The nucleus of a cell plays a pivotal role in regulating cellular function and providing mechanical integrity. We present a three-dimensional discrete particle model of the nucleus that incorporates the nuclear lamina and chromatin-containing nucleoplasm. The exterior, including the lamina, is modeled by a shell of bonded particles that can exhibit elastic, geometrically nonlinear, and buckling characteristics. The interior, comprising the viscous fluid-like nucleoplasm and the elastic chromatin meshwork, is modeled with particles that undergo viscoelastic interactions. Such a particle framework allows for a realistic representation of the discreteness in nuclear structure and heterogeneity in nuclear properties. In addition, contact dynamics between particles is naturally handled within this framework. This is advantageous when considering the dynamic linkages between intranuclear components (chromatin and the lamina) or between the nucleus and the cytoskeleton. The efficacy of this particle model is compared with different experimental assays, and relevant insights are provided.

Efficient backward-time and forward-time simulation of simple to complex evolutionary scenarios are combined in order to describe the branch length distributions of branches with i underlying leaves in the extant sample in the correlated coalescent trees across linked loci in the genetic basis of a single independent trait. This takes into account the effect of genetic linkage on the decay of coalescent tree correlation across neighboring loci. Specifically, also the distributional shape under polygenic adaptation is investigated. Generally, there is no analytical expression for these branch length distributions which raises the importance of a computational insight. Ultimately, this distribution is used in order to construct a hypothesis test of selection versus no selection which does not only make use of singletons as in the singleton density score (SDS), but generally the density of i-tons via the newly introduced i-ton density score (IDS) test statistic. In this way, attention is placed on the characteristics of this distribution under different evolutionary scenarios, in particular when we are not only facing a simple recent hard selective sweep. Among other organisms, this method may then for instance be applied to human genetic data sets.

This contribution is about a Bayesian framework devoted to parameter estimation of an ordinary differential equation (ODE) model describing pharmacokinetic (PK) profiles of magnetic nanoparticles. Data comes from in vivo experiments in which one injected the nanoparticles into the bloodstream and measured them by alternate current biosusceptometry both in the heart and liver. The non-linear ODE model comprises three compartments, one for the heart and the other two for the liver, from which the nanoparticles partially return to the bloodstream. Reported simulations and calibration of curves and parameters were performed in R language using FME Package and others. As for results, it includes uncertainty analysis, credibility regions, and an identifiability discussion. As a perspective, we intend to use the described methodology for investigating possible changes in PK profiles originated by liver cancers. This work is supported by funding from grant #2020/05556-0, São Paulo Research Foundation (FAPESP).

The cyanobacterium Microcystis aeruginosa is one of the most common algal species capable of forming harmful algal blooms. There are two key traits related to the ubiquity of M. aeruginosa: colony formation under stressful environmental conditions and vertical motility via buoyancy regulation. While the importance and mechanisms of these traits have been thoroughly investigated, there is currently no model of M. aeruginosa transport and population dynamics that couples colony formation and motility. This talk will introduce such a model, consisting of a system of partial differential equations describing (i) the vertical diffusion of M. aeruginosa colonies in a stratified lake environment, (ii) the vertical advection of M. aeruginosa colonies as a function of water temperature and colony size, and (iii) a Smoluchowski term for the aggregation of colonies due to Brownian motion, shear, and differential settling. Model results will be compared to field trends, and the promises and perils of the method will be discussed.

