Mean square displacement for a discrete centroid model of cell motion

The mean square displacement (MSD) is an important statistical measure on a stochastic process or a trajectory. In this paper we find an approximation to the mean square displacement for a model of cell motion. The model is a discrete-time jump process which approximates a force-based model for cell motion. In cell motion, the mean square displacement not only gives a measure of overall drift, but it is also an indicator of mode of transport. The key to finding the approximation is to find the mean square displacement for a subset of the state space and use it as an approximation for the entire state space. We give some intuition as to why this is an unexpectedly good approximation. A lower bound and upper bound for the mean square displacement are also given. We show that, although the upper bound is far from the computed mean square displacement, in rare cases the large displacements are approached.

The Critical Importance of Spatial and Temporal Scales in Designing and Interpreting Immune Cell Migration Assays

Intravital microscopy and other direct-imaging techniques have allowed for a characterisation of leukocyte migration that has revolutionised the field of immunology, resulting in an unprecedented understanding of the mechanisms of immune response and adaptive immunity. However, there is an assumption within the field that modern imaging techniques permit imaging parameters where the resulting cell track accurately captures a cell’s motion. This notion is almost entirely untested, and the relationship between what could be observed at a given scale and the underlying cell behaviour is undefined. Insufficient spatial and temporal resolutions within migration assays can result in misrepresentation of important physiologic processes or cause subtle changes in critical cell behaviour to be missed. In this review, we contextualise how scale can affect the perceived migratory behaviour of cells, summarise the limited approaches to mitigate this effect, and establish the need for a widely implemented framework to account for scale and correct observations of cell motion. We then extend the concept of scale to new approaches that seek to bridge the current “black box” between single-cell behaviour and systemic response.

A systematic approach for developing mechanistic models for realistic simulation of cancer cell motion and deformation

Understanding and predicting metastatic progression and developing novel diagnostic methods can highly benefit from accurate models of the deformability of cancer cells. Spring-based network models of cells can provide a versatile way of integrating deforming cancer cells with other physical and biochemical phenomena, but these models have parameters that need to be accurately identified. In this study we established a systematic method for identifying parameters of spring-network models of cancer cells. We developed a genetic algorithm and coupled it to the fluid–solid interaction model of the cell, immersed in blood plasma or other fluids, to minimize the difference between numerical and experimental data of cell motion and deformation. We used the method to create a validated model for the human lung cancer cell line (H1975), employing existing experimental data of its deformation in a narrow microchannel constriction considering cell-wall friction. Furthermore, using this validated model with accurately identified parameters, we studied the details of motion and deformation of the cancer cell in the microchannel constriction and the effects of flow rates on them. We found that ignoring the viscosity of the cell membrane and the friction between the cell and wall can introduce remarkable errors.

Ergodic patterns of cell state transitions underlie the reproducibility of embryonic development

The reproducibility of embryonic development is a remarkable feat of biological organization, but the underlying mechanisms are poorly understood. Clearly, gene regulatory networks are central to the orderly progression of development, but noisy molecular and cellular processes should reduce reproducibility. Here, we identify ergodicity, a type of dynamical stability, as underlying the reproducibility of development. In ergodic systems, a single timepoint measurement equals a time average. Focusing on the zebrafish tailbud, we define gene expression and cell motion states using a parallel statistical analyses of single cell RNA sequencing data and in vivo timelapse cell tracking data and a change point detection algorithm. Strikingly, the cell motion state transitions in each embryo exhibit the same patterns for both a single timepoint and a 2-3 hour time average. Both the cell motion and gene expression cell states exhibit balanced influx and outflux rates reflecting a spatiotemporal stability. Stated simply, these data indicate the pattern of changes in the tailbud doesn’t change. This ergodic pattern of cell state transitions may represent an emergent meta-state that links gene networks to the reproducible progression of embryogenesis.

