18,702 research outputs found
Bridging the gap between the micro- and the macro-world of tumors
At present it is still quite difficult to match the vast knowledge on the
behavior of individual tumor cells with macroscopic measurements on clinical
tumors. On the modeling side, we already know how to deal with many molecular
pathways and cellular events, using systems of differential equations and other
modeling tools, and ideally, we should be able to extend such a mathematical
description up to the level of large tumor masses. An extended model should
thus help us forecast the behavior of large tumors from our basic knowledge of
microscopic processes. Unfortunately, the complexity of these processes makes
it very difficult -- probably impossible -- to develop comprehensive analytical
models. We try to bridge the gap with a simulation program which is based on
basic biochemical and biophysical processes -- thereby building an effective
computational model -- and in this paper we describe its structure, endeavoring
to make the description sufficiently detailed and yet understandable.Comment: 24 pages, 10 figures. Accepted for publication in AIP Advances, in
the special issue on the physics of cance
Computational modeling to elucidate molecular mechanisms of epigenetic memory
How do mammalian cells that share the same genome exist in notably distinct
phenotypes, exhibiting differences in morphology, gene expression patterns, and
epigenetic chromatin statuses? Furthermore how do cells of different phenotypes
differentiate reproducibly from a single fertilized egg? These are fundamental
problems in developmental biology. Epigenetic histone modifications play an
important role in the maintenance of different cell phenotypes. The exact
molecular mechanism for inheritance of the modification patterns over cell
generations remains elusive. The complexity comes partly from the number of
molecular species and the broad time scales involved. In recent years
mathematical modeling has made significant contributions on elucidating the
molecular mechanisms of DNA methylation and histone covalent modification
inheritance. We will pedagogically introduce the typical procedure and some
technical details of performing a mathematical modeling study, and discuss
future developments.Comment: 36 pages, 4 figures, 2 tables, book chapte
Detailed simulations of cell biology with Smoldyn 2.1.
Most cellular processes depend on intracellular locations and random collisions of individual protein molecules. To model these processes, we developed algorithms to simulate the diffusion, membrane interactions, and reactions of individual molecules, and implemented these in the Smoldyn program. Compared to the popular MCell and ChemCell simulators, we found that Smoldyn was in many cases more accurate, more computationally efficient, and easier to use. Using Smoldyn, we modeled pheromone response system signaling among yeast cells of opposite mating type. This model showed that secreted Bar1 protease might help a cell identify the fittest mating partner by sharpening the pheromone concentration gradient. This model involved about 200,000 protein molecules, about 7000 cubic microns of volume, and about 75 minutes of simulated time; it took about 10 hours to run. Over the next several years, as faster computers become available, Smoldyn will allow researchers to model and explore systems the size of entire bacterial and smaller eukaryotic cells
Investigating biocomplexity through the agent-based paradigm.
Capturing the dynamism that pervades biological systems requires a computational approach that can accommodate both the continuous features of the system environment as well as the flexible and heterogeneous nature of component interactions. This presents a serious challenge for the more traditional mathematical approaches that assume component homogeneity to relate system observables using mathematical equations. While the homogeneity condition does not lead to loss of accuracy while simulating various continua, it fails to offer detailed solutions when applied to systems with dynamically interacting heterogeneous components. As the functionality and architecture of most biological systems is a product of multi-faceted individual interactions at the sub-system level, continuum models rarely offer much beyond qualitative similarity. Agent-based modelling is a class of algorithmic computational approaches that rely on interactions between Turing-complete finite-state machines--or agents--to simulate, from the bottom-up, macroscopic properties of a system. In recognizing the heterogeneity condition, they offer suitable ontologies to the system components being modelled, thereby succeeding where their continuum counterparts tend to struggle. Furthermore, being inherently hierarchical, they are quite amenable to coupling with other computational paradigms. The integration of any agent-based framework with continuum models is arguably the most elegant and precise way of representing biological systems. Although in its nascence, agent-based modelling has been utilized to model biological complexity across a broad range of biological scales (from cells to societies). In this article, we explore the reasons that make agent-based modelling the most precise approach to model biological systems that tend to be non-linear and complex
Multiple verification in computational modeling of bone pathologies
We introduce a model checking approach to diagnose the emerging of bone
pathologies. The implementation of a new model of bone remodeling in PRISM has
led to an interesting characterization of osteoporosis as a defective bone
remodeling dynamics with respect to other bone pathologies. Our approach allows
to derive three types of model checking-based diagnostic estimators. The first
diagnostic measure focuses on the level of bone mineral density, which is
currently used in medical practice. In addition, we have introduced a novel
diagnostic estimator which uses the full patient clinical record, here
simulated using the modeling framework. This estimator detects rapid (months)
negative changes in bone mineral density. Independently of the actual bone
mineral density, when the decrease occurs rapidly it is important to alarm the
patient and monitor him/her more closely to detect insurgence of other bone
co-morbidities. A third estimator takes into account the variance of the bone
density, which could address the investigation of metabolic syndromes, diabetes
and cancer. Our implementation could make use of different logical combinations
of these statistical estimators and could incorporate other biomarkers for
other systemic co-morbidities (for example diabetes and thalassemia). We are
delighted to report that the combination of stochastic modeling with formal
methods motivate new diagnostic framework for complex pathologies. In
particular our approach takes into consideration important properties of
biosystems such as multiscale and self-adaptiveness. The multi-diagnosis could
be further expanded, inching towards the complexity of human diseases. Finally,
we briefly introduce self-adaptiveness in formal methods which is a key
property in the regulative mechanisms of biological systems and well known in
other mathematical and engineering areas.Comment: In Proceedings CompMod 2011, arXiv:1109.104
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