Neural crest cells (NCCs) exhibit highly invasive phenotypes in vertebrates; they migrate from the neural tube of an embryo throughout its developing tissues. Since many NCC progenitors contribute to homeostasis in mature organisms, it is unsurprising that disruptions to NCC migration can have severe consequences on individual health, ranging from developmental defects to embryonic lethality. However, the relative importance of the biological mechanisms that contribute to the emergence and maintenance of NCC migration patterns remains to be established. Here, we model discrete NCC migratory streams using experimental data in the chick embryo. In collaboration with developmental biologists, we create a new agent-based model (ABM) for NCC migration that examines how remodelling of the extracellular matrix (ECM) can provide a non-local signal that allows cells to maintain coherent streams. We perform a global sensitivity analysis to identify model mechanisms that most contribute to successful migration, and use the ABM to generate in silico predictions to test through in vivo experiments. We find that ECM remodelling, haptotaxis, and contact guidance provide sufficient signals for NCCs to establish robust in silico streams; however, additional mechanisms are required to steer cells towards appropriate target sites.

The organic anion transporters (OATs) in the kidney are mainly responsible for transepithelial removal of uremic toxins out of the blood. To improve current (passive) dialysis treatments, researchers are trying to mimic this active removal by culturing kidney cells expressing the toxin transporters directly on outer surface of a hollow fibre membrane. Using a computational model with independent contributions of the activity and density of the toxin transporters, we have theoretically shown how the transporter density distribution can influence the local toxin clearance. More specifically, we tested twelve different patterns with varying total cell area, while keeping the total number of transporters constant. The computational findings showed that a more homogeneous transporter distribution resulted in a higher toxin clearance. We also demonstrated that short, serially connected cultures of cells would provide equivalent clearance compared to long fibers. In summary, this study contributes to an improved understanding of toxin transport in cellularized hollow fibers, which represent a promising strategy for renal replacement therapies.

The formation of new vascular networks is essential for tissue development and regeneration, in addition to playing a key role in pathological settings such as ischemia and tumour development. Experimental findings in the past two decades have led to the identification of a new mechanism of neovascularisation - cluster-based vasculogenesis - occurring in a variety of hypoxic settings in vivo. The focus of this talk is on the early stages of cluster-based vasculogenesis, during which endothelial progenitor cell (EPC) cluster formation is mediated by the action of matrix degrading enzymes and EPC proliferation. We present a mathematical model which sheds light on the spatio-temporal mechanisms responsible for cluster formation and cluster size. The numerical results, which qualitatively compare with data from in vitro experiments, provide further insights on the underlying dynamics indicating promising, fruitful future modelling and experimental research perspectives.

A fundamental problem in ecology is how individual-level behavior affects emergent macro-ecological patterns. In marine ecosystems, this issue is intimately related to the interaction between physical and biological forces. For example, while being advected by the turbulent ocean, plankton can actively move in search for resources, establishing a tug-of-war between behavior and turbulence. The spatial structures that emerge from this interplay, especially at small scales, are key to community diversity and stability. To further the understanding about this issue, we developed an agent-based model that keeps track of a grazer-resource community advected by a turbulent flow. Our model accounts for this flow by using the “seeded-eddy” model to generate a velocity vector field that mimics the main hydrodynamic signatures of turbulence. The ecological dynamics include reproduction, grazing, natural mortality, as well as grazer capabilities of swimming and sensing resources' hydrodynamic and chemical cues. We observe that, as the grazer shifts from a purely planktonic to an active behavior, mesoscale patchiness and a new phase portrait for the population dynamics emerge. In detail, we investigate how the grazer swimming velocity affects these outcomes.

We present, analyse and simulate a model for predator-prey interaction structured by hunger. The model consists of a nonlocal transport equation for the predator, coupled to an ordinary differential equation for the prey. We deduce a system of 3 ODEs for integral quantities of the transport equation, which generalises some classical Lotka-Volterra systems. By taking an asymptotic regime of fast hunger variation, we find that this system provides new interpretations and derivations of several variations of the classical Lotka-Volterra system, including the Holling-type functional responses. We next establish a well-posedness result for the nonlocal transport equation. Finally, we show that in the basin of attraction of the nontrivial equilibrium, the asymptotic behaviour of the original coupled PDE-ODE system is completely described by solutions of the ODE system.

