The jellyfish has been the subject of numerous mathematical and physical studies ranging from the discovery of reentry phenomenon in electrophysiology to the development of axisymmetric methods for solving fluid-structure interaction problems. In this presentation, we develop and test mathematical models describing the pulsing dynamics and the resulting fluid flow generated by the upside down jellyfish, Cassiopea. The kinematics of contraction and distributions of pulse frequencies were obtained from videos and used as inputs into numerical simulations. Particle image velocimetry was used to obtain spatially and temporally resolved flow fields experimentally. The immersed boundary method was then used to solve the fluid-structure interaction problem and explore how changes in morphology and pulsing dynamics alter the resulting fluid flow. Unlike pelagic (swimming) jellyfish, there is no evidence of the formation of a train of vortex rings. Instead, significant mixing occurs around and directly above the oral arms and secondary mouths. We found good agreement between the numerical simulations and experiments, suggesting that the presence of porous oral arms induce net horizontal flow towards the bell and mixing.

Genetic intratumoral heterogeneity is a natural consequence of imperfect DNA replication. Any two randomly selected cells, whether normal or cancerous, are therefore genetically different. I will discuss the extent of genetic heterogeneity within untreated cancers with particular regard to its clinical relevance. While genomic heterogeneity within primary tumors is associated with relapse, heterogeneity among treatment‑naïve metastases has not been comprehensively assessed. We analyzed sequencing data for 76 untreated metastases from 20 patients and inferred cancer phylogenies for breast, colorectal, endometrial, gastric, lung, melanoma, pancreatic, and prostate cancers. We found that within individual patients a large majority of driver gene mutations are common to all metastases. Further analysis revealed that the driver gene mutations that were not shared by all metastases are unlikely to have functional consequences. A mathematical model of tumor evolution and metastasis formation provides an explanation for the observed driver gene homogeneity. Last, we found that individual metastatic lesions responded concordantly to targeted therapies in 91% of 44 patients. These data indicate that the cells within the primary tumors that gave rise to metastases are genetically homogeneous with respect to functional driver gene mutations and suggest that future efforts to develop combination therapies have the capacity to be curative.

It is well-known that genomes encode ancestry through replication errors - on average the greater the numbers of differences between two genomes, the greater the time since they shared a common ancestor ("molecular clock hypothesis"). This approach is commonly used to infer ancestries of species and populations, and these same tools can be applied to somatic cell evolution, in particular to better infer ancestries of normal and neoplastic tissues. For example, by sampling from opposite sides of the same human colorectal tumor, one can coalesce back to the earliest tumor cells. Such studies reveal that many human colorectal tumors are simple single "Big Bang" expansions, with evidence of neutral evolution during growth. It may be possible to understand in detail what is impossible to directly observe - the first few divisions of human tumors.

We report the results of our integrated experimental and theoretical investigations of biological systems dominated by interfacial effects. Particular attention is given to elucidating natural strategies for water-repellency, walking on water, underwater breathing, and drinking.

It is common to use a multitype branching process to model the accumulation of mutations that leads to cancer progression, metastasis, and resistance to treatment. In this talk I will describe results about the time until the first type k (cell with k mutations) and the growth of the type k population obtained in joint work with Stephen Moseley, and their use in evaluating possible screening strategies for ovarian cancer, work in progress with Duke undergraduate Kaveh Danesh. The point process representation of the limit, which is a one-sided stable law, together with results from 10-60 years ago leads to remarkable explicit formulas for Simpson's index and the size of the largest clone. These results are important in understanding tumor diversity which can present serious obstacles to treatment. The last topic is joint work with Jasmine Foo, Kevin Leder, John Mayberry, and Franziska Michor

Stimulus tuning in a reduced model for neural competition leads to mixed-mode oscillations (MMOs), a temporal pattern featuring alternating small- and large-amplitude oscillations. Key ingredients for the generation of MMOs are mutual inhibition, slow negative-feedback in the form of adaptation, and nonlinearity of the gain function. Exploiting a normal form calculation, we show that MMOs occur due to the interaction of canard and singular Hopf mechanisms as the stimulus strength approaches a critical regime. We show then that local excitation and lateral inhibition-type coupling combined with the underlying MMOs produces complex spatio-temporal patterns in larger networks.

