I will survey what some recent mathematical results suggest about the design principles behind circadian clocks. In particular, I will discuss flexibility, robustness, buffering mechanisms against environmental heterogeneity, temperature compensation in physiological entrained conditions and tracking of multiple phases. If time permits I will also discuss new methods for f...
Ion channels are irresistible objects for biological study because they are the 'nanovalves of life' controlling most biological functions, much as transistors control computers. Channels contain an enormous density of crowded charged spheres, fixed and mobile, and induced polarization charge as well. Direct simulation of channel behavior in atomic detail is diff...
As a mean-field continuum model, Poisson Nernst-Planck (PNP) theory is an efficient computational tool for the study of ion transport phenomenon in the biological systems such as ion channels, which are important in the cell survival and the regulation of cellular activity. The present talk reports advanced numerical schemes and modified PNP models for ion channels. Based ...
Theories like Poisson-Nernst-Planck that model ions as point charge are very useful in many applications. However, when ions are near highly-charged binding sites on proteins or inside ion channels, the size of the ions produces first-order effects because the ions' concentration is very large and/or because the ions are in a crevice or pore that is not much wider tha...
The Navier-Stokes/Poisson-Nernst-Planck model assumes significance because of its connection to the electrophysiology of the cell, including neuronal cell monitoring and microfluidic devices in biochip technology. The model has also been used in other applications, including electro- osmosis. The steady model is especially important in ion channel model- ing, because the c...
Proton transport across membranes is one of the most important and interesting phenomena in living cells. The present work proposes a multiscale/multiphysical model for the understanding of atomic level mechanism of proton transport in transmembrane proteins. We describe proton dynamics quantum mechanically via a density functional approach while implicitly model numerous ...
Continuum modeling can be a proper choice to overcome the limitations on time and length scales of all-atom biomolecular simulations. The main concerns in this area are the model's accuracy and the numerical techniques/implementation. Besides, the molecular surface/volume meshing is also an unavoidable issue in many cases. I'll talk about our works on calculation...
We utilize the MARTINI coarse-grained force field to simulate lipid monolayers during the compression and re-expansion, to determine the effect of monolayer components on lung surfactant functioning. Our simulated monolayers contain pure dipalmitoylphosphatidylcholine (DPPC) and DPPC mixed with palmitoyloleoylphosphatidylglycerol (POPG), palmitic acid (PA), and/or peptides...
Several different circadian rhythms, as well as an annual rhythm, have been studied in the marine dinoflagellate Gonyaulax polyedra (now Lingulodinium polyedrum), many features of which may be grist for modeling mills, whatever they may be. The rhythm of bioluminescence provides an easy "hand" for the automation of its measurement in vivo, and the luciferase and ...
About 20% of Neurospora genes are under control of the circadian clock system at the level of transcript accumulation, and the bulk of the clock-controlled mRNAs have peak accumulation in the late night to early morning. These data suggested the existence of global mechanisms for rhythmic control of gene expression. Consistent with this idea, we found that the Neurospora O...
In most eukaryotic organisms, networks of cell cycle and circadian rhythms coexist and work coordinately to create optimal conditions for cells to grow and adapt to the surrounding environment. Cell cycle regulatory mechanisms include multiple checkpoints for controlled growth and cell divisions. The period of this oscillation, however, varies with external conditions such...
Pelagic copepods are the dominant mesozooplankton in much of the world's oceans. They form a crucial link in the transfer of energy from primary production to upper trophic levels, and they are a significant contributor to vertical carbon flux through migration and fecal pellets. Much effort has gone into studying the effects of climate change on individual species. T...
The Arctic environment is experiencing a rapid change due to the ongoing climate warming, with an especially high rate of temperature increase in the Arctic. The core of this change is the cryosphere destruction: an abrupt decrease in sea ice extent and volume, intensified glacier melting, and degradation of the permafrost. These processes profoundly affect the entire Arct...
