Rate equation and scaling for fragmentation with mass loss

Ultrasound frequency sonication facilitates high-throughput and uniform dissociation of cellular aggregates and tissues

A sample preparation step involving dissociation of tissues into their component cells is often required to conduct analysis of nucleic acids and other constituents from tissue samples. Frequently, the extracellular matrix and cell-cell adhesions are disrupted via treatment with a chemical dissociating reagent or various mechanical forces. In this work, a new, high-throughput, multiplexed method of dissociating tissues and cellular aggregates into single cells using ultrasound frequency bath sonication is explored and characterized. Different operating parameters are evaluated, and a treatment protocol with potential for uniform, high-throughput tissue dissociation is compared to the existing best chemical and orbital plate shaking protocol. Metrics such as percent dissociation, cellular recovery, average aggregate size, proportion of various aggregate sizes, membrane circularity, and cellular viability are subsequently assessed and found to be favorable. In optimized conditions, 53 ± 8% of 1 mm biopsy cores are dissociated within 30 min using sonication alone, surpassing leading high-throughput orbital plate shaking techniques five-fold. Chemical digestion is also 2 times more effective when complexed with sonication rather than orbital plate shaking. RNA content, quality, and expression are found to be superior to the standard protocol in terms of transcriptional preservation.

On conservativity and shattering for an equation of phytoplankton dynamics

A model of phytoplankton dynamics introduced by Arino describes the evolution of aggregates of phytoplankton by a kinetic-type equation composed of terms describing the growth of the aggregates and their splitting, where the latter is modelled by a singular integral operator of the same form as in the classical fragmentation theory. In this paper we shall show that despite the presence of the growth term, the model displays the typical properties of the fragmentation models, in particular, if the fragmentation rate is unbounded as the size of aggregates tends to zero, then there occurs an unaccounted for loss of the phytoplankton though formally nothing is taken out of the system.

Phytoplankton dynamics

We present a model of the phytoplankton dynamics. The distribution of the size of the phytoplankton aggregates is described by a non-linear transport equation that contains terms responsible for the growth of phytoplankton aggregates, their fragmentation and coagulation. We study asymptotic behaviour of moments of the solutions and we explain why phytoplankton tends to create large aggregates.

Transition from random to ordered fractals in fragmentation of particles in an open system

We consider the fragmentation process with mass loss and discuss self-similar properties of the arising structure both in time and space, focusing on dimensional analysis. This exhibits a spectrum of mass exponents theta, whose exact numerical values are given for which x(-theta) or t(theta z) has the dimension of particle size distribution function psi(x,t), where z is the kinetic exponent. We obtained conditions for which the scaling and fragmentation process altogether breaks down, and we give an explicit scaling solution for a special case. Finally, we identify a new class of fractals ranging from random to nonrandom and show that the fractal dimension increases with increasing order and a transition to a strictly self-similar pattern occurs when randomness completely ceases.

Fragmentation of percolation clusters in general dimensions

The scaling behavior for binary fragmentation of critical percolation clusters in general dimensions is investigated by Monte Carlo simulation as well as by exact series expansions. We obtain values of critical exponents lambda and phi describing the scaling of the fragmentation rate and the distribution of cluster masses produced by binary fragmentation. Our results for lambda and phi in two to nine dimensions agree with the conjectured scaling relation sigma=1+lambda-phi by Edwards and co-workers [Phys. Rev. Lett. 68, 2692 (1992); Phys. Rev. A 46, 6252 (1992)], which in turn excludes the other scaling relations suggested by Gouyet (for d=2), and by Roux and Guyon [J. Phys. A 22, 3693 (1989)], where sigma is the crossover exponent for the cluster numbers in percolation theory.

Scaling in animal group-size distributions

An elementary model of animal aggregation is presented. The group-size distributions resulting from this model are truncated power laws. The predictions of the model are found to be consistent with data that describe the group-size distributions of tuna fish, sardinellas, and African buffaloes.