Ductal carcinoma in situ (DCIS) is an early stage non-invasive breast cancer that originates in the epithelial lining of the milk ducts, but it can evolve into comedo DCIS and ultimately, into the most common type of breast cancer, invasive ductal carcinoma. Understanding the progression and how to effectively intervene in it presents a major scientific challenge. The extracellular matrix surrounding a duct contains several types of cells and several types of growth factors that are known to individually affect tumor growth, but at present the complex biochemical and mechanical interactions of these stromal cells and growth factors with tumor cells is poorly understood. We will discuss a mathematical model that incorporates the cross-talk between stromal and tumor cells, and which can predict how perturbations of the local biochemical and mechanical state influence tumor evolution. We focus on the EGF and TGF-$\beta$ signaling pathways and show how up- or down-regulation of components in these pathways affects cell growth and proliferation, and describe a hybrid model for the interaction of cells with the tumor microenvironment. The analysis sheds light on the interactions between growth factors, mechanical properties of the ECM, and feedback signaling loops between stromal and tumor cells, and suggests how epigenetic changes in transformed cells affect tumor progression.

Viscoelastic interactions of Myxococcus xanthus cells in a low-density domain close to the edge of a swarm have been recently studied in [1] using a combination of a cell-based three-dimensional Subcellular Element (SCE) model [1,2] and cell-tracking experiments. The model takes into account the flexible nature of M. xanthus as well as the effects of adhesion between cells arising from the interaction of the capsular polysaccharide covering two cells in contact with each other. New image and dynamic cell curvature analysis algorithms were used to track and measure the change in cell shapes that occur as flexible cells undergo significant bending during collisions resulting in direct calibration of the model parameters. It will be shown in this talk that flexibility of cells and the adhesive cell–cell and cell–substrate interactions of M. xanthus together with cell to aspect-ratio and directional reversals [3], play an important role in smooth cell gliding and more efficient swarming. In the second part of the talk results of the analysis of the three dimensional structures of fibrin networks, with and without cells, reconstructed from two-dimensional z-stacks of confocal microscopy sections using novel image analysis algorithms, will be presented. These images were used to establish microstructure-based models for studying the relationship between the structural features and the mechanical properties of the fibrin networks in blood clots. The change in the fibrin network alignment under applied strain and the elastic modulus values will be shown to agree well with the experimental data [4]. 1. C.W. Harvey, F. Morcos, C.R. Sweet, D. Kaiser, S. Chatterjee, X. Lu, D. Chen and M. Alber [2011], Study of elastic collisions of M. xanthus in swarms, Physical Biology 8, 026016. 2. C.R. Sweet, S. Chatterjee, Z. Xu, K. Bisordi, E.D. Rosen and M. Alber [2011], Modeling Platelet-Blood Flow Interaction Using Subcellular Element Langevin Method, J R Soc Interface, 2011 May 18. [Epub ahead of print], doi: 10.1098/rsif.2011.0180. 3. Y. Wu, Y. Jiang, D. Kaiser and M. Alber [2009], Periodic reversal of direction allows Myxobacteria to swarm, Proc. Natl. Acad. Sci. USA 106 4 1222-1227. 4. E. Kim, O.V. Kim, K.R. Machlus, X. Liu, T. Kupaev, J. Lioi, A.S. Wolberg, D.Z. Chen, E.D. Rosen, Z. Xu and M. Alber [2011], Soft Matter 7, 4983-4992.

The ability of animals to self-organize into remarkable patterns of movement is seen throughout nature from herds of large mammals, to flocks of birds, schools of fish, and swarms of insects. Remarkably, patterns of collective movement can be seen even in the simplest forms of life such as bacteria. M. xanthus are common soil bacteria that are among the most “social" bacteria in nature. In this talk clustering mechanism of swarming M. xanthus will be described using combination of experimental movies and stochastic model simulations. Continuous limits of discrete stochastic dynamical systems simulating cell aggregation will be described in the form of reaction-diffusion and nonlinear diffusion equations. Surface motility such as swarming is thought to precede biofilm formation during infection. Population of bacteria P. aeruginosa, major infection in hospitals, will be shown to efficiently propagate as high density waves that move symmetrically as rings within swarms towards the extending tendrils. Multi-scale model simulations suggest a mechanism of wave propagation as well as branched tendril formation at the edge of the population that depend upon competition between the changing viscosity of the bacterial liquid suspension and the liquid film boundary expansion caused by Marangoni forces. This collective mechanism of cell- cell coordination was recently shown to moderate swarming direction of individual bacteria to avoid a toxic environment. In the last part of the talk a three-dimensional multiscale modeling approach will be described for studying fluid–viscoelastic cell interaction during blood clot formation.