In this talk, we will present analytic results concerning phytoplankton growth under nutrient-light co-limitation. The model we employ consists of two reaction-advection-diffusion PDEs for the plankton and nutrient concentrations and incorporates self-shading effects.
In the first part of this talk, we will work with a single spatial dimension (depth) and lo...
In this talk, we will consider the problem of bifurcating DCMs under nutrient-light co-limitation from a weakly nonlinear point of view. In particular, we will work with the plankton-nutrient model in one spatial dimension introduced in A. Zagaris's talk and investigate the weakly nonlinear stability problem for these bifurcating DCMs.
The polar oceans have already experienced significant ecosystem shifts associated with sea ice retreat. Earth system models suggest that major changes in marine ecosystems and biogeochemistry will keep on going through the 21st century. However, future projections of the polar oceans are subject to some of the largest uncertainties. Among the sources of uncertainty is the ...
Climate driven changes to the physical structure of the ocean will modify oceanic temperature, light, and nutrients, essential ingredients for the growth of ocean phytoplankton. In turn, resulting changes in phytoplankton growth and community structure will affect export production, deep ocean carbon storage, and ultimately atmospheric carbon. The questions I work on a...
Our best examples of coevolution come from simplified interactions, but communities are rarely simple. Are complex communities less coevolved, or is coevolution just harder to recognize? I discuss coevolution and community complexity in light of both natural and invaded systems....
Most theoretical work on the evolution of competing species has used models having the minimum number of species (i.e. two), and has not represented either enemies or resources of those two consumer species. Empirical studies of character displacement involve species that share multiple resources, and usually multiple predators as well. Although some prominent experimental...
Differential geometry of curves uses the Frenet-Serret moving frame. A curve can be defined by scalar quantities of curvature and torsion and these quantities are defined by differentiating the frame. Similar techniques can be used for discrete curves formed by sequences of bonded atoms. The frames are related to molecular frames and are useful in finding protein structure...
Structures of membrane proteins have been challenging to solve by any structural technique. We are developing solution NMR spectroscopy as a tool to study the structure and dynamics of membrane proteins, including bacterial outer membrane porins. This class of membrane proteins has proven particularly beneficial for these studies because (i) a larger chemical shift dispers...
We present a computationally efficient method for flexible refinement of docking predictions that reflects observed motions within a protein's structural class. Using structural homologs, we derive deformation models that capture likely motions. The models or "replicates" typically align along a rigid core, with a handful of flexible loops, linkers and tails...
Understanding how biological sequences encode structural and functional information is a fundamental scientific challenge. For RNA viral genomes, the information encoded in the sequence extends well-beyond their protein coding role to the role of intra-sequence base pairing in viral packaging, replication, and gene expression. Working with the Pariacoto virus as a model se...
Implicit solvent models are important components of modern biomolecular simulation methodology due to their efficiency and dramatic reduction of dimensionality. However, such models are often constructed in an ad hoc manner with an arbitrary decomposition and specification of the polar and nonpolar components. In this talk, we review current implicit solvent models and sug...
Recently, we have introduced a differential geometry based model, the minimal molecular surface, to characterize the dielectric boundary between biomolecules and the surrounding aqueous environment. The mean curvature flow is used to minimize a surface free energy functional to drive the surface formation and evolution. More recently, several potential driven geometric flo...
Human DNA sequence differs among individuals and the most common variations are known as single nucleotide polymorphisms, or SNPs. Studies have shown that non-synonymous coding SNPs (nsSNPs - SNPs occurring in protein coding regions which lead to amino acid substitutions) can be responsible for many human diseases or cause the natural differences among the individuals by a...
We show how mathematics can help in the complex process of drug discovery. We give an example of modification of a common cancer drug that reduces unwanted side effects. The mathematical model used to do this relates to the hydrophobic effect, something not yet fully understood. The hydrophobic effect modulates the dielectric behavior of water, and this has dramatic effect...
