The general growth logistics of cell populations

Modelling and Differential Quantification of Electric Cell-Substrate Impedance Sensing Growth Curves

Measurement of cell surface coverage has become a common technique for the assessment of growth behavior of cells. As an indirect measurement method, this can be accomplished by monitoring changes in electrode impedance, which constitutes the basis of electric cell-substrate impedance sensing (ECIS). ECIS typically yields growth curves where impedance is plotted against time, and changes in single cell growth behavior or cell proliferation can be displayed without significantly impacting cell physiology. To provide better comparability of ECIS curves in different experimental settings, we developed a large toolset of R scripts for their transformation and quantification. They allow importing growth curves generated by ECIS systems, edit, transform, graph and analyze them while delivering quantitative data extracted from reference points on the curve. Quantification is implemented through three different curve fit algorithms (smoothing spline, logistic model, segmented regression). From the obtained models, curve reference points such as the first derivative maximum, segmentation knots and area under the curve are then extracted. The scripts were tested for general applicability in real-life cell culture experiments on partly anonymized cell lines, a calibration setup with a cell dilution series of impedance versus seeded cell number and finally IPEC-J2 cells treated with 1% and 5% ethanol.

Colloidal Silver Induces Cytoskeleton Reorganization and E-Cadherin Recruitment at Cell-Cell Contacts in HaCaT Cells

Up until the first half of the 20th century, silver found significant employment in medical applications, particularly in the healing of open wounds, thanks to its antibacterial and antifungal properties. Wound repair is a complex and dynamic biological process regulated by several pathways that cooperate to restore tissue integrity and homeostasis. To facilitate healing, injuries need to be promptly treated. Recently, the interest in alternatives to antibiotics has been raised given the widespread phenomenon of antibiotic resistance. Among these alternatives, the use of silver appears to be a valid option, so a resurgence in its use has been recently observed. In particular, in contrast to ionic silver, colloidal silver, a suspension of metallic silver particles, shows antibacterial activity displaying less or no toxicity. However, the human health risks associated with exposure to silver nanoparticles (NP) appear to be conflicted, and some studies have suggested that it could be toxic in different cellular contexts. These potentially harmful effects of silver NP depend on various parameters including NP size, which commonly range from 1 to 100 nm. In this study, we analyzed the effect of a colloidal silver preparation composed of very small and homogeneous nanoparticles of 0.62 nm size, smaller than those previously tested. We found no adverse effect on the cell proliferation of HaCaT cells, even at high NP concentration. Time-lapse microscopy and indirect immunofluorescence experiments demonstrated that this preparation of colloidal silver strongly increased cell migration, re-modeled the cytoskeleton, and caused recruitment of E-cadherin at cell-cell junctions of human cultured keratinocytes.

Model-Based Phenotypic Signatures Governing the Dynamics of the Stem and Semi-differentiated Cell Populations in Dysplastic Colonic Crypts

Mathematical modeling of cell differentiated in colonic crypts can contribute to a better understanding of basic mechanisms underlying colonic tissue organization, but also its deregulation during carcinogenesis and tumor progression. Here, we combined bifurcation analysis to assess the effect that time delay has in the complex interplay of stem cells and semi-differentiated cells at the niche of colonic crypts, and systematic model perturbation and simulation to find model-based phenotypes linked to cancer progression. The models suggest that stem cell and semi-differentiated cell population dynamics in colonic crypts can display chaotic behavior. In addition, we found that clinical profiling of colorectal cancer correlates with the in silico phenotypes proposed by the mathematical model. Further, potential therapeutic targets for chemotherapy resistant phenotypes are proposed, which in any case will require experimental validation.

The fractal heart - embracing mathematics in the cardiology clinic

For clinicians grappling with quantifying the complex spatial and temporal patterns of cardiac structure and function (such as myocardial trabeculae, coronary microvascular anatomy, tissue perfusion, myocyte histology, electrical conduction, heart rate, and blood-pressure variability), fractal analysis is a powerful, but still underused, mathematical tool. In this Perspectives article, we explain some fundamental principles of fractal geometry and place it in a familiar medical setting. We summarize studies in the cardiovascular sciences in which fractal methods have successfully been used to investigate disease mechanisms, and suggest potential future clinical roles in cardiac imaging and time series measurements. We believe that clinical researchers can deploy innovative fractal solutions to common cardiac problems that might ultimately translate into advancements for patient care.

Modelling the growth of plants with a uniform growth logistics

BACKGROUND AND AIMS

The increment model has previously been used to describe the growth of plants in general. Here, we examine how the same logistics enables the development of different superstructures.

METHODS

Data from the literature are analyzed with the increment model. Increments are growth-invariant molecular clusters, treated as heuristic particles. This approach formulates the law of mass action for multi-component systems, describing the general properties of superstructures which are optimized via relaxation processes.

RESULTS

The daily growth patterns of hypocotyls can be reproduced implying predetermined growth invariant model parameters. In various species, the coordinated formation and death of fine roots are modeled successfully. Their biphasic annual growth follows distinct morphological programs but both use the same logistics. In tropical forests, distributions of the diameter in breast height of trees of different species adhere to the same pattern. Beyond structural fluctuations, competition and cooperation within and between the species may drive optimization.

CONCLUSION

All superstructures of plants examined so far could be reproduced with our approach. With genetically encoded growth-invariant model parameters (interaction with the environment included) perfect morphological development runs embedded in the uniform logistics of the increment model.

On the structure-bounded growth processes in plant populations

If growing cells in plants are considered to be composed of increments (ICs) an extended version of the law of mass action can be formulated. It evidences that growth of plants runs optimal if the reaction-entropy term (entropy times the absolute temperature) matches the contact energy of ICs. Since these energies are small, thermal molecular movements facilitate via relaxation the removal of structure disturbances. Stem diameter distributions exhibit extra fluctuations likely to be caused by permanent constraints. Since the signal-response system enables in principle perfect optimization only within finite-sized cell ensembles, plants comprising relatively large cell numbers form a network of size-limited subsystems. The maximal number of these constituents depends both on genetic and environmental factors. Accounting for logistical structure-dynamics interrelations, equations can be formulated to describe the bimodal growth curves of very different plants. The reproduction of the S-bended growth curves verifies that the relaxation modes with a broad structure-controlled distribution freeze successively until finally growth is fully blocked thus bringing about "continuous solidification".

Variable renewal rate and growth properties of cell populations in colon crypts

A nonlinear mathematical model is used to investigate the time evolution of the cell populations in colon crypts (stem, semidifferentiated and fully differentiated cells). To mimic pathological alteration of the biochemical pathways leading to abnormal proliferative activity of the population of semidifferentiated cells their renewal rate is assumed to be dependent on the population size. Then, the effects of such perturbation on the population dynamics are investigated theoretically. Using both theoretical methods and numerical simulations it is shown that the increase in the renewal rate of semidifferentiated cells strongly impacts the dynamical behavior of the cell populations.