In this talk, I will discuss a new result in fluid flows through channels with permeable membranes with simple pumping dynamics. Fluid will be exchanged and metabolized in a simple reservoir and I will demonstrate the existence of optimal reservoir properties that may either maximize or minimized the amount of fluid being extracted across the channel walls. The biological relevance of this work may be seen by noting that all living organisms of a sufficient size rely on complex systems of tubular networks to efficiently collect, transport and distribute nutrients or waste. These networks exchange material with the interstitium via embedded channels leading to effective permeabilities across the wall separating the channel interior from the interstitium. In many invertebrates, for example, respiratory systems are made of complex tracheal systems that branch out through the entire body allowing for passive exchange of oxygen and carbon dioxide. In many of these systems, certain animals utilize various pumping mechanisms that alter the flow of the air or fluid being transported. Although the net effect of pumping of the averaged rates of fluid flow through the channel is typically well understood, it is still a largely open problem to understand how, and in what circumstances, pumping enables and enhances the exchange of material across channel walls. It has been demonstrated experimentally, for example, that when certain insects flap their wings, compression of the trachea allow for more efficient oxygen extraction, however it is unclear if this pumping is optimized for flight, oxygen uptake or neither, and understanding this problem quantitatively will shed insight on this biological process. Many of these interesting scenarios occur at low Reynolds number and this regime will be the focus of the presentation.

Circadian rhythms are biological oscillations that align our physiology and behavior with the 24-hour environmental cycles conferred by the Earth’s rotation. In this talk, I will discuss two projects that focus on circadian clock cells in the brain and the entrainment of circadian rhythms to the light-dark cycle. Most of what we know about the electrical activity of circadian clock neurons comes from studies of nocturnal (night-active) rodents, hindering the translation of this knowledge to diurnal (day-active) humans. In the first part of the talk, we use data assimilation and patch-clamp recordings from the diurnal rodent Rhabdomys pumilio to build the first mathematical models of the electrophysiology of circadian neurons in a day-active species. We find that the electrical activity of circadian neurons is similar overall between nocturnal and diurnal rodents but that there are some interesting differences in their responses to inhibition. In the second part of the talk, we use tools from dynamical systems theory to study the reentrainment of a model of the human circadian pacemaker following perturbations that simulate jet lag. We show that the reentrainment dynamics are organized by invariant manifolds of fixed points of a 24-hour stroboscopic map and use these manifolds to explain a rapid reentrainment phenomenon that occurs under certain jet lag scenarios.

Persistent homology measures geometric structures using topological invariants. When the structures are magnetic resonance images of branching arteries, for example, persistent homology records the connectedness of an increasing subset of the vessels. Although the theory of persistent homology is relatively well developed, and many aspects of its behavior are understood in synthetic examples, only recently have applications to genuine experimental data begun. This talk explains what we have learned about the geometry of blood vessels in aging human brains, as well as lessons this exploration has taught us about applications of persistent homology in general. These lessons inform further potential applications of persistent homology in statistical problems from biological and medical imaging. The main results are joint with Paul Bendich, Steve Marron, Aaron Pieloch, and Sean Skwerer (Math junior faculty, Stat faculty, Math undergrad, and Operations Research grad student). The talk will be accessible to advanced mathematics and statistics undergraduates, medical and biological researchers, statistics and mathematics faculty, and everybody in between.

In the first part of the talk we present a review of our work on PDE models of swimming bacteria. First we introduce a stochastic PDE model for a dilute suspension of self-propelled bacteria and obtain an explicit asymptotic formula for the effective viscosity (E.V.) that explains the mechanisms of the drastic reduction of E.V.. Next, we introduce a model for semi-dilute suspensions with pairwise interactions and excluded volume constraints. We compute E.V. analytically (based on a kinetic theory approach) and numerically. Comparison with the dilute case leads to a phenomenon of stochasticity arising from a deterministic system. We develop a ODE/PDE model that captures the phase transition, an appearance of correlations and large scale structures due to interbacterial interactions. Collaborators: S. Ryan, B. Haines, (PSU students); I. Aronson, A. Sokolov, D. Karpeev (Argonne); In the second part of the talk we discuss a system of two parabolic PDEs arising in modeling of motility of eukaryotic cells on substrates. The two key properties of this system are (i) presence of gradients in the coupling terms (gradient coupling) and (ii) mass (volume) preservation constraints. We derive the equation of the motion of the cell boundary, which is the mean curvature motion perturbed by a novel nonlinear term and prove that the sharp interface property of initial conditions is preserved in time. This novel term leads to surprising features of the motion of the interface such as discontinuities of the interface velocity and hysteresis. This is joint work with V. Rybalko and M. Potomkin.