Ant-plants are important structural elements in many disturbed tropical ecosystems and the mutualism between plants and their defending ant symbionts is increasingly being used as a model to study general factors that stabilize a horizontally transmitted mutualisms. As these mutualisms must be established anew in every consecutive generation they are particularly prone to ...
Species exist in complex biotic environments, engaging in a variety of antagonistic and cooperative interactions that contribute to their population and evolutionary dynamics. However, studies tend to concentrate on each pairwise interaction in isolation. By doing so, they may overlook significant feedbacks between the interactions. In this talk, I will focus on plant-poll...
In this talk I will present several theories related to co-evolution between plants and insects. First I will present a model of predator-prey coevolution, showing that rapid evolution in the predator can lead to prey diversification and a decrease in the number of preys available to the predator. This correspond to a "Red King" scenario, where rapid evolution le...
(Co)evolutionary ecologists have long appreciated that ecology drives evolution, and that evolution ultimately shapes the ecological processes and patterns of populations and communities over long periods of time. However, it remains unclear how these two processes interact to affects the ecology, evolution and coevolution of communities over short timescales (e.g. one to ...
Recently, several studies have used the geographic matching of morphological traits (e.g. proboscis versus corolla length) to infer that coevolution has taken place between two interacting organisms. However, geographic trait matching alone is not sound evidence for coevolution because it is not a mandatory end point for coevolutionary relationships, and nor is coevolution...
The geographic mosaic theory of coevolution (GMTC) considers that populations differ in evolutionary dynamics due to spatial variation in selective regimes. According to GMTC, three components of geographic structure drive the overall coevolutionary dynamics of such interactions: selection mosaics, coevolutionary hotspots, and trait remixing. Furthermore, the GMTC suggests...
The adaptive landscape, long a useful metaphor, is also a rigorous tool for understanding evolution when it is linked to empirical measurements of fitness. However, empirical estimates of fitness surfaces are often concave, implying an evolutionarily unstable situation under general conditions in the short term, and untenable extrapolations to longer-term evolution under t...
In many plant-pollinator systems, interactions present a high degree of generalism, so that coevolution should be studied at the community level. Indeed intraspecific trait variation in such systems may both lead to variation in the gains that individuals are drawing from their interactions, and to variation in their choice/attraction of interaction partners. In this contr...
One very robust result of models of host-parasite co-evolution is that under regimes of mixed infection, where different strains of parasites compete for limiting host resources, parasites should evolve higher virulence strategies. This has wide reaching ramifications for optimal parasite strategies, since parasites are seldom alone in exploiting hosts. However, not all in...
Structural properties on protein residue-level, such as the distances between two residues and the angles formed by short sequences of residues, can be important for structural analysis and modeling, but they have not been examined and documented in great detail. While these properties are difficult to measure experimentally, they can be statistically estimated based on th...
Homeostatic control mechanisms are essential to keep cells and organisms fit in a changing and challenging environment. An important task is to identify the factors which contribute to the functionality and robustness of homeostatic mechanisms in the presence of environmental perturbations. Kinetic conditions which lead to robust homeostasis and perfect adaptation together...
In the 2002 film by Gurinder Chadha, character Jesminder 'Jess' Bhamra states "No one can cross a ball or bend it like Beckham" in a reference to the international soccer star's ability to cause the ball to swerve. French researchers Guillaume Dupeux, Anne Le Goff, David Quere and Christophe Clanet published a paper earlier this year in the New Jou...
A new way to model the dynamics of malaria transmission that takes into consideration the demography of the transmitting vector will be presented. Model results indicate the existence of nontrivial disease free and endemic steady state solutions which can be driven to instability via a Hopf bifurcation as a parameter is varied in parameter space. The model therefore captur...
Nonlinear partial differential equations arise in stochastic optimal control via dynamic programming equations. In many cases, solutions of these equations aid in the design of optimal controls. We discuss a class of equations where the associated control processes are "singular" with respect to the time variable. These equations arise in models for spacecraft co...
