578 research outputs found
Stochastic Chemical Kinetics. Theory and (Mostly) Systems Biological Applications, P. Erdi, G. Lente. Springer (2014)
Book review of Stochastic Chemical Kinetics. Theory and (Mostly) Systems
Biological Applications, P. Erdi, G. Lente. Springer (2014
Method for finding metabolic properties based on the general growth law. Liver examples. A General framework for biological modeling
We propose a method for finding metabolic parameters of cells, organs and
whole organisms, which is based on the earlier discovered general growth law.
Based on the obtained results and analysis of available biological models, we
propose a general framework for modeling biological phenomena and discuss how
it can be used in Virtual Liver Network project. The foundational idea of the
study is that growth of cells, organs, systems and whole organisms, besides
biomolecular machinery, is influenced by biophysical mechanisms acting at
different scale levels. In particular, the general growth law uniquely defines
distribution of nutritional resources between maintenance needs and biomass
synthesis at each phase of growth and at each scale level. We exemplify the
approach considering metabolic properties of growing human and dog livers and
liver transplants. A procedure for verification of obtained results has been
introduced too. We found that two examined dogs have high metabolic rates
consuming about 0.62 and 1 gram of nutrients per cubic centimeter of liver per
day, and verified this using the proposed verification procedure. We also
evaluated consumption rate of nutrients in human livers, determining it to be
about 0.088 gram of nutrients per cubic centimeter of liver per day for males,
and about 0.098 for females. This noticeable difference can be explained by
evolutionary development, which required females to have greater liver
processing capacity to support pregnancy. We also found how much nutrients go
to biomass synthesis and maintenance at each phase of liver and liver
transplant growth. Obtained results demonstrate that the proposed approach can
be used for finding metabolic characteristics of cells, organs, and whole
organisms, which can further serve as important inputs for many applications in
biology (protein expression), biotechnology (synthesis of substances), and
medicine.Comment: 20 pages, 6 figures, 4 table
Decomposing Noise in Biochemical Signaling Systems Highlights the Role of Protein Degradation
AbstractStochasticity is an essential aspect of biochemical processes at the cellular level. We now know that living cells take advantage of stochasticity in some cases and counteract stochastic effects in others. Here we propose a method that allows us to calculate contributions of individual reactions to the total variability of a system’s output. We demonstrate that reactions differ significantly in their relative impact on the total noise and we illustrate the importance of protein degradation on the overall variability for a range of molecular processes and signaling systems. With our flexible and generally applicable noise decomposition method, we are able to shed new, to our knowledge, light on the sources and propagation of noise in biochemical reaction networks; in particular, we are able to show how regulated protein degradation can be employed to reduce the noise in biochemical systems
Pseudo generators of spatial transfer operators
Metastable behavior in dynamical systems may be a significant challenge for a
simulation based analysis. In recent years, transfer operator based approaches
to problems exhibiting metastability have matured. In order to make these
approaches computationally feasible for larger systems, various reduction
techniques have been proposed: For example, Sch\"utte introduced a spatial
transfer operator which acts on densities on configuration space, while Weber
proposed to avoid trajectory simulation (like Froyland et al.) by considering a
discrete generator.
In this manuscript, we show that even though the family of spatial transfer
operators is not a semigroup, it possesses a well defined generating structure.
What is more, the pseudo generators up to order 4 in the Taylor expansion of
this family have particularly simple, explicit expressions involving no
momentum averaging. This makes collocation methods particularly easy to
implement and computationally efficient, which in turn may open the door for
further efficiency improvements in, e.g., the computational treatment of
conformation dynamics. We experimentally verify the predicted properties of
these pseudo generators by means of two academic examples
Stochastic Representations of Ion Channel Kinetics and Exact Stochastic Simulation of Neuronal Dynamics
In this paper we provide two representations for stochastic ion channel
kinetics, and compare the performance of exact simulation with a commonly used
numerical approximation strategy. The first representation we present is a
random time change representation, popularized by Thomas Kurtz, with the second
being analogous to a "Gillespie" representation. Exact stochastic algorithms
are provided for the different representations, which are preferable to either
(a) fixed time step or (b) piecewise constant propensity algorithms, which
still appear in the literature. As examples, we provide versions of the exact
algorithms for the Morris-Lecar conductance based model, and detail the error
induced, both in a weak and a strong sense, by the use of approximate
algorithms on this model. We include ready-to-use implementations of the random
time change algorithm in both XPP and Matlab. Finally, through the
consideration of parametric sensitivity analysis, we show how the
representations presented here are useful in the development of further
computational methods. The general representations and simulation strategies
provided here are known in other parts of the sciences, but less so in the
present setting.Comment: 39 pages, 6 figures, appendix with XPP and Matlab cod
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