Biological oscillators such as the cell cycle, circadian clocks, and metabolic rhythms are ubiquitous across the domains of life. These biochemical oscillators co-exist in the same cells, often sharing and competing for resources. Are there mechanisms and regulatory principles that ensure harmony between these oscillators? Recent studies have shown that in addition to the transcriptional circadian clock, many organisms (including Arabidopsis) have a circadian redox rhythm driven by the organism's metabolic activities. It has been hypothesized that the redox rhythm is linked to the circadian clock, but the mechanism and the biological significance of this link have only begun to be investigated. In the first half of my talk, I will describe our work (in collaboration with the Dong lab at Duke) on the coupling of redox rhythms and the plant circadian clock. In the second half of my talk, I will discuss our work on the coupling of yeast metabolic cycle and the cell division cycle.

In butterflies and moths, wing scales provide the cellular basis for coloration. Many times these scales are filled with pigments providing colors such as black, brown, red, and yellow. In some cases, however, color is generated structurally, which is often the case for green and blue coloration. Optical physicists have done a remarkable job defining how wing nanostructures create structural color, but we know little about the developmental basis for creating the patterned nanostructures. I will describe our work to understand the developmental and cellular basis for scale formation and the generation of structural color, focusing on a group of butterflies known as the Achillides swallowtails. The scales of these butterflies use a combination of multilayer reflection and scale geometry to create a range of colors. Developmentally, the scale geometry appears to be controlled by cytoskeletal reorganization, and evolutionary changes in geometry appear to contribute to variation between species, between populations, and between seasonal variants.

Parkinson’s disease has been traditionally thought of as a dopaminergic (DA) disease in which cells of the substantia nigra pars compacta (SNc) die. However, accumulating evidence implies an important role for the serotonergic (5HT) system in Parkinson’s disease. We use a mathematical model to investigate the consequences of levodopa therapy on the serotonergic system and on the pulsatile release of DA from dopaminergic and serotonergic terminals in the striatum. We compute the time course of DA release in the striatum from both 5HT and DA neurons and show how the time course changes as more and more SNc cells die. This enables us to explain the shortening of the therapeutic time window for the efficacy of levodopa as Parkinson’s disease progresses. Finally, we study the effects 5HT1a and 5HT1b autoreceptor agonists and explain why they have a synergistic effect and why they lengthen the therapeutic time window for LD therapy. Our results are consistent with and help explain results in the experimental literature and provide new predictions that can be tested experimentally.

Eukaryotic cell microenvironment (inner and outer) is composed in large parts from fluids that interact with solid and elastic bodies, whereas it is the cell cytoplasm, cytoskeleton and basal membrane; the interstitial fluid interpenetrating the stroma and tumor cells; or blood flow carrying the immune or circulating tumor cells. I will discuss the use of two fluid-structure interactions methods, the immersed boundary and the regularized Stokeslets, in applications dealing with the tumor development and treatment. First model operates on the cellular scale and will be used to model various cell processes, such as cell growth, division or death, during the cellular self-organization into a normal mammary acinus, a 3D in vitro structure recapitulating the morphology of breast cysts (acini). I will discuss model development, parameterization and tuning with the experimental data, as well as their subsequent use to investigate the link between morphogenesis of epithelial mutants and molecular alterations of tumor cells. Second model acts on the tissue level, and will be used to investigate the relation between tumor tissue structure and efficacy of anticancer drugs in the context of interstitial fluid flow. I will present simulation results showing non-linear relation between tumor tissue structure and effectiveness of drug penetration. I will also discuss how tumor tissue metabolic state(its oxygenation and acidity) becomes modified due to actions of chemotherapeutic drugs leading to the emergence of tumor zones with potentially drug-resistant cells and/or to tumor areas that are not exposed to drugs at all. Both of these phenomena can contribute to the moderateclinical success of many anticancer drugs.

