Mathematical models in biology

Aerotaxis is the particular form of chemotaxis in which oxygen plays the role of both the attractant and the repellent. Aerotaxis occurs without methylation adaptation, and it leads to fast and complete aggregation toward the most favorable oxygen concentration. Biochemical pathways of aerotaxis remain largely elusive, however, aerotactic pattern formation is well documented. This allows mathematical modeling to test plausible hypotheses about the biochemical mechanisms. Our model demonstrates that assuming fast, non-methylation adaptation produces theoretical results that are consistent with experimental observations. We obtain analytical estimates for parameter values that are difficult to obtain experimentally. Chemotaxis in growth cones differs from gradient sensing in other animal cells, because growth cones can change their attractive or repulsive response to the same chemical gradient based on their internal calcium or cAMP levels. We create two models describing different aspects of growth cone guidance. One model describes the internal switch that determines the direction of movement. However, this model allows chemotaxis under certain conditions only, so a second model is created to propose a mechanism that allows growth cone guidance in any environment. Endothelial cells go through extensive morphological changes when exposed to shear stress due to blood flow. These morphological changes are thought to be at least partially the result of mechanical signals, such as deformations, transmitted to the cell structures. Our model describes an endothelial cell as a network of viscoelastic Kelvin bodies with experimentally obtained parameters. Qualitative predictions of the model agree with experiments.Comment: Dissertation. 214 pages with 82 figures. Parts of the dissertation have been submitted for publication. The chapter on modeling deformation of endothelial cells is published; the reference is given belo

Place-Based Learning Communities on a Rural Campus: Turning Challenges into Assets

At Humboldt State University (HSU), location is everything. Students are as drawn to our spectacular natural setting as they are to the unique majors in the natural resource sciences that the university has to offer. However, the isolation that nurtures the pristine natural beauty of the area presents a difficult reality for students who are accustomed to more densely populated environments. With the large majority of our incoming students coming from distant cities, we set out to cultivate a “home away from home” by connecting first-year students majoring in science, technology, engineering and math (STEM) to the communities and local environment of Humboldt County. To achieve this, we designed first-year place-based learning communities (PBLCs) that integrate unique aspects and interdisciplinary themes of our location throughout multiple high impact practices, including a summer experience, blocked-enrolled courses, and a first-year experience course entitled Science 100: Becoming a STEM Professional in the 21st Century. Native American culture, traditional ways of knowing, and contemporary issues faced by tribal communities are central features of our place-based curriculum because HSU is located on the ancestral land of the Wiyot people and the university services nine federally recognized American Indian tribes. Our intention is that by providing a cross-cultural, validating environment, students will: feel and be better supported in their academic pursuits; cultivate values of personal, professional and social responsibility; and increase the likelihood that they will complete their HSU degree. As we complete the fourth year of implementation, we aim to harness our experience and reflection to improve our programming and enable promising early results to be sustained

Mathematical models in biology

Aerotaxis is the particular form of chemotaxis in which oxygen plays the role of both the attractant and the repellent. Aerotaxis occurs without methylation adaptation, and it leads to fast and complete aggregation toward the most favorable oxygen concentration. Biochemical pathways of aerotaxis remain largely elusive, however, aerotactic pattern formation is well documented. This allows mathematical modeling to test plausible hypotheses about the biochemical mechanisms. Our model demonstrates that assuming fast, non-methylation adaptation produces theoretical results that are consistent with experimental observations. We obtain analytical estimates for parameter values that are difficult to obtain experimentally. Chemotaxis in growth cones differs from gradient sensing in other animal cells, because growth cones can change their attractive or repulsive response to the same chemical gradient based on their internal calcium or cAMP levels. We create two models describing different aspects of growth cone guidance. One model describes the internal switch that determines the direction of movement. However, this model allows chemotaxis under certain conditions only, so a second model is created to propose a mechanism that allows growth cone guidance in any environment. Endothelial cells go through extensive morphological changes when exposed to shear stress due to blood flow. These morphological changes are thought to be at least partially the result of mechanical signals, such as deformations, transmitted to the cell structures. Our model describes an endothelial cell as a network of viscoelastic Kelvin bodies with experimentally obtained parameters. Qualitative predictions of the model agree with experiments

The Effect of Noisy Flow on Endothelial Cell Mechanotransduction: A Computational Study

Associate Editor Scott I. Simon oversaw the review of this article. Abstract—Flow in the arterial system is mostly laminar, but turbulence occurs in vivo under both normal and pathological conditions. Turbulent and laminar flow elicit significantly different responses in endothelial cells (ECs), but the mechanisms allowing ECs to distinguish between these different flow regimes remain unknown. The authors present a computational model that describes the effect of turbulence on mechanical force transmission within ECs. Because turbulent flow is inherently ‘‘noisy’ ’ with random fluctuations in pressure and velocity, our model focuses on the effect of signal noise (a stochastically changing force) on the deformation of intracellular transduction sites including the nucleus, cell–cell adhesion proteins (CCAPs), and focal adhesion sites (FAS). The authors represent these components of the mechanical signaling pathway as linear viscoelastic structures (Kelvin bodies) connected to the cell surface via cytoskeletal elements. The authors demonstrate that FAS are more sensitive to signal noise than the nucleus or CCAP. The relative sensitivity of these various structures to noise is affected by the nature of the cytoskeletal connections within the cell. Finally, changes in the compliance of the nucleus dramatically affect nuclear sensitivity to noise, suggesting that pathologies that alter nuclear mechanical properties will be associated with abnormal EC responsiveness to turbulent flow. Keywords—Endothelium, Disturbed flow, Shear stress