Conformational diseases result from the failure of a specific protein to fold into its correct functional state. The misfolded proteins can lead to the toxic aggregation of proteins. In some cases, misfolded proteins interact with bystanders proteins (unfolded and native folded proteins), eliciting a misfolded phenotype. These bystander polypeptides would follow their norm...
Lee Segel one of the greatest applied mathematicians of our time passed away on January 31, 2005. His obituary (SIAM News, 03-10-2005) read "With his death, the applied mathematics community lost one of its finest practitioners, and the theoretical biology community lost a true pioneer who was still a leader at the cutting edge of so many subjects. And most importantl...
Amplitude is a measurable parameter of an oscillator, yet it is often not considered as a variable, Amplitude can be measured in several ways: 1) as an output of an oscillator; 2) directly as the amplitude of a "key" clock protein; or 3) indirectly via a Phase-response curve. Data will be presented for a particular mutant (frq7) of Neurospora which shows how the ...
Several experimental studies have altered the natural phase relationship between photic and non-photic zeitgebers, in order to assess their hierarchy in the entrainment of circadian rhythms. In order to interpret the complex results that emerge from these conflicting zeitgeber protocols, we present computer simulations of two coupled oscillator systems forced by two indepe...
Cyclic processes in biology span a wide dynamic range, from the sub-second periods of neural spike trains to annual rhythms in animal and plant reproduction. Even an individual cell exposed to a constant environment may exhibit many parallel periodic activities with different frequencies. It is therefore important to elucidate how multiple clocks coordinate their oscillati...
Migration is a widely used strategy for dealing with seasonal environments, yet little work has been done to understand what ultimate factors drive migration. Here I will present joint work with Iain Couzin, where we have developed a spatially explicit, individual-based model in which we can evolve behavior rules via simulations under a wide range of ecological conditions ...
General anesthesia is a drug-induced, reversible condition comprised of five behavioral states: unconsciousness, amnesia (loss of memory), analgesia (loss of pain sensation), akinesia (immobility), and hemodynamic stability with control of the stress response. The mechanisms by which anesthetic drugs induce the state of general anesthesia are considered one of the biggest ...
Eusociality is an advanced form of social organization, where some individuals reduce their reproductive potential to raise the offspring of others. Eusociality is rare but hugely successful: only about 2% of insects are eusocial but they represent 50% of the insect biomass. The biomass of ants alone exceeds that of all terrestrial non-human vertebrates combined. I will pr...
Most of the phenomena of life that attract our attention result from interactions among many components in a network. Examples include the interactions among neurons in the brain, among birds in a flock or fish in a school, and even the interactions among amino acids in a single protein. In all these cases there are "emergent" or collective behaviors that are pro...
Synthetic biology is bringing together engineers, mathematicians and biologists to model, design and construct biological circuits out of proteins, genes and other bits of DNA, and to use these circuits to rewire and reprogram organisms. These re-engineered organisms are going to change our lives in the coming years, leading to cheaper drugs, "green" means to fue...
The modern era of human genomics began ten years ago with the launch of the HapMap project following the publication of the first draft of the human genome. Although the sequencing of the genome was a major scientific achievement, it has become clear that naive analysis of sequence will not be sufficient to address the fundamental challenge in genomics: determination of th...
The collective movement of cells in tissue is vital for normal development but also occurs in abnormal development, such as in cancer. We will review three different models: (i) A vertex-based model to describe cell motion in the early mouse embryo; (ii) A individual-based model for neural crest cell invasion; (iii) A model for acid-mediated tumour invasion.
The subject of mathematical ecology is one of the oldest in mathematical biology, having its formal roots a century ago in the work of the great mathematician Vito Volterra, with links, some long before, to demography, epidemiology and genetics. Classical challenges remain in understanding the dynamics of populations and connections to the structure of ecological communiti...
