Obscurin, a giant modular cytoskeletal protein, is comprised mostly of tandem immunoglobulinlike (Ig-like) domains. This architecture allows obscurin to connect distal targets within the cell. The linkers connecting the Ig domains are usually short (3-4 residues). The physical effect arising from these short linkers is not known; such linkers may lead to a stiff elongated molecule or, conversely, may lead to a more compact and dynamic structure. In an effort to better understand how linkers affect obscurin flexibility, and to better understand the physical underpinnings of this flexibility, here we study the structure and dynamics of four representative sets of dual obscurin Ig domains using experimental and computational techniques.We find in all cases tested that tandem obscurin Ig domains interact at the poles of each domain and tend to stay relatively extended in solution. NMR, SAXS, and MD simulations reveal that while tandem domains are elongated, they also bend and flex significantly. By applying this behavior to a simplified model, it becomes apparent obscurin can link targets more than 200 nm away. However, as targets get further apart, obscurin begins acting as a spring and requires progressively more energy to further elongate.
Running and walking are integral to most sports and there is a considerable amount of mathematics involved in examining the forces produced by each foot contacting the ground. In this paper we discuss biomechanical terms related to running and walking. We then use experimental ground reaction force data to calculate the impulse of running, speed-walking, and walking. We then mathematically model the vertical ground reaction force curves for both running and walking, successfully reproducing experimental data. Finally, we discuss the biological implications of the mathematical models and give suggestions for numerous classroom or research projects.
The migration pattern of the eastern monarch butterfly (Danaus plexippus) consists of a sequence of generations of butterflies that originate in Mexico each spring, travel as far north as Southern Canada, and ultimately return to the original location in Mexico the following fall. Estimates of monarch populations in the Oyamel firs in Mexico have caused concern within the scientific community about the long-term stability of this phenomenon. We use periodic population matrices to model the life cycle of the eastern monarch butterfly and find that, under this linear model, this migration is not currently at risk. We extend the model to address the three primary obstacles for the long-term survival of this migratory pattern: deforestation in Mexico, increased extreme weather patterns, and milkweed decline. Incorporating these obstacles into the model shows that there is a definite need to take action to alleviate the aforementioned obstacles. K E Y W O R D SDanaus plexippus, mathematical model, monarch butterfly, periodic matrix population model Natural Resource Modeling. 2017;e12123.wileyonlinelibrary.com/journal/nrm
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