Biological projectiles range from a 10-micrometer spore to a 1-meter leaping mammal. Pre-launch accelerations scale inversely with length, with that of the smallest projectile approaching a million times gravity. These projectiles follow Borelli's rule, that all jumpers should jump to the same height. Nonetheless, his rationale is wrong on at least two accounts. For one thing, it presumes a muscular engine operating with no energy storage, often far from the case. For another, it ignores drag, critical for small projectiles, which operate in an overwhelmingly drag-dominated rather than gravity- dominated domain and whose optimal trajectories look decidedly unfamiliar. But the rule can be given quite a different—and more general—basis. And a simple dimensionless index helps us anticipate best launch angles and path lengths, these latter illustrated with a simple computer simulation.

Certain strains of the influenza virus form coherent single, globally circulating viral populations. Multiple models of viral evolution have considered the virus on this level, identifying immune and structural factors underlying the observed changes in viral genotype. In this talk, I outline an alternative approach for studying viral evolution, considering events at the level of within-host viral growth and transmission. In particular, I describe statistical approaches to infer the extent to which natural selection acts upon the viral population within the course of a single infection, on the basis of genome sequencing data from Sanger sequencing, and next-generation technologies. Examining data from evolutionary experiments conducted with a reassortant H5N1 influenza virus, I discuss the potential for using data from evolutionary experiments to predict the potential evolution of this virus in a human population.

In a 2009 paper Yu, Etheridge and Cuthbertson proposed a model that was intended to address two questions. The first was a question related to Muller's ratchet, "What ratio of mutations must be beneficial for the meanfitness of a population to increase in time?" The second question was related to the Hill-Robertson effect, "If many beneficial mutations are introduced into a population, how much will competition slow the rate of adaptation?" They introduced a model of an asexually reproducing population of fixed size N and mutation rate mu and conjectured that the rate of adaptation is O(logN/(log logN)^2) for large N so long as there is some positive ratio of beneficial mutations. I will present an outline of my proof of this conjecture.

A ureteric stent is a slender polymer tube that can be placed within the ureter (the muscular tube that conveys urine from the kidney to the bladder) to relieve a blockage due, for example, to a kidney stone in transit, or to external pressure from a tumor. A urinary catheter can be placed similarly within the urethra (the muscular tube conveying urine from the bladder out of the body), either again to relieve a blockage, or to allow control of urination in incontinent patients or those recovering from surgery. Several clinical complications are associated with each of these biomedical devices. Both become encrusted, over time, with salts that precipitate out from the urine. Such encrustation is often associated with infection and the presence of bacterial biofilm on the device and, if severe, can make removal of the device difficult and painful. Ureteric stents are also associated with urinary reflux: retrograde flow of urine back towards the kidney. This arises because the stent prevents proper function of the sphincter between ureter and bladder that normally closes off when bladder pressure rises. Such reflux can expose the kidney to dangerously high pressures, and increase the risk of renal infection, both of which can lead to long-term damage. This talk will highlight aspects of our interdisciplinary work on such problems. We present mathematical models of the reflux and encrustation processes and consider the implications for device design and clinical practice.

RNA-Seq is a new technology for measuring the content of a transcriptome using high-throughput sequencing technology. I will provide a self-contained introduction to the technology, and proceed to discuss some interesting mathematical questions we have had to address in order to realize the potential of "comparative transcriptomics" for comparing and contrasting transcriptomes. We will start with the "freshman's dream", and proceed to examine issues related to maximum matching, the (phylogenetic) space of trees and Simpson's paradox. This is joint work with my current and former students Natth Bejraburnin, Nicolas Bray, Adam Roberts, Cole Trapnell and Meromit Singer.

Glutathione (GSH), a tripeptide formed from glutamate, cysteine, and
glycine, is arguably the most important antioxidant in the body. NAPQI, a
byproduct of acetaminophen (APAP) metabolism which is toxic to liver
cells, is neutralized by GSH. Although produced in great quantity by the
liver, in cases of APAP overdose demand for GSH can outstrip supply,
causing liver failure. Currently, patients presenting to the ER with APAP
overdose are given an infusion of cysteine since it is believed to be the
rate-limiting amino acid in GSH synthesis, however, there is evidence that
under some circumstances glutamate can become rate-limiting. Complicating
the issue is that in most hepatocytes, glutamate is not absorbable from
blood plasma but is formed from glutamine, which is produced in large
amounts by the skeletal muscle. In order to develop better rescue
protocols for APAP overdose, we have developed a mathematical model of
glutamate and glutamine metabolism in the rat. We have also investigated
how model parameters should change in the case of increased cortisol
production, such as occurs during sepsis, trauma, burns, and other
pathological states; the cortisol-stressed state has been studied in rats
by giving them dexamethasone. We compare model predictions with
experimental data for the normal, healthy rat and dexamethasone-stressed
rat. Biological parameters are taken from the literature wherever possible.

