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Proteins make up much of the machinery of cells and perform many roles that are essential for life. Some important proteins – known as intrinsically disordered proteins – lack any stable three-dimensional structure. One such protein, called tau, is best known for its ability to form tangles in the brain, and a buildup of these tangles is a hallmark of Alzheimer’s disease and many other dementias. Tau is also one of a number of proteins that can undergo a process called liquid-liquid phase separation: essentially, a solution of tau separates into a very dilute solution interspersed with droplets of a concentrated tau solution, similar to an oil-water mixture separating into a very watery solution with drops of oil. Understanding the conditions that lead to spontaneous liquid-liquid phase separation might give insight into how the tau tangles form. However, it was not known whether it is possible in principle for liquid-liquid phase separation of tau to occur in a living brain. Lin, McCarty et al. have now used an advanced computer simulation method together with experiments to map the conditions under which a solution containing tau undergoes liquid-liquid phase separation. Temperature as well as the concentrations of salt and the tau protein all influenced how easily tau droplets formed or dissolved, and the narrow range of conditions that encouraged droplet formation fell within the normal conditions found in the body, also known as “physiological conditions”. This suggested that tau droplets might form and dissolve easily in living systems, and possibly in the brain, depending on the precise physiological conditions. To explore this possibility further, tau protein was added to a dish containing living cells. As the map suggested, slightly adjusting temperature or protein concentrations caused tau droplets to form and dissolve, all while the cells remained alive. The map provided by this study may offer guides to researchers looking for liquid-liquid phase separation in the brain. If liquid-liquid phase separation of tau occurs in living brains, it may be important for determining whether and when damaging tau tangles emerge. For example, the high concentration of tau in droplets might speed up tangle formation. Ultimately, a better understanding of the conditions and mechanism for liquid-liquid phase separation of tau can help researchers understand the role of protein droplet formation in living systems. This may be a process that promotes, or possibly a regulatory mechanism that prevents, the formation of tau tangles associated with dementia.
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Tangle decompositions of alternating link complements
Decomposing knots and links into tangles is a useful technique for understand- ing their properties. The notion of prime tangles was introduced by Kirby and Lickorish in [3]; Lickorish proved [5] that by summing prime tangles one obtains a prime link. In a similar spirit, summing two prime alternating tangles will produce a prime alternating link, if summed correctly with respect to the alternating property. Given a prime alter- nating link, we seek to understand whether it can be decomposed into two prime tangles each of which is alternating. We re ne results of Menasco and Thistlethwaite to show that if such a decomposition exists either it is visible in an alternating link diagram or the link is of a particular form, which we call a pseudo-Montesinos link.
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- Award ID(s):
- 1934568
- PAR ID:
- 10349469
- Date Published:
- Journal Name:
- Illinois journal of mathematics
- Volume:
- 65
- ISSN:
- 0019-2082
- Page Range / eLocation ID:
- 533-546
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript
- Journal Article:
- https://doi.org/10.1215/00192082-9291846
