Anastasios Matzavinos

Nucleation-dependent Tau Filament Formation THE IMPORTANCE OF DIMERIZATION AND AN ESTIMATION OF ELEMENTARY RATE CONSTANTS

Filamentous inclusions composed of the microtubule-associated protein tau are found in Alzheimer disease and other tauopathic neurodegenerative diseases, but the mechanisms underlying their formation from full-length protein monomer under physiological conditions are unclear. To address this issue, the fibrillization of recombinant full-length four-repeat human tau was examined in vitro as a function of time and submicromolar tau concentrations using electron microscopy assay methods and a small-molecule inducer of aggregation, thiazine red. Data were then fit to a simple homogeneous nucleation model with rate constant constraints established from filament dissociation rate, critical concentration, and mass-per-unit length measurements. The model was then tested by comparing the predicted time-dependent evolution of length distributions to experimental data. Results indicated that once assembly-competent conformations were attained, the rate-limiting step in the fibrillization pathway was tau dimer formation. Filament elongation then proceeded by addition of tau monomers to nascent filament ends. Filaments isolated at reaction plateau contained ∼2 tau protomers/β-strand spacing on the basis of mass-per-unit length measurements. The model suggests four key steps in the aggregation pathway that must be surmounted for tau filaments to form in disease.

Mitochondrial fission in endothelial cells after simulated ischemia/reperfusion: role of nitric oxide and reactive oxygen species.

Ischemia (I)/reperfusion (RP)-induced endothelial cell (EC) injury is thought to be due to mitochondrial reactive oxygen species (mtROS) production. MtROS have been implicated in mitochondrial fission. We determined whether cultured EC exposure to simulated I/RP causes morphological changes in the mitochondrial network and the mechanisms behind those changes. Because shear stress results in nitric oxide (NO)-mediated endothelial mtROS generation, we simulated I/RP as hypoxia (H) followed by oxygenated flow over the ECs (shear stress of 10dyn/cm(2)). By exposing ECs to shear stress, H, H/reoxygenation (RO), or simulated I/RP and employing MitoTracker staining, we assessed the differential effects of changes in mechanical forces and/or O(2) levels on the mitochondrial network. Static or sheared ECs maintained their mitochondrial network. H- or H/RO-exposed ECs underwent changes, but mitochondrial fission was significantly less compared to that in ECs exposed to I/RP. I/RP-induced fission was partially inhibited by antioxidants, a NO synthase inhibitor, or an inhibitor of the fission protein dynamin-related protein 1 (Drp1) and was accompanied by Drp1 oligomerization and phosphorylation (Ser616). Hence, shear-induced NO, ROS (including mtROS), and Drp1 activation are responsible for mitochondrial fission in I/RP-exposed ECs, and excessive fission may be an underlying cause of EC dysfunction in postischemic hearts.

On Immunotherapies and Cancer Vaccination Protocols: A Mathematical Modelling Approach

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

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

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

Mitochondrial Dynamics and Motility Inside Living Vascular Endothelial Cells: Role of Bioenergetics

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

Fractional Adams-Bashforth/Moulton methods

We first formulate a fractional class of explicit Adams-Bashforth (A-B) and implicit Adams-Moulton (A-M) methods of first- and second-order accuracy for the time-integration of D t ? 0 C u ( x , t ) = g ( t ; u ) , ? ? ( 0 , 1 , where D t ? 0 C denotes the fractional derivative in the Caputo sense. In this fractional setting and in contrast to the standard Adams methods, an extra history load term emerges and the associated weight coefficients are ?-dependent. However when ? = 1 , the developed schemes reduce to the well-known A-B and A-M methods with standard coefficients. Hence, in terms of scientific computing, our approach constitutes a minimal modification of the existing Adams libraries. Next, we develop an implicit-explicit (IMEX) splitting scheme for linear and nonlinear fractional PDEs of a general advection-reaction-diffusion type, and we apply our scheme to the time-space fractional Keller-Segel chemotaxis system. In this context, we evaluate the nonlinear advection term explicitly, employing the fractional A-B method in the prediction step, and we treat the corresponding diffusion term implicitly in the correction step using the fractional A-M scheme. Moreover, we perform the corresponding spatial discretization by employing an efficient and spectrally-accurate fractional spectral collocation method. Our numerical experiments exhibit the efficiency of the proposed IMEX scheme in solving nonlinear fractional PDEs.

Mathematical Modelling of Spatio-temporal Phenomena in Tumour Immunology

Cancer still remains one of the most difficult diseases to treat clinically and is one of the main causes of mortality in developed western societies. The mortality statistics for the United Kingdom for the year 2002 show that 155,180 people were registered as dying from a malignant neoplasm.1 This figure represents 26% of all causes of death in the UK for 2002. Similar statistics hold for the United States as can be seen in Fig. 1, which shows the main causes of death in the USA during the two years 1975 and 2001.

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

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

Modeling oxygen transport in surgical tissue transfer

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

Random walk distances in data clustering and applications

In this paper, we develop a family of data clustering algorithms that combine the strengths of existing spectral approaches to clustering with various desirable properties of fuzzy methods. In particular, we show that the developed method “Fuzzy-RW,” outperforms other frequently used algorithms in data sets with different geometries. As applications, we discuss data clustering of biological and face recognition benchmarks such as the IRIS and YALE face data sets.