The 20th century revolution in statistics focused on measurement, experimental design, modeling and computational issues in a world of "small" data where the number of observations and/or variables were typically limited and information available in single sources. Scientists face very different challenges in the current age where data is often streamed in real t...
Interaction between gene products forms the basis of essential biological processes like signal transduction, cell metabolism or embryonic development. The variety of interactions between genes, proteins and molecules are well captured by network (graph) representations. Experimental advances in the last decade helped uncover the structure of many molecular-to-cellular lev...
All populations experience stochastic
uctuations in abiotic factors such as temperature, nutrient avail-
ability, precipitation. This environmental stochasticity in conjunction with biotic interactions can facilitate
or disrupt persistence. One approach to examining the interplay between these deterministic and stochastic
forces is the construc...
Rapid recent progress in advanced microscopy has revealed that nano-particles
immersed in biological
uids exhibit rich and widely varied behaviors. In some
cases, biology serves to enhance the mobility of small scale entities. Cargo-laden
vesicles in axons undergo stark periods of forward and backward motion, inter-
rupted by sudden paus...
Rapid recent progress in advanced microscopy has revealed that nano-particles
immersed in biological
uids exhibit rich and widely varied behaviors. In some
cases, biology serves to enhance the mobility of small scale entities. Cargo-laden
vesicles in axons undergo stark periods of forward and backward motion, inter-
rupted by sudden paus...
As a warming up, we will start with a brief overview of the main results about the voter model: clustering versus coexistence, cluster size and occupation time. The voter model is an example of interacting particle system - individual-based model - that models social influence, the tendency of individuals to become more similar when they interact. Each vertex of the lattic...
We will work through some of the basic ideas involved in modeling various types of interactions in spatial population biology using interacting particle systems (sometimes referred to as stochastic cellular automata). Some of the essential ingredients and behaviors come from simple models like the contact process and the voter model. These components can be combined and tw...
As a warming up, we will start with a brief overview of the main results about the voter model: clustering versus coexistence, cluster size and occupation time. The voter model is an example of interacting particle system - individual-based model - that models social influence, the tendency of individuals to become more similar when they interact. Each vertex of the lattic...
We will work through some of the basic ideas involved in modeling various types of interactions in spatial population biology using interacting particle systems (sometimes referred to as stochastic cellular automata). Some of the essential ingredients and behaviors come from simple models like the contact process and the voter model. These components can be combined and tw...
This set of lectures and discussions will provide a quick one-day conceptual overview of stochastic issues in biology. Time permitting, I will point out the major conceptual approaches to stochasticity as typically applied in biology (random walks, Markov chains, birth and death processes, branching processes, agent-based models, stochastic DEs, diffusion processes, statis...
Properties of the Wiener process are reviewed and stochastic integration is explained. Stochastic diï¬€erential equations are introduced and some of their properties
are described. Equivalence of SDE systems is explained. Commonly used numerical
procedures are discussed for computationally solving systems of stochastic diï¬€erentia...
Properties of the Wiener process are reviewed and stochastic integration is explained. Stochastic diï¬€erential equations are introduced and some of their properties are described. Equivalence of SDE systems is explained. Commonly used numerical procedures are discussed for computationally solving systems of stochastic diï¬€erential equations. A...
A brief introduction is presented to modeling in stochastic epidemiology. Several
useful epidemiological concepts such as the basic reproduction number and the nal size
of an epidemic are dened. Three well-known stochastic modeling formulations are in-
troduced: discrete-time Markov chains, continuous-time Markov chains, and stochastic
dieren...
While the impact of single extracellular matrix (ECM) proteins and mechanical stiffness on cell function have been thoroughly probed individually, little work has been put into to understanding their interactions in the context of cell function. This is particularly important as the ECM is a complex mixture of proteins that change throughout normal development both in comp...
