3,069 research outputs found
Mathematics at the eve of a historic transition in biology
A century ago physicists and mathematicians worked in tandem and established
quantum mechanism. Indeed, algebras, partial differential equations, group
theory, and functional analysis underpin the foundation of quantum mechanism.
Currently, biology is undergoing a historic transition from qualitative,
phenomenological and descriptive to quantitative, analytical and predictive.
Mathematics, again, becomes a driving force behind this new transition in
biology.Comment: 5 pages, 2 figure
Quantitative Analysis of the Effective Functional Structure in Yeast Glycolysis
Yeast glycolysis is considered the prototype of dissipative biochemical
oscillators. In cellular conditions, under sinusoidal source of glucose, the
activity of glycolytic enzymes can display either periodic, quasiperiodic or
chaotic behavior.
In order to quantify the functional connectivity for the glycolytic enzymes
in dissipative conditions we have analyzed different catalytic patterns using
the non-linear statistical tool of Transfer Entropy. The data were obtained by
means of a yeast glycolytic model formed by three delay differential equations
where the enzymatic speed functions of the irreversible stages have been
explicitly considered. These enzymatic activity functions were previously
modeled and tested experimentally by other different groups. In agreement with
experimental conditions, the studied time series corresponded to a
quasi-periodic route to chaos. The results of the analysis are three-fold:
first, in addition to the classical topological structure characterized by the
specific location of enzymes, substrates, products and feedback regulatory
metabolites, an effective functional structure emerges in the modeled
glycolytic system, which is dynamical and characterized by notable variations
of the functional interactions. Second, the dynamical structure exhibits a
metabolic invariant which constrains the functional attributes of the enzymes.
Finally, in accordance with the classical biochemical studies, our numerical
analysis reveals in a quantitative manner that the enzyme phosphofructokinase
is the key-core of the metabolic system, behaving for all conditions as the
main source of the effective causal flows in yeast glycolysis.Comment: Biologically improve
Graph Theory and Networks in Biology
In this paper, we present a survey of the use of graph theoretical techniques
in Biology. In particular, we discuss recent work on identifying and modelling
the structure of bio-molecular networks, as well as the application of
centrality measures to interaction networks and research on the hierarchical
structure of such networks and network motifs. Work on the link between
structural network properties and dynamics is also described, with emphasis on
synchronization and disease propagation.Comment: 52 pages, 5 figures, Survey Pape
CANA: A python package for quantifying control and canalization in Boolean Networks
Logical models offer a simple but powerful means to understand the complex
dynamics of biochemical regulation, without the need to estimate kinetic
parameters. However, even simple automata components can lead to collective
dynamics that are computationally intractable when aggregated into networks. In
previous work we demonstrated that automata network models of biochemical
regulation are highly canalizing, whereby many variable states and their
groupings are redundant (Marques-Pita and Rocha, 2013). The precise charting
and measurement of such canalization simplifies these models, making even very
large networks amenable to analysis. Moreover, canalization plays an important
role in the control, robustness, modularity and criticality of Boolean network
dynamics, especially those used to model biochemical regulation (Gates and
Rocha, 2016; Gates et al., 2016; Manicka, 2017). Here we describe a new
publicly-available Python package that provides the necessary tools to extract,
measure, and visualize canalizing redundancy present in Boolean network models.
It extracts the pathways most effective in controlling dynamics in these
models, including their effective graph and dynamics canalizing map, as well as
other tools to uncover minimum sets of control variables.Comment: Submitted to the Systems Biology section of Frontiers in Physiolog
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