. During mitosis, chromosomal segregation is one such process that is crucial for successful progression. Accurate segregation of chromosomes during mitosis requires regulation of the interactions between chromosomes and spindle microtubules. If left uncorrected, chromosome attachment errors can cause chromosome segregation defects which have serious effects on cell fates. In early prometaphase, where kinetochores are exposed to multiple microtubules originating from the two poles, there are frequent errors in kinetochore-microtubule attachment. Erroneous attachments are classified into two categories, syntelic and merotelic. In this paper, we consider a stochastic model for a possible function of syntelic and merotelic kinetochores, and we provide theoretical evidence that merotely can contribute to lessening the stochastic noise in the time for completion of the mitotic process in eukaryotic cells.

Selectivity requirements for diagnostic imaging of neurofibrillary lesions in Alzheimer's disease: a simulation study.

Whole-brain imaging is a promising strategy for premortem detection of tau-bearing neurofibrillary lesions that accumulate in Alzheimer's disease. However, the approach is complicated by the high concentrations of potentially confounding binding sites presented by beta-amyloid plaques. To predict the contributions of relative binding affinity and binding site density to the imaging-dynamics and selectivity of a hypothetical tau-directed radiotracer, a nonlinear, four-tissue compartment pharmacokinetic model of diffusion-mediated radiotracer uptake and distribution was developed. Initial estimates of nonspecific binding and brain uptake parameters were made by fitting data from a previously published kinetic study of Pittsburgh Compound B, an established amyloid-directed radiotracer. The resulting estimates were then used to guide simulations of tau binding selectivity while assuming early-stage accumulation of disease pathology. The simulations suggest that for tau aggregates to represent at least 80% of specific binding signal, binding affinity or density selectivities for tau over beta-amyloid should be at least 20- or 50-fold, respectively. The simulations also suggest, however, that overcoming nonspecific binding will be an additional challenge for tau-directed radiotracers owing to low concentrations of available binding sites. Overall, nonlinear modeling can provide insight into the performance characteristics needed for tau-directed radiotracers in vivo.

Modeling oxygen transport in surgical tissue transfer.

Reconstructive microsurgery is a clinical technique used to transfer large amounts of a patient's tissue from one location used to another in order to restore physical deformities caused by trauma, tumors, or congenital abnormalities. The trend in this field is to transfer tissue using increasingly smaller blood vessels, which decreases problems associated with tissue harvest but increases the possibility that blood supply to the transferred tissue may not be adequate for healing. It would thus be helpful to surgeons to understand the relationship between the tissue volume and blood vessel diameter to ensure success in these operations. As a first step towards addressing this question, we present a simple mathematical model that might be used to predict successful tissue transfer based on blood vessel diameter, tissue volume, and oxygen delivery.

The mitochondrial Ca2+ uniporter channel synergizes with fluid shear stress to induce mitochondrial Ca2+ oscillations.

The mitochondrial calcium (Ca2+) uniporter (MCU) channel is responsible for mitochondrial Ca2+ influx. Its expression was found to be upregulated in endothelial cells (ECs) under cardiovascular disease conditions. Since the role of MCU in regulating cytosolic Ca2+ homeostasis in ECs exposed to shear stress (SS) is unknown, we studied mitochondrial Ca2+ dynamics (that is known to decode cytosolic Ca2+ signaling) in sheared ECs. To understand cause-and-effect, we ectopically expressed MCU in ECs. A higher percentage of MCU-transduced ECs exhibited mitochondrial Ca2+ transients/oscillations, and at higher frequency, under SS compared to sheared control ECs. Transients/oscillations correlated with mitochondrial reactive oxygen species (mROS) flashes and mitochondrial membrane potential (ΔΨm) flickers, and depended on activation of the mechanosensitive Piezo1 channel and the endothelial nitric oxide synthase (eNOS). A positive feedback loop composed of mitochondrial Ca2+ uptake/mROS flashes/ΔΨm flickers and endoplasmic reticulum Ca2+ release, in association with Piezo1 and eNOS, provided insights into the mechanism by which SS, under conditions of high MCU activity, may shape vascular EC energetics and function.

Stochastic analysis of the motion of DNA nanomechanical bipeds.

In this paper, we formulate and analyze a Markov process modeling the motion of DNA nanomechanical walking devices.We consider a molecular biped restricted to a well-defined one-dimensional track and study its asymptotic behavior.Our analysis allows for the biped legs to be of different molecular composition, and thus to contribute differently to the dynamics. Our main result is a functional central limit theorem for the biped with an explicit formula for the effective diffusivity coefficient in terms of the parameters of the model. A law of large numbers, a recurrence/transience characterization and large deviations estimates are also obtained.Our approach is applicable to a variety of other biological motors such as myosin and motor proteins on polymer filaments.