Societies have always struggled with violence, but recently there has been a push to understand violence as a disease and public health issue. This idea has unified professionals in medicine, epidemiology, and psychology with a goal to end violence and help heal those exposed to it. Recently, analogies have been made between community-level infectious disease epidemiology and how violence spreads within a community. Experts in public health and medicine suggest an epidemiological framework could be used to study violence. Since mathematical modeling plays an important role in epidemiology and community level organizations have previously shown success in addressing violence using disease mitigating-like techniques, we see that mathematical modeling could be useful tool in violence prevention. In this talk I will expand on the analogy of violence as an infectious disease and show how mathematical epidemiology is a useful framework for understanding the dynamics of violence. Then we will examine a susceptible-exposed-infected mathematical model for violence spread in a community and explore its usefulness by looking at some example numerical simulations. To end we will explore some of the primary insight these simulations offer on the effectiveness of different potential violence prevention strategies that have been considered for deployment.

Because of the profound ecological and economic impacts of many non-native insect species, early detection and eradication of newly founded, isolated populations is a high priority for preventing damages. Though successful eradication is often challenging, the effectiveness of several treatment methods/tactics is enhanced by the existence of Allee dynamics in target populations. Historically, successful eradication has often relied on the application of several tactics. We ask how to combine three treatment tactics in the most cost-effective manner, either simultaneously or sequentially in a multiple-annum process. We construct an optimal-control model that describes the population dynamics of the invading insect population and how it is affected by three types of treatments: pesticide cation, mating disruption, and sterile male release. Then, we use stochastic programming to find the optimal treatment over time. We show that each of the three tactics is most efficient across a specific range of population densities. Furthermore, we show that mating disruption and sterile male release inhibit the efficiency of each other, and therefore, they should not be used simultaneously. However, since each tactic is effective at different population densities, different combinations of tactics should be applied sequentially through time when a multiple-annum eradication program is needed.

Random evolutionary games, where the payoff entries are random variables, play an important role in the modelling of social and biological systems under uncertainty which is due to, for instance, the lack of information or the rapidly change of environment. As in classical game theory with the foundational concept of Nash equilibrium, the analysis of equilibrium points in evolutionary game theory has been of special interest because these equilibrium points provide essential understanding of complexity in a dynamical system, such as its behavioural, cultural or biological diversity and the maintenance of polymorphism.In this talk, I will discuss our recent works on the statistics of the number of equilibriums in multi-player multi-strategy games. Existing methods in the literature involve solving a system of polynomial equations, thus are restricted to systems consisting of small numbers of players and/or strategies due to Abel's impossibility theorem. By connecting to the rich theory of random polynomial theory, our approach allows overcoming this difficulty, enabling us to study general systems with arbitrarily large numbers of strategies and players.

We consider a well-known observation at the interface of phylogeny and population genetics: Mutation rates estimated via phylogenetic methods tend to be much smaller than direct estimates from pedigree studies. To understand this, we consider the Moran model with two types, mutation, and selection, and investigate the line of descent of a randomly-sampled individual from a contemporary population. We trace this ancestral line back into the distant past, far beyond the most recent common ancestor of the population (thus connecting population genetics to phylogeny) and analyze the mutation process along this line. We use a probabilistic tool, namely the pruned lookdown ancestral selection graph, which consists of the set of potential ancestors of the sampled individual at any given time. A crucial observation is that the mutation process on the ancestral line is not a Markov process by itself, but it becomes Markov when consindering a broader state space. Relative to the neutral case (that is, without selection), we obtain a general bias towards beneficial mutations, while (depending on the parameters) both a speedup and a slowdown of the mutation process are possible. These results shed new light on previous analytical findings of Fearnhead (2002).

