Insights into the dynamic trajectories of protein filament division revealed by numerical investigation into the mathematical model of pure fragmentation

The dynamics by which polymeric protein filaments divide in the presence of negligible growth, for example due to the depletion of free monomeric precursors, can be described by the universal mathematical equations of ‘pure fragmentation’. The rates of fragmentation reactions reflect the stability of the protein filaments towards breakage, which is of importance in biology and biomedicine for instance in governing the creation of amyloid seeds and the propagation of prions. Here, we devised from mathematical theory inversion formulae to recover the division rates and division kernel information from time dependent experimental measurements of filament size distribution. The numerical approach to systematically analyze the behaviour of pure fragmentation trajectories was also developed. We illustrate how these formulae can be used, provide some insights on their robustness, and show how they inform the design of experiments to measure fibril fragmentation dynamics. These advances are made possible by our central theoretical result on how the length distribution profile of the solution to the pure fragmentation equation aligns with a steady distribution profile for large times.

Low-Energy Fragmentation Dynamics at Copahue Volcano (Argentina) as Revealed by an Infrasonic Array and Ash Characteristics

Ash-rich eruptions represent a serious risk to the population living nearby as well as at thousands of kilometers from a volcano. Volcanic ash is the result of extensive magma fragmentation during an eruption, and it depends upon a combination of magma properties such as rheology, vesicularity and permeability, gas overpressure and the possible involvement of external fluids during magma ascent. The explosive process generates infrasonic waves which are directly linked to the outflow of the gas-particle mixture in the atmosphere. The higher the overpressure in the magma, the higher should be the exit velocity of the ejected material and the acoustic pressure related to this process. During violent eruptions, fragmentation becomes more efficient and is responsible for the extensive production of ash which is dispersed in the atmosphere. We show that the phase of intense ash emission that occurred during March 2016 at Copahue volcano (Argentina) generated a very low (0.1 Pa) infrasonic amplitude at 13 km, raising a number of questions concerning the links among acoustic pressure, gas overpressure and efficiency of magma fragmentation. Infrasound and direct observations of the eruptive plume indicate that the large quantity of ash erupted at Copahue was ejected with a low exit velocity. Thus, it was associated with eruptive dynamics driven by a low magma overpressure. This is more evident when infrasonic activity at Copahue is compared to the moderate explosive activity of Villarrica (Chile), recorded by the same array, at a distance of 193 km. Our data suggest a process of rigid fragmentation under a low magma overpressure which was nearly completely dissipated during the passage of the erupting mixture through the granular, ash-bearing crater infilling. We conclude that ash released into the atmosphere during low-energy fragmentation dynamics can be difficult to monitor, with direct consequences for the assessment of the related hazard and management of eruptive crises.

Integrative dynamics in psychological science

The observed increase in the number of psychological research entails both the expansion and deepening of psychological knowledge, and the escalation of the theoretical and methodological problems of its systematization and practical application. The widely discussed problems of the theoretical foundations and methodology of psychological research, in generalized formulations, are reduced to a statement of the growing fragmentation and searching the foundations of the integration prospects for psychology. At the same time, there are problems that have not yet been given due attention, one of such problems is the conceptualization of the integration and fragmentation dynamics in psychological knowledge. In the proposed conceptualization, the dynamics of the psychological knowledge development occurs in the original studies of the expansion, deployment, narrowing, folding of its structure. From these methodological positions, psychological research is categorized into deepening, fragmenting and integrating. According to the results of the methodological analysis, the ratio of the integration and fragmentation processes types is 1: 3. That is, even in the case of putting forward and starting an integration project in psychology, the coexistence of integrative and fragmented processes is inevitable, with the latter prevailing. If the psychological knowledge integration is carried out by descriptive methodological tools, then the array of fragmented studies will not shrink, and the current ratio of integration and fragmentation studies is unlikely to change. In this scenario, new research will continue with heterogeneous methodological tools, and since systematizing research remains not a priority, the carried out integration of psychological knowledge in terms of its volume will decrease relative to the total volume of studies. A dynamic balancing the integration and fragmentation processes is seen as an acceptable state of psychological knowledge. However, even for achieving it, it is necessary to reach positive integration dynamics at the first stage. The dynamic balance of integration and fragmentation processes can be established at various levels of their correlation – determining a sufficient level will be one of the most pressing issues in the case of implementing an integration project in psychology.