Data-driven prediction and origin identification of epidemics in population networks.

Effective intervention strategies for epidemics rely on the identification of their origin and on the robustness of the predictions made by network disease models. We introduce a Bayesian uncertainty quantification framework to infer model parameters for a disease spreading on a network of communities from limited, noisy observations; the state-of-the-art computational framework compensates for the model complexity by exploiting massively parallel computing architectures. Using noisy, synthetic data, we show the potential of the approach to perform robust model fitting and additionally demonstrate that we can effectively identify the disease origin via Bayesian model selection. As disease-related data are increasingly available, the proposed framework has broad practical relevance for the prediction and management of epidemics.

Modelling contact spread of infection in host-parasitoid systems: vertical transmission of pathogens can cause chaos.

All animals and plants are, to some extent, susceptible to disease caused by varying combinations of parasites, viruses and bacteria. In this paper, we develop a mathematical model of contact spread infection to investigate the effect of introducing a parasitoid-vectored infection into a one-host-two-parasitoid competition model. We use a system of ordinary differential equations to investigate the separate influences of horizontal and vertical pathogen transmission on a model system appropriate for a variety of competitive situations. Computational simulations and steady-state analysis show that the transient and long-term dynamics exhibited under contact spread infection are highly complex. Horizontal pathogen transmission has a stabilising effect on the system whilst vertical transmission can destabilise it to the point of chaotic fluctuations in population levels. This has implications when considering the introduction of host pathogens for the control of insect vectored diseases such as bovine tuberculosis or yellow fever.

On immunotherapies and cancer vaccination protocols: a mathematical modelling approach.

In this paper we develop a new mathematical model of immunotherapy and cancer vaccination, focusing on the role of antigen presentation and co-stimulatory signaling pathways in cancer immunology. We investigate the effect of different cancer vaccination protocols on the well-documented phenomena of cancer dormancy and recurrence, and we provide a possible explanation of why adoptive (i.e. passive) immunotherapy protocols can sometimes actually promote tumour growth instead of inhibiting it (a phenomenon called immunostimulation), as opposed to active vaccination protocols based on tumour-antigen pulsed dendritic cells. Significantly, the results of our computational simulations suggest that elevated numbers of professional antigen presenting cells correlate well with prolonged time periods of cancer dormancy.

Dissipative particle dynamics simulation of critical pore size in a lipid bilayer membrane.

We investigate with computer simulations the critical radius of pores in a lipid bilayer membrane. Ilton et al. (Ilton et al. 2016 Phys. Rev. Lett. 117, 257801 (doi:10.1103/PhysRevLett.117.257801)) recently showed that nucleated pores in a homopolymer film can increase or decrease in size, depending on whether they are larger or smaller than a critical size which scales linearly with film thickness. Using dissipative particle dynamics, a particle-based simulation method, we investigate the same scenario for a lipid bilayer membrane whose structure is determined by lipid-water interactions. We simulate a perforated membrane in which holes larger than a critical radius grow, while holes smaller than the critical radius close, as in the experiment of Ilton et al. (Ilton et al. 2016 Phys. Rev. Lett. 117, 257801 (doi:10.1103/PhysRevLett.117.257801)). By altering key system parameters such as the number of particles per lipid and the periodicity, we also describe scenarios in which pores of any initial size can seal or even remain stable, showing a fundamental difference in the behaviour of lipid membranes from polymer films.

Detection of arterial wall abnormalities via Bayesian model selection.

Patient-specific modelling of haemodynamics in arterial networks has so far relied on parameter estimation for inexpensive or small-scale models. We describe here a Bayesian uncertainty quantification framework which makes two major advances: an efficient parallel implementation, allowing parameter estimation for more complex forward models, and a system for practical model selection, allowing evidence-based comparison between distinct physical models. We demonstrate the proposed methodology by generating simulated noisy flow velocity data from a branching arterial tree model in which a structural defect is introduced at an unknown location; our approach is shown to accurately locate the abnormality and estimate its physical properties even in the presence of significant observational and systemic error. As the method readily admits real data, it shows great potential in patient-specific parameter fitting for haemodynamical flow models.

Travelling-wave analysis of a model of the immune response to cancer.