Multiple modes of asexual reproduction are observed among microbial organisms in natural populations. These modes are not only subject to evolution, but may drive evolutionary competition directly through their impact on population growth rates. The most prominent transition between two such modes is the one from unicellularity to multicellularity. So far, an analysis of general reproduction modes in terms of the optimality of the biomass distribution between daughter organisms is missing. We found that such considerations can greatly reduce the number of possible reproduction modes. This has important direct implications on microbial life: For unicellular species, the interplay between cell shape and kinetics of the cell growth implies that the largest and the smallest possible cells should be rod-shaped rather than spherical. For primitive multicellular species, these considerations can explain why rosette cell colonies evolved a mechanistically complex binary split reproduction. Finally, we show that the loss of organism mass during sporulation can explain the macroscopic sizes of the formally unicellular microorganism Myxomycetes plasmodium. Our findings demonstrate that a number of seemingly unconnected phenomena observed in unrelated species may be different manifestations of the same underlying process.

Different ecological processes lead to polymorphism at different spatial scales. While spatially divergent selection favors phenotypic differentiation between habitats, competitive exclusion promotes variation within patches. Both of these processes have been shown to depend on dispersal. High dispersal can restrict spatial phenotypic variation when counteracting local adaptation, while facilitating phenotypic variation within groups when reducing kin competition. Here, we investigate the evolution of quantitative traits that control the feeding rate on resources when both processes act in concert. Using the adaptive dynamics framework, we study intra-specific competition for locally and globally varying resources that triggered both divergent and negative frequency-dependent selection. We derive explicit expressions for the selection gradient and the disruptive selection coefficient for an infinite island model, while accounting for kin selection when patch sizes were small. We further tested the analytical predictions using individual-based simulations. Our results illustrate the relationship between the spatial scale of resource variation and the resulting intra-specific polymorphism in consumer traits. We further discuss how phenotypic polymorphism varies with regard to dispersal rate, patch size, and life history. All in all, our results shed light on the interaction between two major drivers of biological diversity in spatially varying environments when dispersal was limited.

The 2014 West Africa Ebola virus (EBOV) epidemic resulted in an increased desire and urgency to identify the mechanisms explored by EBOV to subvert immune responses; in particular that of type I interferon, which is a prototype innate immune response to a viral infection. This family of cytokines is important in the early stages of infection and key to inducing antiviral states within infected cells. There exists ample experimental evidence of the role that the EBOV 'multi-function'' protein VP35 has in promoting antagonism in a number of antiviral signalling pathways. We have developed novel stochastic models of VP35 antagonismin the type I interferon induction pathway based on current empirical evidence.Making use of approximate Bayesian computation, the mathematical modelsand experimental data sets, we have carried out model selection (to test differentmolecular hypotheses) and parameter calibration. Experimentaldata from the EBOV animal model of in vivo infection of rhesus monkeys.With a wish to gain further understanding into early time dynamics of type I interferon production during EBOV infections (or other viral infections, such as SARS-CoV-2), we hope that these models can be further extended to other viruses and their methods of innate immuneinhibition.

The COVID-19 pandemic, caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), has affected millions of people worldwide. Although the majority of cases present asymptomatic or mild symptoms that do not require hospitalisation, many cases can develop into severe disease (such as acute respiratory disease syndrome (ARDS)) requiring hospitalisation, ventilation and may result in death. A hyper-active or dysfunctional immune response (such as increased monocyte/macrophage and neutrophil infiltration) coupled with an excessive pro-inflammatory cytokine response (such as high levels of interleukin-6) are believed to play a prominent role in the development of severe disease. However, the precise mechanisms that lead to severe disease remain unclear. In this talk, we employ a hybrid multi-scale individual-based model to study the spread of SARS-CoV-2 on an epithelial monolayer. We focus our attention on the early dynamics of the host innate immune response and the immune cell cross-talk, as well as the interaction with secreted cytokines.

