2,545 research outputs found
Mathematical modeling of tumor therapy with oncolytic viruses: Effects of parametric heterogeneity on cell dynamics
One of the mechanisms that ensure cancer robustness is tumor heterogeneity,
and its effects on tumor cells dynamics have to be taken into account when
studying cancer progression. There is no unifying theoretical framework in
mathematical modeling of carcinogenesis that would account for parametric
heterogeneity. Here we formulate a modeling approach that naturally takes stock
of inherent cancer cell heterogeneity and illustrate it with a model of
interaction between a tumor and an oncolytic virus. We show that several
phenomena that are absent in homogeneous models, such as cancer recurrence,
tumor dormancy, an others, appear in heterogeneous setting. We also demonstrate
that, within the applied modeling framework, to overcome the adverse effect of
tumor cell heterogeneity on cancer progression, a heterogeneous population of
an oncolytic virus must be used. Heterogeneity in parameters of the model, such
as tumor cell susceptibility to virus infection and virus replication rate, can
lead to complex, time-dependent behaviors of the tumor. Thus, irregular,
quasi-chaotic behavior of the tumor-virus system can be caused not only by
random perturbations but also by the heterogeneity of the tumor and the virus.
The modeling approach described here reveals the importance of tumor cell and
virus heterogeneity for the outcome of cancer therapy. It should be
straightforward to apply these techniques to mathematical modeling of other
types of anticancer therapy.Comment: 45 pages, 6 figures; submitted to Biology Direc
Biological applications of the theory of birth-and-death processes
In this review, we discuss the applications of the theory of birth-and-death
processes to problems in biology, primarily, those of evolutionary genomics.
The mathematical principles of the theory of these processes are briefly
described. Birth-and-death processes, with some straightforward additions such
as innovation, are a simple, natural formal framework for modeling a vast
variety of biological processes such as population dynamics, speciation, genome
evolution, including growth of paralogous gene families and horizontal gene
transfer, and somatic evolution of cancers. We further describe how empirical
data, e.g., distributions of paralogous gene family size, can be used to choose
the model that best reflects the actual course of evolution among different
versions of birth-death-and-innovation models. It is concluded that
birth-and-death processes, thanks to their mathematical transparency,
flexibility and relevance to fundamental biological process, are going to be an
indispensable mathematical tool for the burgeoning field of systems biology.Comment: 29 pages, 4 figures; submitted to "Briefings in Bioinformatics
Macroscopic Pure State of Light Free of Polarization Noise
The preparation of completely non-polarized light is seemingly easy: an
everyday example is sunlight. The task is much more difficult if light has to
be in a pure quantum state, as required by most quantum-technology
applications. The pure quantum states of light obtained so far are either
polarized or, in rare cases, manifest hidden polarization: even if their
intensities are invariant to polarization transformations, higher-order moments
are not. We experimentally demonstrate the preparation of the macroscopic
singlet Bell state, which is pure, completely non-polarized, and has no
polarization noise. Simultaneous fluctuation suppression in three Stokes
observables below the shot-noise limit is demonstrated, opening perspectives
for noiseless polarization measurements. The state is shown to be invariant to
polarization transformations. This robust highly entangled isotropic state
promises to fuel important applications in photonic quantum technologies.Comment: 4 pages, 2 figures, 1 tabl
- …