In the seventies, biologists Maynard Smith and Price used concepts from game theory to describe animal conflicts. Their work is at the origin of the popular framework of evolutionary game theory. Space is another component that has been identified as a key factor in how communities are shaped. Spatial game models are therefore of primary interest for biologists and sociolo...
In models of disease transmission on contact networks, the probability of exposure is determined by the connectivity (degree) of the individual (node). Thus, the most highly connected individuals in a contact network have both a higher probability of spreading infection through the population and a higher rate of exposure (susceptibility) through social contacts. As an epi...
Mathematical and computational models are increasingly used in support decisions in public health, however the perception of their reliability and the criteria for their uses is contrasted among domain experts. We consider the Global Epidemic and Mobility model that generates stochastic realizations of epidemic evolution worldwide from which we can gather information such ...
We present a method for obtaining survival and coexistence results for a class of interacting particle systems. This class includes: a stochastic spatial Lotka-Volterra model of Neuhauser and Pacala, a model for the evolution of cooperation of Ohtsuki, Hauert, Lieberman and Nowak, and a continuous time version of a non-linear voter model of Molofsky, Durrett, Dushoff, Grif...
In this talk I will analyse the effects of various treatments on cotton aphids Aphis gossypii. The standard analysis of count data on cotton aphids determines parameter values by assuming a deterministic growth model and combines these with the corresponding stochastic model to make predictions on population sizes, depending on treatment. Here, we use an integrated stochas...
This will be something of an introductory talk that considers two types of spatial models used in population biology, and connections between them. Interacting particle systems can be thought of as "microscopic" level descriptions of populations, including interactions between discrete individuals and stochasticity. Reaction-diffusion equations provide determinis...
Parameter inference of ordinary differential equations from noisy data can be seen as a nonlinear regression problem, within a parametric setting. The use of a classical statistical method such as Nonlinear Least Squares (NLS) gives rise to difficult and heavy optimization problems due to the corresponding badly posed inverse problem. Gradient Matching algorithms use a smo...
Biochemical processes typically involve huge numbers of individual reversible steps, each with its own dynamical rate constants. For example, kinetic proofreading processes rely upon numerous sequential reactions in order to guarantee the precise construction of specific macromolecules. I will present a characterizati...
Evolution is the movement of populations through a space of genotypes. This space can be modeled as an undirected network connecting genotypes that can be reached through mutation. In this view, the mutational robustness of a genotype is the proportion of its mutational neighbors that are viable. Robustness can facilitate the exploration of genotype networks, or evolvabili...
When natural selection is acting at the level of the the individual phenotype, we expect selection to favor more robust phenotypes. However, selection acting at the level of the gene can undermine adaptation of the individual organism, and lead to the fixation of suboptimal traits. Genomic imprinting, the phenomenon where the pattern of expression of an allele depends on i...
Screens monitoring the effects of deletion, knock-down or over expression of regulatory genes on the expression of their target genes are critical for deciphering the organization of complex regulatory networks. However, since perturbation assays cannot distinguish direct from indirect effects, the derived networks are significantly more complex than the true underlying on...
Fruit flies are models for understanding the genetic regulation involved in specifying the complex body plans of higher animals. The head-to-tail (anterior-posterior) axis of the fly (Drosophila) is established in the first hours of development. Maternally supplied factors form concentration gradients which direct embryonic (zygotic) genes where to be activated to express ...
Making genes into gene products is subject to predictable errors, each with a phenotypic effect that depends on a normally cryptic sequence. The distribution of fitness effects of these cryptic sequences, like that of new mutations, is bimodal. For example, a cryptic sequence might be strongly deleterious if it causes protein misfolding, or it might have only a minor effec...
The problem of how often to disperse in a randomly fluctuating environment has long been investigated, primarily using patch models with uniform dispersal. Here, we consider the problem of choice of seed size for plants in a stable environment when there is a trade off between survivability and dispersal range. For this we analyze a stochastic spatial model to study the co...