Many biological processes are modelled using Markov chains; thus, the inter-event times are assumed to be exponentially distributed. This hypothesis fails when cell proliferation plays a key role in the system of interest. Indeed, the history-dependence nature of the cell cycle breaks the Markov property. Our description of a population of stimulated cells preserves some of the convenient properties of a Markov process. A cell's time to division is a random variable with an Erlang distribution; its time to death has an exponential distribution. The underlying idea is to divide the cell cycle into a number of stages, each exponentially distributed and independent of the others. We can then consider cell generations in the model; that is all the cells that have divided the same number of times. Hence, the number of divisions that the cell has undergone is tracked, and this makes the model parameterisation feasible. The parameters are inferred using an Approximate Bayesian Computation approach based on sequential Monte Carlo methods with CFSE data of human and murine T lymphocytes. We calibrated the exponential model and the multi-stage one, and compared them using the corrected Akaike Information Criterion to prove statistically the better fit of the multi-stage model.

A mechanism used to maintain the naive T cell repertoire is competition for homeostatic proliferation stimuli. We propose a multivariate competition model to study the dynamics of n clonotypes competing for proliferation stimulus provided by self peptides bound to Major Histocompatibility Complexes (self pMHC). We assume the population of self pMHC to be at steady state (thus providing constant stimulus) and study the long-term behaviour of the system by analysing: (i) dynamics in the long-term before extinction through the quasi-stationary distribution; (ii) time to extinction of the first clonotype, probabilities of extinction for each clonotype, and size of the surviving ones when extinction occurs. Additionally we analyse the distribution of the number of divisions of a given clonotype before its extinction.

Rats have long been thought to drive plague epidemics, specifically bubonic plague. However an alternative theory for plague transmission has been posited by Dean et al. (PNAS 2018) where ectoparasites living on human hosts drive spread. This talk will present a new mathematical model for the spread of the plague based on rat-flea interactions with the human population and compare our results to existing models. Our results suggest that rat-flea transmission of the plague is still a plausible explanation.

Modeling human behavior within mathematical modeling of infectious diseases is key to understand and control disease spread. We present a mathematical compartmental model of Susceptible - Infectious - Removed to compare the infected curves given by four different functional forms describing the transmission rate. These depend on social-distance, which varies according to the balance between two opposite thrives: the self-protecting reaction of individuals upon the presence of disease to increase social distancing and their necessity to return to a culturally dependent natural social distance that occurs in the absence of disease. We present results for different society types on point prevalence, the peak size of a first epidemic outbreak and the time of occurrence of that peak, for four different transmission rate functional forms and parameters of interest related to distancing behavior. We observe the vulnerability to disease spread of close contact societies, and also that certain social distancing behavior may provoke an early occurring small peak of a first epidemic outbreak, observing differences in this regard between society types. We discuss the appearance of oscillations of the transmission rates and how these oscillations are impacted through social distancing; breaking the unimodality of the actives-curve produced by the classical SIR-model.

As part of a concerted pandemic response to protect public health, businesses can enact non-pharmaceutical controls to minimise exposure to pathogens in workplaces and premises open to the public. Amendments to working practices can lead to the amount, duration and/or proximity of interactions being changed, ultimately altering the dynamics of disease spread.We use a data-driven approach to parameterise an individual-based network model for transmission of SARS-CoV-2 amongst the working population, stratified into work sectors. The network comprises layered contacts to consider risk of spread in multiple encounter settings (workplaces, households, social and other). We analyse several interventions targeted towards working practices: mandating a fraction of the population to work from home; using temporally asynchronous work patterns; and introducing 'COVID-secure' workplaces. We also assess the general role of adherence to (or effectiveness of) isolation and test and trace measures and demonstrate the impact of these interventions on epidemiological metrics.Given the heterogeneity of demographic attributes across worker roles, in addition to the individual nature of controls such as contact tracing, we demonstrate the utility of a network model approach to investigate workplace-targeted intervention strategies and the role of test, trace and isolation in tackling disease spread.

