Kinetics of the formation of cancer metastases via induced premetastatic cancer-stem-cell niches

Kinetics of cancer metastasis

The formation of metastases during cancer is now considered to be induced by migrating metastatic stem cells (MetSCs) in preexisting niches or niches induced by MetSCs or tumor-derived exosomes (TDEs). I propose and compare two simplest generic models describing these two scenarios. The number of tumors is predicted (i) to increase exponentially in the case of preexisting niches and (ii) to diverge during a finite time interval in the case of induced niches. The latter prediction is novel and of interest because rapid collapse in the end of a finite time interval is a well-known feature of the cancer metastasis. Two advanced models describing the two scenarios of cancer metastasis have been scrutinized as well. These models clarify the likely role of various specific factors in the metastasis. In particular, the equations derived in the framework of the advanced model with preexisting niches have been solved analytically allowing (i) to clarify the factors determining the duration of the period from the initiation of the primary tumor to the phase when the metastases start to dominate, (ii) to estimate the number of metastases in the end of this period, and (iii) to explains why the use of chemotherapy typically results in the improvement of the patient state only for a relatively short period. The equations derived in the framework of the advanced model with induced niches have no analytical solution, and their analysis merits additional attention.

Kinetics of enzymatic reactions in lipid membranes containing domains

An appreciable part of enzymes operating in vivo is associated with lipid membranes. The function of such enzymes can be influenced by the presence of domains containing proteins and/or composed of different lipids. The corresponding experimental model-system studies can be performed under well controlled conditions, e.g., on a planar supported lipid bilayer or surface-immobilized vesicles. To clarify what may happen in such systems, we propose general kinetic equations describing the enzyme-catalyzed substrate conversion occurring via the Michaelis-Menten (MM) mechanism on a membrane with domains which do not directly participate in reaction. For two generic situations when a relatively slow reaction takes place primarily in or outside domains, we take substrate saturation and lateral substrate-substrate interactions at domains into account and scrutinize the dependence of the reaction rate on the average substrate coverage. With increasing coverage, depending on the details, the reaction rate reaches saturation via an inflection point or monotonously as in the conventional MM case. In addition, we show analytically the types of reaction kinetics occurring primarily at domain boundaries. In the physically interesting situation when the domain growth is fast on the reaction time scale, the latter kinetics are far from conventional. The opposite situation when the reaction is fast and controlled by diffusion has been studied by using the Monte Carlo technique. The corresponding results indicate that the dependence of the reaction kinetics on the domain size may be weak.

Monte Carlo simulation-based approach to model the size distribution of metastatic tumors

The size distribution of metastatic tumors and its time evolution are traditionally described by integrodifferential equations and stochastic models. Here we develop a simple Monte Carlo approach in which each event of metastasis is treated as a chance event through random-number generation. We demonstrate the accuracy of this approach on a specific growth and metastasis model by showing that it quantitatively reproduces the size distribution and the total number of tumors as a function of time. The approach also yields statistical distribution of patient-to-patient variations, and has the flexibility to incorporate many real-life complexities.