Virulence evolution has a long history, including the now-classic paper of Gandon et al. 2001 on the impact of malaria vaccination on the virulence of the parasite. Gandon et al. found that a vaccine with the action of reducing the pathogen growth rate in the host selects for more virulent pathogens, while an infection-blocking vaccine selects for less virulent pathogens. ...
Continuum, partial differential equation models are often used to describe the collective motion of cell populations, with various types of motility represented by the choice of diffusion coefficient, and cell proliferation captured by the source terms. Previously, the choice of diffusion coefficient has been largely arbitrary, with the decision to choose a particular line...
Organisms reproduce in environments that vary in both time and space. Even if an individual currently resides in a region that is typically quite favorable, it may be optimal for it to "not put all its eggs in the one basket" and disperse some of its off spring to locations that are usually less favorable because the eff ect of unexpectedly poor conditions in one...
In joint work with Brett Melbourne we have studied highly replicated spatial population dynamics of flour beetles in a lab setting. I will describe the results of experiments on single species and spatial spread, and corresponding models. The models have to incorporate stochasticity of different forms to provide a good match to the data. In particular, demographic heteroge...
Postharvest diseases, especially those caused by fungi, can cause considerable damage to harvested apples in controlled atmosphere storage. Fungicides are used to control the disease, but resistance to fungicides is increasing and there is pressure by consumers and ecologists to reduce reliance on chemical controls. There is some evidence that physical conditions related t...
There is a long history of research on the mathematical modeling of animal populations, largely built on diffusion models. The classical literature, however, is inadequate to explain observed spatial patterning, or foraging and anti-predator behavior, because animals actively aggregate. This lecture will discuss models of animal aggregation, and the role of leadership in c...
Dispersal and the resulting genetic exchange between populations in spatially heterogeneous environments is typically expected to impede adaptation to local conditions. However, theory suggests some cases where this paradigm breaks down, such as when dispersal provides demographic support and gene flow enhances adaptive capacity to populations experiencing variable populat...
For the past decade, Internet worms (a type of malicious software similar to a virus) spreading through networks have been using biological strategies, such as hierarchical dispersal and adaptive strategies, to spread more efficiently among susceptible computers. There is a direct analogy between susceptible computers on the Internet and susceptible hosts in community-stru...
In the evolving voter model we choose oriented edges (x,y) at random. If the two individuals have the same opinion, nothing happens. If not, x imitates y with probability 1-Î±, and otherwise severs the connection with y and picks a new neighbor at random (i) from the graph, or (ii) from those with the same opinion as x. Despite the similarity of the rules, the...
Presentation: http://mbi.osu.edu/2011/rasmaterials/mbibayes20121_chow.pdf
Differential equations are often used to model biological and physiological systems. An important and difficult problem is how to estimate parameters and decide which model among possible models is the best. I will show in several examples how Bayesian and Markov Chain Monte Carlo approaches p...
Ed Ionides, Statistics, University of Michigan
Presentation: http://mbi.osu.edu/2011/rasmaterials/mbi12_ionides.pdf
Characteristic features of biological dynamic systems include stochasticity, nonlinearity, measurement error, unobserved variables, unknown system parameters, and even unknown system mechanisms. I will consider the resulting inferential ...
Douglas Bates, Department of Statistics, University of Wisconsin - Madison
Presentation (slides version): http://mbi.osu.edu/2011/rasmaterials/ProfilingD.pdf
Presentation (notes version): http://mbi.osu.edu/2011/rasmaterials/ProfilingN.pdf
The use of Markov-chain Monte Carlo methods for Bayesian inference has increased awareness of the need to ...
Most ecological models are constructed to understand the relationship between environmental variables and an ecological response, be it site occupancy or population abundance or changes to them. The usual regression models take into account the environmental variation in the response but in many cases, the measurement of the environmental variables themselves are made with...