Insufficient testing capacity has proven to be a critical bottleneck in the fight against COVID-19, especially during the early stages of the pandemic. Prioritizing allocation of limited testing resources based on symptom severity (among other factors) has therefore emerged has a key component of public policy ripe for mathematical analysis and optimization, but the typical testing rate expressions utilized in compartmental disease models are inadequate for describing severely constrained resource scenarios. Here, we propose a testing model which flexibly accounts for both limited and plentiful resources, and we use a modified SEIR model with quarantine to find optimal allocations of testing capacity for flattening the epidemic curve. We balance resources between two testing strategies: clinical testing focused only on severely symptomatic individuals and non-clinical testing focused on mild and asymptomatic individuals, where contact tracing and case monitoring are incorporated by an information parameter. We find that purely clinical testing is optimal at very low testing capacities, supporting early guidance to ration tests for the sickest patients. Additionally, we find that a mix of clinical and non-clinical testing becomes optimal as testing capacity increases. Further, we find that reduction of our model's R0 is an unreliable metric for epidemic peak reduction.

Background: Identifiability analysis is a crucial step in improving reliability and predictability of biological models. Profile Likelihood (PL) is a reliable though computationally expensive approach to identifiability analysis. PL-based algorithm Confidence Intervals by Constraint Optimization (CICO), which was recently published (https://doi.org/10.1371/journal.pcbi.1008495/), reduces computational requirements and increases the accuracy of the estimated parameters' confidence intervals. The CICO algorithm is available in a free software package LikelihoodProfiler based on Julia (https://github.com/insysbio/LikelihoodProfiler.jl). CICO can be potentially extended to predictability analysis and confidence bands estimation.Objectives: The goal of this study is to examine the application of CICO to estimation of confidence and prediction bands. The analysis was performed on a number of published biological models, including STAT5 Dimerization model, Cancer Taxol Treatment model, etc.Results: The original CICO algorithm can be extended to a broader use-case of confidence bands. The analysis demonstrates good performance characteristics for both identifiable and non-identifiable cases. The approach can be used with complex biological models where each likelihood estimation is computationally expensive and some output values are non-identifiable. Detailed analysis of each model can be found on the GitHub repository likelihoodprofiler-cases https://github.com/insysbio/likelihoodprofiler-cases.

Comparison of long symbolic sequences corresponding to various biological macromolecules is the principal tool in bioinformatics, biophysics, and other life sciences. However, symbolic sequence alignment, currently widely used for computing comparison, suffers from multiple downsides. Some of them are subjective parameters' choice, divergence, and high computational complexity. The paper proposes an alignment-free non-parametric, highly efficient novel method to compare symbolic sequences based on a binary multi-channel encoding and their Fourier convolution. Due to the high O(n*log(n)) efficiency of the Fourier convolution, the method can process sequences up to 10^7 symbols long on consumer-level hardware under half an hour. Also, the method lends itself to a straightforward parallelization. The base version of the algorithm determines the number of exact matches in any overlapping configuration of two sequences and provides it in a single run of the convolution calculation. The advanced version determines the number of exactly matching k-mers in those configurations. The insertions and deletions, which present significant challenges for the alignment-based computations, do not affect the proposed method's efficiency.

The recent advances in cancer immunotherapy paved the way for the development of mathematical models formulating the complex interactions between the tumor and the immune system, with the aim to indicate more efficient treatment regimes. However, the complexity of such models and their multi-scale character renders them inaccessible for wide utilization and hinders the acquisition of physical understanding. In order to tackle these obstacles, here the algorithmic tools of asymptotic analysis are utilized in a fundamental model formulating the interactions of tumor cells with natural killer cells, CD8+ T cells and circulating lymphocytes. It is firstly revealed that the long-term evolution of the system towards the high-tumor or the tumor-free equilibrium is determined by the dynamics of an initial explosive stage of tumor progression. Focusing on this stage, the algorithmic Computational Singular Perturbation methodology is employed to identify the underlying mechanisms confining the system to evolve towards the high-tumor equilibrium and the governing slow dynamics along them. The results demonstrate the potential of algorithmic asymptotic analysis to simplify the complex, overeparameterized and multi-scale cancer immunology models and to indicate the interactions and cell types to target for more effective treatment development.

