Sorry for the editorial interjection here, but I've just put a post on my own blog Connecting the Dots, which I think is appropriate for this forum as well. In short, there is a new pre-print forum coming out for biologically oriented papers called the bioRxiv. I think it is an excellent opportunity for us theorists to get our work seen by the experimental crowd in our various fields. Check out my blog post, check out the bioRxiv, and consider putting your work there.
Now... back to our regularly scheduled programming.
Tuesday, October 22, 2013
Wednesday, October 9, 2013
Is cancer growth random and stochastic or ordered and deterministic? Are these ideas mutually exclusive?
(Submitted on 8 Oct 2013)
Studying the development of malignant tumours, it is important to know and predict the proportions of different cell types in tissue samples. Knowing the expected temporal evolution of the proportion of normal tissue cells, compared to stem-like and non-stem like cancer cells, gives an indication about the progression of the disease and indicates the expected response to interventions with drugs. Such processes have been modeled using Markov processes. An essential step for the simulation of such models is then the determination of state transition probabilities. We here consider the experimentally more realistic scenario in which the measurement of cell population sizes is noisy, leading to a hidden Markov model. In this context, extrinsic randomness is related to noisy measurements, which are used for the estimation of the transition probability matrix. Intrinsic randomness, on the other hand, is here related to the error in estimating the state probability from small cell populations. Using aggregated data of fluorescence-activated cell sorting (FACS) measurement, we develop a minimum mean square error estimator (MMSE) and maximum likelihood (ML) estimator and formulate two problems to find the minimum number of required samples and measurements to guarantee the accuracy of predicted population sizes using a transition probability matrix estimated from noisy data. We analyze the properties of two estimators for different noise distributions and prove an optimal solution for Gaussian distributions with the MMSE. Our numerical results show, that for noisy measurements the convergence mechanism of transition probabilities and steady states differ widely from the real values if one uses the standard deterministic approach in which measurements are assumed to be noise free.
Tuesday, October 8, 2013
(Submitted on 4 Oct 2013)
We investigate the dynamics of cancer initiation in a model with one driver mutation and several passenger mutations. In contrast to previous models, the change in fitness induced by the driver mutation depends on the genetic background of the cell, in our case on the number of passenger mutations. The passenger mutations themselves have no or only a very small impact on the cell's fitness. This approach is motivated by the Burkitt Lymphoma, where the hallmark mutation, a translocation between the MYC gene and an immunoglobulin gene, alters the rate of apoptosis, but also the proliferation rate of cells. This way we obtain an epistatic fitness landscape, where the fitness of cells with the driver mutation is advantageous only if enough passenger genes have mutated. Otherwise the fitness might even be deleterious. Our analysis is based on an individual cell model in which the cells can divide or undergo apoptosis. In case of division the two daughter cells can mutate. This model shows a very interesting dynamical behavior. Since the driver mutation is deleterious on a background with only a few passenger mutations, there is a long period of stasis in the number of cells until a clone of cells has evolved with enough passenger mutations. Only when the driver mutation occurs in one of those cells, the cell population starts to grow exponentially.
Cancer does not always develop to become a clinically manifest disease. Most of the population actually carries small occult tumors that remain asymptomatic and undetectable. Here, we propose a theoretical study of this phenomenon by defining and simulating a novel mathematical model able to describe the development of a population of tumors at the organism scale. After demonstrating the model can explain experimental data on metastatic development, we go on to test the hypothesis of global dormancy resulting from inhibitory signaling interactions among the tumors. These interactions are targeted against the tumor's vascular support development (angiogenesis), known to be essential for tumor growth, by means of inhibitory molecules released in the circulation. By quantifying their consequences on the establishment of metastases and maintenance of the dormant state, our model shows for the first time how a previously unrecognized phenomenon - systemic inhibition of angiogenesis (SIA) - regulates tumor development. We show SIA alone is not sufficient for global dormancy but can suppress the growth of the total metastatic burden, even to the point of producing an equilibrium state with low and stable total cancerous mass.
Sebastien BenzekryAlberto GandolfiPhilip Hahnfeldt
Sebastien BenzekryAlberto GandolfiPhilip Hahnfeldt