Bridging the Gap between mesoscopic and macroscopic models: the case of multicellular tumor spheroids

Effects of a differentiating therapy on cancer-stem-cell-driven tumors

The growth of many solid tumors has been found to be driven by chemo- and radiotherapy-resistant cancer stem cells (CSCs). A suitable therapeutic avenue in these cases may involve the use of a differentiating agent (DA) to force the differentiation of the CSCs and of conventional therapies to eliminate the remaining differentiated cancer cells (DCCs). To describe the effects of a DA that reprograms CSCs into DCCs, we adapt a differential equation model developed to investigate tumorspheres, which are assumed to consist of jointly evolving CSC and DCC populations. We analyze the mathematical properties of the model, finding the equilibria and their stability. We also present numerical solutions and phase diagrams to describe the system evolution and the therapy effects, denoting the DA strength by a parameter adif. To obtain realistic predictions, we choose the other model parameters to be those determined previously from fits to various experimental datasets. These datasets characterize the progression of the tumor under various culture conditions. Typically, for small values of adif the tumor evolves towards a final state that contains a CSC fraction, but a strong therapy leads to the suppression of this phenotype. Nonetheless, different external conditions lead to very diverse behaviors. For microchamber-grown tumorspheres, there is a threshold in therapy strength below which both subpopulations survive, while high values of adif lead to the complete elimination of the CSC phenotype. For tumorspheres grown on hard and soft agar and in the presence of growth factors, the model predicts a threshold not only in the therapy strength, but also in its starting time, an early beginning being potentially crucial. In summary, our model shows how the effects of a DA depend critically not only on the dosage and timing of the drug application, but also on the tumor nature and its environment.

Oscillations in growth of multicellular tumour spheroids: a revisited quantitative analysis

OBJECTIVES

Multicellular tumour spheroids (MTS) provide an important tool for study of the microscopic properties of solid tumours and their responses to therapy. Thus, observation of large-scale volume oscillations in MTS, reported several years ago by two independent groups (1,2), in our opinion represent a remarkable discovery, particularly if this could promote careful investigation of the possible occurrence of volume oscillations of tumours 'in vivo'.

MATERIALS AND METHODS

Because of high background noise, quantitative analysis of properties of observed oscillations has not been possible in previous studies. Such an analysis can be now performed, thanks to a recently proposed approach, based on formalism of phenomenological universalities (PUN).

RESULTS

Results have provided unambiguous confirmation of the existence of MTS volume oscillations, and quantitative evaluation of their properties, for two tumour cell lines. Proof is based not only on quality of fitting of the experimental datasets, but also on determination of well-defined values of frequency and amplitude of the oscillations for each line investigated, which would not be consistent with random fluctuation.

CONCLUSIONS

Biological mechanisms, which can be directly responsible for observed oscillations, are proposed, which relates also to recent work on related topics. Further investigations, both at experimental and at modelling levels, are also suggested. Finally, from a methodological point of view, results obtained represent further confirmation of applicability and usefulness of the PUN approach.

A new computational tool for the phenomenological analysis of multipassage tumor growth curves

Multipassage experiments are performed by subcutaneous implantation in lab animals (usually mice) of a small number of cells from selected human lines. Tumor cells are then passaged from one mouse to another by harvesting them from a growing tumor and implanting them into other healthy animals. This procedure may be extremely useful to investigate the various mechanisms involved in the long term evolution of tumoral growth. It has been observed by several researchers that, contrary to what happens in in vitro experiments, there is a significant growth acceleration at each new passage. This result is explained by a new method of analysis, based on the Phenomenological Universalities approach. It is found that, by means of a simple rescaling of time, it is possible to collapse all the growth curves, corresponding to the successive passages, into a single curve, belonging to the Universality Class U2. Possible applications are proposed and the need of further experimental evidence is discussed.

Scaling, growth and cyclicity in biology: a new computational approach

Background

The Phenomenological Universalities approach has been developed by P.P. Delsanto and collaborators during the past 2–3 years. It represents a new tool for the analysis of experimental datasets and cross-fertilization among different fields, from physics/engineering to medicine and social sciences. In fact, it allows similarities to be detected among datasets in totally different fields and acts upon them as a magnifying glass, enabling all the available information to be extracted in a simple way. In nonlinear problems it allows the nonscaling invariance to be retrieved by means of suitable redefined fractal-dimensioned variables.

Results

The main goal of the present contribution is to extend the applicability of the new approach to the study of problems of growth with cyclicity, which are of particular relevance in the fields of biology and medicine.

Conclusion

As an example of its implementation, the method is applied to the analysis of human growth curves. The excellent quality of the results (R² = 0.988) demonstrates the usefulness and reliability of the approach.

Multiple mutant clones in blood rarely coexist

Leukemias arise due to mutations in the genome of hematopoietic (blood) cells. Hematopoiesis has a multicompartment architecture, with cells exhibiting different rates of replication and differentiation. At the root of this process, one finds a small number of stem cells, and hence the description of the mutation-selection dynamics of blood cells calls for a stochastic approach. We use stochastic dynamics to investigate to which extent acquired hematopoietic disorders are associated with mutations of single or multiple genes within developing blood cells. Our analysis considers the appearance of mutations both in the stem cell compartment as well as in more committed compartments. We conclude that in the absence of genomic instability, acquired hematopoietic disorders due to mutations in multiple genes are most likely very rare events, as multiple mutations typically require much longer development times compared to those associated with a single mutation.

Classification scheme for phenomenological universalities in growth problems in physics and other sciences

A classification in universality classes of broad categories of phenomenologies, belonging to physics and other disciplines, may be very useful for a cross fertilization among them and for the purpose of pattern recognition and interpretation of experimental data. We present here a simple scheme for the classification of nonlinear growth problems. The success of the scheme in predicting and characterizing the well known Gompertz, West, and logistic models, suggests to us the study of a hitherto unexplored class of nonlinear growth problems.