Heterogeneity in cancer is an observed fact, both genotypically and phenotypically. Cell-cell variation is seen in almost all aspects of cancer from early development all the way through to invasion and subsequent metastasis. Our current understanding of this heterogeneity has mainly focused at the genetic scale with little information on how this variation translates to actual changes in cell phenotypic behavior. Given that many genotypes can lead to the same cellular phenotype, it is important that we quantify the range and scope of this heterogeneity at the phenotypic scale as ultimately this variability will dictate the aggressiveness of the tumor and its treatability. Central to our understanding of this heterogeneity is how the tumor cells interact with each other and with their microenvironment. Since it is these very interactions that drive selection and that ultimately define the ecology of the tissue in which the tumor is developing. Considering an organ as an ecological system, means that we should view normal tissue homeostasis as an equilibrium that cancer cells must disrupt if they are to be successful. Disruption of this equilibrium is often one of the first events in cancer development, as the normal control mechanisms of the tissue are damaged or ignored. We will discuss the interplay between homeostasis, heterogeneity, evolution and ecology in cancer progression and treatment failure with an emphasis on the metabolism of breast cancer.

Certain neurons can, in isolation, generate a bursting rhythm, in which phases of active spiking alternative repetitively with phases of quiescence. This behavior is itself mathematically interesting, and neurons with this capability have been found in the mammalian respiratory brain stem, suggesting that they might drive the respiratory rhythm. In this talk, I will survey some mathematical and computational work that runs counter to this suggestion. The methods involved include slow-fast decomposition and associated bifurcation analysis in single-neuron and few-neuron ODE models as well as a genetic algorithm applied to larger network models. The larger network results may have general implications for networks of nodes with heterogeneous dynamics, coupled in small-world, scale-free, and other architectures

Stochastic modeling and analysis can help answer pressing medical questions. In this talk, I will attempt to justify this claim by describing recent work on two problems in medicine. The first problem concerns ovarian tissue cryopreservation, which is a proven tool to preserve ovarian follicles prior to gonadotoxic treatments. Can this procedure be applied to healthy women to delay or eliminate menopause? How can it be optimized? The second problem concerns medication nonadherence. What should you do if you miss a dose of medication? How can physicians design dosing regimens that are robust to missed/late doses? I will describe (a) how stochastics theory offers insights into these questions and (b) the mathematical questions that emerge from this investigation. The first problem is based on joint work with Joshua Johnson (University of Colorado School of Medicine), John Emerson (Yale University), and Kutluk Oktay (Yale School of Medicine).

This talk provides some fundamentals of statistical techniques for data on non-Euclidean spaces. Such data occur in the analysis of shape of geometrical objects, e.g. in applications studying biological growth. Naturally, shape is modeled on a manifold quotient (e.g. unit size objects) under a Lie group action (e.g. translations and rotations) which can be given a manifold structure, possibly with singularities. We show how this scenario allows for one and two sample tests as well as principal component analysis.

Inside every eukaryotic cell is the nucleus, organelles, and the surrounding cytoplasm, which typically accounts for 50% of the cell volume. The cytoplasm is a complex mixture of water, protein, and a dynamic polymer network. Cells use cytoplasmic streaming to transmit chemical signals, to distribute nutrients, and to generate forces involved in locomotion. In this talk we present two different models related to cytoplasmic streaming in amoeboid cells. In the first part of the talk, we present a computational model to describe the dynamics of blebbing, which occurs when the cytoskeleton detaches from the cell membrane, resulting in the pressure-driven flow of cytosol towards the area of detachment and the local expansion of the cell membrane. The model is used to explore the relative roles in bleb dynamics of cytoplasmic viscosity, permeability of the cytoskeleton, and elasticity of the membrane and cytoskeleton. In the second part of the talk we examine how flow-induced instabilities of cytoplasm are related to the structural organization of the giant amoeboid cell Physarum polycephalum. We use a multiphase flow model that treats both the cytosol and cytoskeleton as fluids each with its own material properties and internal forces, and we discuss instabilities of the sol/gel mixture that produce flow channels within the gel. We analyze a reduced model and offer a new and general explanation for how fluid flow is involved in cytoskeletal reorganization.