public 01:34:52

Punit Gandhi : Conceptual modeling of dryland vegetation patterns across timescales

  -   Mathematical Biology ( 17 Views )

Strikingly regular, large-scale patterns of vegetation growth were first documented by aerial photography in the Horn of Africa circa 1950 and are now known to exist in drylands across the globe. The patterns often appear on very gently sloped terrain as bands of dense vegetation alternating with bare soil, and models suggest that they may be a strategy for maximizing usage of the limited water available. A particular challenge for modeling these patterns is appropriately resolving fast processes such as surface water flow during rainstorms while still being able to capture slow dynamics such as the uphill migration of the vegetation bands, which has been observed to occur on the scale of a band width per century. We propose a pulsed-precipitation model that treats rainstorms as instantaneous kicks to the soil water as it interacts with vegetation on the timescale of plant growth. We use a stochastic rainfall model with the influence of fast storm-level hydrology captured by the spatial distribution of the soil water kicks. The model allows for predictions about the influence of storm characteristics on the large-scale patterns. Analysis and simulations suggest that the distance water travels on the surface before infiltrating into the soil during a typical storm plays a key role in determining the spacing between the bands.

public 01:14:53

Stephan Huckemann : Statistical challenges in shape prediction of biomolecules

  -   Mathematical Biology ( 130 Views )

The three-dimensional higher-order structure of biomolecules determines their functionality. While assessing primary structure is fairly easily accessible, reconstruction of higher order structure is costly. It often requires elaborate correction of atomic clashes, frequently not fully successful. Using RNA data, we describe a purely statistical method, learning error correction, drawing power from a two-scale approach. Our microscopic scale describes single suites by dihedral angles of individual atom bonds; here, addressing the challenge of torus principal component analysis (PCA) leads to a fundamentally new approach to PCA building on principal nested spheres by Jung et al. (2012). Based on an observed relationship with a mesoscopic scale, landmarks describing several suites, we use Fréchet means for angular shape and size-and-shape, correcting within-suite-backbone-to-backbone clashes. We validate this method by comparison to reconstructions obtained from simulations approximating biophysical chemistry and illustrate its power by the RNA example of SARS-CoV-2.

This is joint work with Benjamin Eltzner, Kanti V. Mardia and Henrik Wiechers.


Eltzner, B., Huckemann, S. F., Mardia, K. V. (2018): Torus principal component analysis with applications to RNA structure. Ann. Appl. Statist. 12(2), 1332?1359.

Jung, S., Dryden, I. L., Marron, J. S. (2012): Analysis of principal nested spheres. Biometrika, 99 (3), 551-568

Mardia, K. V., Wiechers, H., Eltzner, B., Huckemann, S. F. (2022). Principal component analysis and clustering on manifolds. Journal of Multivariate Analysis, 188, 104862, https://www.sciencedirect.com/science/article/pii/S0047259X21001408

Wiechers, H., Eltzner, B., Mardia, K. V., Huckemann, S. F. (2021). Learning torus PCA based classification for multiscale RNA backbone structure correction with application to SARS-CoV-2. To appear in the Journal of the Royal Statistical Society, Series C, bioRxiv https://doi.org/10.1101/2021.08.06.455406

public 01:34:56

Casey Diekman : Data Assimilation and Dynamical Systems Analysis of Circadian Rhythmicity and Entrainment

  -   Mathematical Biology ( 80 Views )

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.

public 01:34:42

Johannes Reiter : Minimal intratumoral heterogeneity in untreated cancers

  -   Mathematical Biology ( 191 Views )

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.

public 01:34:59

Andrew Brouwer : Harnessing environmental surveillance: mathematical modeling in the fight against polio

  -   Mathematical Biology ( 190 Views )

Israel experienced an outbreak of wild poliovirus type 1 (WPV1) in 2013-14, detected through environmental surveillance of the sewage system. No cases of acute flaccid paralysis were reported, and the epidemic subsided after a bivalent oral polio vaccination (bOPV) campaign. As we approach global eradication, polio will increasingly be detected only through environmental surveillance. However, we have lacked the theory to translate environmental surveillance into public health metrics; it is a priori unclear how much environmental surveillance can even say about population-level disease dynamics. We developed a framework to convert quantitative polymerase chain reaction (qPCR) cycle threshold data into scaled WPV1 and OPV1 concentrations for inference within a deterministic, compartmental infectious disease transmission model. We used differential algebra and profile likelihood techniques to perform identifiability analysis, that is, to assess how much information exists in the data for the model, and to quantify inference uncertainty. From the environmental surveillance data, we estimated the epidemic curve and transmission dynamics, determining that the outbreak likely happened much faster than previously thought. Our mathematical modeling approach brings public health relevance to environmental data that, if systematically collected, can guide eradication efforts.