Andrew Golightly, School of Mathematics & Statistics, Newcastle University
Presentation: http://mbi.osu.edu/2011/rasmaterials/AGmbi12.pdf
We consider the problem of performing Bayesian inference for the rate constants governing stochastic kinetic models. As well as considering inference for the resulting Markov jump process (MJP) we consider worki...
Dennis Prangle, Mathematics & Statistics, Lancaster University
Presentation: http://mbi.osu.edu/2011/rasmaterials/MBI_DennisPrangle.pdf
ABC is a powerful method for inference of statistical models with intractable likelihoods. Recently there has been much interest in using ABC for model choice and concerns have been raised that the results are not...
A central challenge in computational modeling of dynamic biological systems is parameter inference from experimental time course measurements. Here we present an overview of the modeling approaches based on stochastic population dynamic models and their approximations. For an application on the mesoscopic scale, we present a two dimensional continuous-time Bayesian hierarc...
Dynamic models of biochemical networks contain unknown parameters like the reaction rates and the initial concentrations of the compounds. The large number of parameters as well as their nonlinear impact on the model responses hampers the determination of confidence regions for parameter estimates. At the same time, classical approaches translating the uncertainty of the p...
Bursting is a ubiquitous phenomenon in neuroscience which involves multiple time scales (fast spikes vs. long quiescent intervals). Parameter estimation for bursting models is difficult due to these multiple scales. I will describe an approach to parameter estimation for these models which utilizes the geometry underlying bursting. This is joint work with John Guckenheimer...
In the talk we present a simple extension of the configuration model to weighted networks, and state some asymptotic properties of the network model. The weights may be used for some stochastic process taking place on the network; for example an epidemic where the probability of transmission between two individuals depends on the weight of the connected edge (the weight fo...
We consider a SIR epidemic model propagating on a random network generated by a configuration model, where the degree distribution of the vertices is given and where the edges are randomly matched. The evolution of the epidemics is summed up into three measure-valued equations that describe the degrees of the susceptible individuals and the number of edges from an infectio...
Parasite evolution is increasingly being recognized as one of the most important challenges in applied evolutionary biology. Understanding how parasites maximize fitness whilst facing the diverse challenges of living in cells, hosts, and vectors, is central to disease control and offers a novel testing ground for evolutionary theory. Along with Sam Brown, I recently hosted...
Tuberculosis is one of the major global diseases in terms of both prevalance and mortality. In recent decades, strains of the disease have evolved that are resistant to several, or all, of the drugs used to treat the disease. Drug resistance is conferred by rare mutations, raising the question of how multiple mutations might have arisen in a single strain. Motivated by thi...
The basic reproduction number R0 is one of the most important quantities in epidemiology. However, for epidemic models with explicit social structure involving small mixing units such as households, its definition is not straightforward and a wealth of other threshold parameters has appeared in the literature. In this talk I use branching processes to define R0, apply this...
Multi-drug resistant pathogens such as MRSA and VRE give rise to substantial morbidity and mortality, and impose a huge economic burden on healthcare systems. In this talk we describe a framework for analysing patient-level data from hosptials on such pathogens, employing stochastic transmission models and using Markov chain Monte Carlo methods witin a Bayesian statistical...
HIV has been introduced in Cuban in 1986. From the beginning of the epidemics, contact-tracing is used, in the purpose of detecting more HIV-positive individuals and of controlling the spread of the disease. The data generated from this contact-tracing program provide some partial information on the social networks underlying the propagation of HIV. In this talk, we presen...
We consider an stochastic, individual-based model of an evolving population with logistic density-dependence, where individuals are characterized by a quantitative phenotypic trait. Under appropriate parameters scalings of rare mutations and large populations, we obtain a stochastic jump process on the mutation time-scale, where evolution proceeds through successive invasi...
Our understanding of the ecological and evolutionary conditions that permit the establishment and persistence of different bacterial species in host-associated microbial communities is incomplete. Recent work done to characterize human vaginal bacterial communities by experimental and analytical approaches has shown that idiosyncratic changes in species composition and wid...