We studied the relation between triplet composition of genes and taxonomy of the bearers in case of plant genes. There are two gene families that are common for mitochondria and chloroplast genomes of plants: atp genes family and nad family. In this study we compared mitochondrial and chloroplast atp genes of the same species. These genes encode subunits of ATP synthase. Totally, 170 (85 mitochondrial and 85 chloroplast) plant genomes were studied. Each gene sequence was transformed into a triplet frequency dictionary, where the reading frame shift was equal to t = 1. Then the points in 64-dimensional space of the triplet frequencies of the genes were clustered with ViDaExpert software. Three types of clustering have been analyzed: for mitochondria genes solely, for chloroplast genes solely, and for the merged set of the genes from both organelles' genomes. It was observed that clusters are formed on a functional basis. To be more precise, the genes encoded different subunits were split into separate clusters. Moreover, each cluster contained genes encoding only one subunit of ATP synthase. Thus, the prevalence of function over the taxonomy for atp genes family of organelles genomes of plants has been proven.

While basic retinal architecture is conserved across vertebrates, each species' retina is unique, having evolved to detect and interpret the visual scenes particular to its environment. It is therefore important to build towards a broad understanding of the types of computations performed within the eyes of different species. Here, adult zebrafish are of particular interest. While considerable work has gone into studying the structure and function of the larval visual system, we know comparatively little about visual function in adults which differ vastly in size, swimming speed and visual-ecological niche. Anatomically, the mere 4,000 retinal ganglion cells (RGCs) of the larval eye increase to around 150,000 in the adult, all crammed into an eye that remains substantially smaller than that of the mouse with its 50,000 RGCs. What do all these “extra” RGCs encode, and how uniformly are any computations performed across different parts of the eye?In this work we take a truly interdisciplinary approach, combining cutting edge experimental techniques with the latest theoretical methods. In this way, we aim to build towards a first overview of the major visual computations performed by the adult zebrafish eye.

Recently, biologists have shown fractal and oscillatory characteristics in animal behaviortime series. Aspects so different can be explained by a model with added components thatinclude deterministic cycles (ultradian and circadian rhythms), polynomial tendencies, and anunderlying nonlinear process with stationary increments. Such components can be extractedfrom the data using wavelet analysis by selecting the transformation appropriately. In this talk, we will discuss a five-step method that describes the data without making any parametric assumptions about trends in the frequency or amplitude of the components signals and is resilient to noise.1. Visual inspection by Continuous wavelet transform based on real Gaussian motherwavelet in the Cartesian time scale plane2. Visual inspection by Continuous wavelet transform based on complex Morlet motherwavelet in the Polar time scale plane.3. Modal frequency detection by Synchrosqueezed wavelet transform, a linear timescale analysis followed by a synchrosqueezing technique.4. Modal frequency corroboration by Empirical wavelet transform, a wavelet analysis in theFourier domain followed by frequency segmentation to extract the modal components.5- Quantification of coherence and phase difference between different series.

In Drosophila, circadian rhythms are regulated by about 150 pacemaker neurons. In each pacemaker neuron, circadian gene expression is driven by a transcriptional-translational feedback loop (TTFL). Interestingly, with dCLK-Δ mutation, which has impaired binding with PER, the amplitude of PER rhythms is greatly reduced in small ventral lateral neurons (sLNvs), but not in dorsal neuron 1s (DN1s). We investigated this unexpected difference between LNvs and DN1s by developing a mathematical model describing the TTFL. Our model predicted the differences in the molecular stoichiometry and regulatory mechanism of clock proteins between sLNvs and DN1s, which were validated by the experiments. We will discuss the biological significance of those differences between LNvs and DN1s for circadian clock system to work.