In this paper we present a travelling-wave analysis of a mathematical model describing the growth of a solid tumour in the presence of an immune system response. From a modelling perspective, attention is focused upon the attack of tumour cells by tumour infiltrating cytotoxic lymphocytes (TICLs), in a small multicellular tumour, without necrosis and at some stage prior to (tumour-induced) angiogenesis. As we have shown in previous work, for a particular choice of parameters, the underlying reaction-diffusion-chemotaxis system of partial differential equations is able to simulate the well-documented phenomenon of cancer dormancy by depicting spatially heterogeneous tumour cell distributions that are characterized by a relatively small total number of tumour cells. This behaviour is consistent with several immunomorphological investigations. Moreover, the alteration of certain parameters of the model is enough to induce bifurcations into the system, which in turn result in tumour invasion in the form of a standard travelling wave. The work presented in this paper complements the bifurcation analysis undertaken by Matzavinos et al. [Math. Med. Biol. IMA 21 (2004) 1-34] and establishes the existence of travelling-wave solutions for the system under discussion by promoting the understanding of the geometry of an appropriate phase space.

Mathematical modelling of the spatio-temporal response of cytotoxic T-lymphocytes to a solid tumour.

In this paper a mathematical model describing the growth of a solid tumour in the presence of an immune system response is presented. In particular, attention is focused upon the attack of tumour cells by so-called tumour-infiltrating cytotoxic lymphocytes (TICLs), in a small, multicellular tumour, without necrosis and at some stage prior to (tumour-induced) angiogenesis. At this stage the immune cells and the tumour cells are considered to be in a state of dynamic equilibrium--cancer dormancy--a phenomenon which has been observed in primary tumours, micrometastases and residual disease after ablation of the primary tumour. Nonetheless, the precise biochemical and cellular mechanisms by which TICLs control cancer dormancy are still poorly understood from a biological and immunological point of view. Therefore we focus on the analysis of the spatio-temporal dynamics of tumour cells, immune cells and chemokines in an immunogenic tumour. The lymphocytes are assumed to migrate into the growing solid tumour and interact with the tumour cells in such a way that lymphocyte-tumour cell complexes are formed. These complexes result in either the death of the tumour cells (the normal situation) or the inactivation (sometimes even the death) of the lymphocytes. The migration of the TICLs is determined by a combination of random motility and chemotaxis in response to the presence of chemokines. The resulting system of four nonlinear partial differential equations (TICLs, tumour cells, complexes and chemokines) is analysed and numerical simulations are presented. We consider two different tumour geometries--multi-layered cell growth and multi-cellular spheroid growth. The numerical simulations demonstrate the existence of cell distributions that are quasi-stationary in time and heterogeneous in space. A linear stability analysis of the underlying (spatially homogeneous) ordinary differential equation (ODE) kinetics coupled with a numerical investigation of the ODE system reveals the existence of a stable limit cycle. This is verified further when a subsequent bifurcation analysis is undertaken using a numerical continuation package. These results then explain the complex heterogeneous spatio-temporal dynamics observed in the partial differential equation (PDE) system. Our approach may lead to a deeper understanding of the phenomenon of cancer dormancy and may be helpful in the future development of more effective anti-cancer vaccines.

Spatial stochastic modelling of the Hes1 gene regulatory network: intrinsic noise can explain heterogeneity in embryonic stem cell differentiation.

Individual mouse embryonic stem cells have been found to exhibit highly variable differentiation responses under the same environmental conditions. The noisy cyclic expression of Hes1 and its downstream genes are known to be responsible for this, but the mechanism underlying this variability in expression is not well understood. In this paper, we show that the observed experimental data and diverse differentiation responses can be explained by a spatial stochastic model of the Hes1 gene regulatory network. We also propose experiments to control the precise differentiation response using drug treatment.

Mitochondrial dynamics and motility inside living vascular endothelial cells: role of bioenergetics.

The mitochondrial network is dynamic with conformations that vary between a tubular continuum and a fragmented state. The equilibrium between mitochondrial fusion/fission, as well as the organelle motility, determine network morphology and ultimately mitochondrial/cell function. Network morphology has been linked with the energy state in different cell types. In this study, we examined how bioenergetic factors affect mitochondrial dynamics/motility in cultured vascular endothelial cells (ECs). ECs were transduced with mitochondria-targeted green fluorescent protein (mito-GFP) and exposed to inhibitors of oxidative phosphorylation (OXPHOS) or ATP synthesis. Time-lapse fluorescence videos were acquired and a mathematical program that calculates size and speed of each mitochondrial object at each time frame was developed. Our data showed that inner mitochondrial membrane potential (ΔΨ(m)), ATP produced by glycolysis, and, to a lesser degree, ATP produced by mitochondria are critical for maintaining the mitochondrial network, and different metabolic stresses induce distinct morphological patterns (e.g., mitochondrial depolarization is necessary for "donut" formation). Mitochondrial movement, characterized by Brownian diffusion with occasional bursts in displacement magnitude, was inhibited under the same conditions that resulted in increased fission. Hence, imaging/mathematical analysis shed light on the relationship between bioenergetics and mitochondrial network morphology; the latter may determine EC survival under metabolic stress.