Identification of Distinct Molecular Subtypes of Endometrioid Adenocarcinoma

Endometrial carcinoma (EC) is one of the most common gynecological cancers worldwide. Endometrioid adenocarcinoma (EAC) is the major form of EC, accounting for 75–80% of cases. Currently, there is no molecular classification system for EAC, so there are no corresponding targeted treatments. In this study, we identified two distinct molecular subtypes of EAC with different gene expression patterns and clinicopathologic characteristics. Subtype I EAC cases, accounting for the majority of cases (56%), were associated with an earlier stage, a more well-differentiated grade, a lower tumor invasion rate, and a more favorable prognosis, and the median tumor necrosis percent (15%) was also significantly higher in subtype I EAC. In contrast, subtype II EAC represents high-grade EAC, with a higher tumor invasion rate and tumor weight. The up-regulated genes in subtype I EAC were associated with the immune response, defense response, cell motion, and cell motility pathway, whereas the up-regulated genes in subtype II EAC were associated with the cell cycle, DNA replication, and RNA processing pathways. Additionally, we identified three potential subtype-specific biomarkers, comprising MDM2 (MDM2 proto-oncogene) for subtype I, and MSH2 (mutS homolog 2) and MSH6 (mutS homolog 6) for subtype II.

Mechanism of tissue expansion in the early stage of the migration

The collective cell migration is observed in many biological processes such as wound healing, embryogenesis, and cancer metastasis. Despite extensive theoretical and experimental studies on collective cell motion, there is no unified mechanism to explain it. In this work, we experimentally report the collectively growing cell colonies in the sub-marginal region of a freely expanding cell monolayer. These colonies could be responsible for the highly aligned collective cell migration observed in front cell rows. Our results provide a basic framework to understand the physical mechanism responsible for collective cell migration in the freely expanding monolayer.

Actin dynamics as a multiscale integrator of cellular guidance cues

Cells are able to integrate multiple, and potentially competing, cues to determine a migration direction. For instance, in wound healing, cells follow chemical signals or electric fields to reach the wound edge, regardless of any local guidance cues. To investigate this integration of guidance cues, we monitor the actin-polymerization dynamics of immune cells in response to cues on a subcellular scale (nanotopography) and on the cellular scale (electric fields, EFs). In the fast, amoeboid-type migration, commonly observed in immune cells, actin polymerization at the cell's leading edge is the driver of motion. The excitable systems character of actin polymerization leads to self-propagating, two-dimensional wavefronts that enable persistent cell motion. We show that EFs guide these wavefronts, leading to turning of cells when the direction of the EF changes. When nanoridges promote one-dimensional (1D) waves of actin polymerization that move along the ridges (esotaxis), EF guidance along that direction is amplified. 1D actin waves cannot turn or change direction, so cells respond to a change in EF direction by generating new 1D actin waves. At the cellular scale, the emergent response is a turning of the cell. For nanoridges perpendicular to the direction of the EF, the 1D actin waves are guided by the nanotopography, but both the average location of new actin waves and the whole cell motion are guided by the EF. Thus, actin waves respond to each cue on its intrinsic length scale, allowing cells to exhibit versatile responses to the physical microenvironment.

Investigating the Kinetics of Blood Coagulation Using High-Frequency Ultrasound

Blood circulation requires regulated clot formation and breakdown to prevent blood loss following an injury and to ensure that clots do not form and circulate within the vasculature. Known as hemostasis, this delicate balance between coagulant and anti-coagulant pathways can be disrupted by disease, medication, or trauma, and may lead to morbidity or mortality. Current in vitro hemostatic tests have shown promise as tools for diagnosis and risk assessment in certain disorders. However, these tests are limited in their ability to assess the complete hemostatic process or are restricted to studies of blood plasma. In this work, high frequency ultrasound is proposed as a method of assessing hemostasis in whole blood samples. A system was developed and experiments were performed by monitoring acoustic changes in mouse blood during coagulation. Blood cell motion and frequency dependant changes in ultrasound intensity were found to be sensitive to the kinetics of clot formation