Current radiotherapy (RT) treatment schedules are not personalized for individual patients, with the prescribed dose being uniform for particular subtypes and stages of cancer, despite variable responses between patients. Our objective is to determine optimal personalized RT dose in order to minimize excess RT dose without sacrificing tumor control. Weekly tumor volume data were collected for 39 head and neck cancer patients from Moffitt and M.D. Anderson Cancer Centers that received RT over 6-8 weeks. Tumor growth was modeled as logistic growth, and the effect of RT was modeled as an instantaneous reduction in carrying capacity. Tumor volume reduction was connected to locoregional control (LRC) by a volume reduction threshold associated with LRC.The in silico trial was performed in a leave-one-out fashion where model parameters calibrated to tumor volume data from N-1 patients and then the calibrated model parameters were combined with the Nth patient's tumor volume data from weeks 1-4 of RT to simulate tumor volumes forward in order to estimate minimum dose required for LRC. We found that 87% of the patients received a higher total dose than estimated as necessary by our model, while the remaining patients were estimated to have received too little dose.

The production of blood can be disturbed by mutations in haematopoietic stem cells (HSCs). Though mostly inconsequential, some mutations confer fitness advantages resulting in growth of fitter clones (all progeny of a HSCs carrying the same mutation) that represent disproportionately large fractions of all blood cells. Clonal Haematopoiesis of Indeterminate Potential (CHIP) affects more than 10% of the population aged over 65 years and is currently diagnosed when 4% of blood cells carry the same mutation. CHIP is linked with a ten-fold increase in later onset of haematological cancers, highlighting the importance of detecting and predicting clonal growth early.We investigate CHIP in the Lothian Birth Cohort through targeted error-corrected sequencing of blood samples taken from participants every 3 years.Modelling the population dynamics of clones shows the commonly used threshold to diagnose CHIP can be reached due to neutral drift in synonymous mutations. This clinical detection method therefore leads to a ~50% false discovery rate of fit mutations. Using longitudinal data, we instead detect clones whose growth exceeds the distribution of fluctuations of neutral mutations. This allows us to uncover fitness-inducing mutations with high sensitivity and detect highly fit mutations before they achieve the threshold-based definition of CHIP.

Glioblastoma grade IV is a highly aggressive form of brain cancer, with a short duration of survival after diagnosis even in the presence of treatment. A challenge with surgical removal is the diffuse nature of tumors, and the difficulty of removing the whole tumor when cancer cells have migrated away from the primary tumor site. During migration, cells are influenced by their microenvironment, and it has been observed that cells tend to migrate along white matter tracts or towards blood vessels. A great variation in growth patterns is found when glioblastoma cells from different patients are grown ex vivo in the brain of mice. In order to quantify these differences we construct an agent based model of tumor growth in the brain of mice. We make use of diffusion tensor imaging data to obtain information about the white matter tracts, as well as a dataset of the whole brain vasculature. The migration direction is biased by either the white matter, the blood vessels or both. The model is fitted to experimental data using Approximate Bayesian Computation to provide insights into the differences between both proliferation as well as migratory preference for white matter or blood vessels.

Glioblastoma (GBM) is the most common and aggressive type of brain tumor in adults, with a median patient survival slightly above one year, despite aggressive combination therapy with the alkilating agent temozolomide (TMZ) and radiation therapy. Phase III clinical trials of the combination of bevacizumab (BEV, anti-angiogenic drug) with the standard chemoradiation protocol were negative in terms of providing survival improvements. In a very interesting study, Balaña et al. (2016) sought to determine the impact of BEC on reduction of tumor size prior tochemoradiotherapy treatment in unresected GBM patients. They found that the combination of BEV and TMZ was more active than TMZ alone and may confer benefit in terms of tumor shrinkage in unresected patients. We propose a simple mathematical model of tumor growth taking into account hypoxic cells and treatments (radiotheraphy, chemotherapy and anti-angiogenic treatment). We study mathematical properties of the model. Moreover, we show that solution of the model mimic well results of clinical trials.