299 research outputs found
Simplicity of Completion Time Distributions for Common Complex Biochemical Processes
Biochemical processes typically involve huge numbers of individual reversible
steps, each with its own dynamical rate constants. For example, kinetic
proofreading processes rely upon numerous sequential reactions in order to
guarantee the precise construction of specific macromolecules. In this work, we
study the transient properties of such systems and fully characterize their
first passage (completion) time distributions. In particular, we provide
explicit expressions for the mean and the variance of the completion time for a
kinetic proofreading process and computational analyses for more complicated
biochemical systems. We find that, for a wide range of parameters, as the
system size grows, the completion time behavior simplifies: it becomes either
deterministic or exponentially distributed, with a very narrow transition
between the two regimes. In both regimes, the dynamical complexity of the full
system is trivial compared to its apparent structural complexity. Similar
simplicity is likely to arise in the dynamics of many complex multi-step
biochemical processes. In particular, these findings suggest not only that one
may not be able to understand individual elementary reactions from macroscopic
observations, but also that such understanding may be unnecessary
A rule-based kinetic model of RNA polymerase II C-terminal domain phosphorylation
The complexity ofmany RNA processing pathways is such that a conventional systemsmodelling approach is inadequate to represent all themolecular species involved. We demonstrate that rule-based modelling permits a detailed model of a complex RNA signalling pathway to be defined. Phosphorylation of the RNApolymerase II (RNAPII)C-terminal domain (CTD; a flexible tail-like extension of the largest subunit) couples pre-messenger RNA capping, splicing and 30 end maturation to transcriptional elongation and termination, and plays a central role in integrating these processes. The phosphorylation states of the serine residues of many heptapeptide repeats of the CTD alter along the coding region of genes as a function of distance from the promoter. From a mechanistic perspective, both the changes in phosphorylation and the location atwhich they take place on the genes are a function of the time spent byRNAPII in elongation as this interval provides the opportunity for the kinases and phosphatases to interactwith theCTD.On this basis,we synthesize the available data to create a kinetic model of the action of the known kinases and phosphatases to resolve the phosphorylation pathways and their kinetics.</p
Thermodynamic graph-rewriting
We develop a new thermodynamic approach to stochastic graph-rewriting. The
ingredients are a finite set of reversible graph-rewriting rules called
generating rules, a finite set of connected graphs P called energy patterns and
an energy cost function. The idea is that the generators define the qualitative
dynamics, by showing which transformations are possible, while the energy
patterns and cost function specify the long-term probability of any
reachable graph. Given the generators and energy patterns, we construct a
finite set of rules which (i) has the same qualitative transition system as the
generators; and (ii) when equipped with suitable rates, defines a
continuous-time Markov chain of which is the unique fixed point. The
construction relies on the use of site graphs and a technique of `growth
policy' for quantitative rule refinement which is of independent interest. This
division of labour between the qualitative and long-term quantitative aspects
of the dynamics leads to intuitive and concise descriptions for realistic
models (see the examples in S4 and S5). It also guarantees thermodynamical
consistency (AKA detailed balance), otherwise known to be undecidable, which is
important for some applications. Finally, it leads to parsimonious
parameterizations of models, again an important point in some applications
Toward a comprehensive language for biological systems
Rule-based modeling has become a powerful approach for modeling intracellular networks, which are characterized by rich molecular diversity. Truly comprehensive models of cell behavior, however, must address spatial complexity at both the intracellular level and at the level of interacting populations of cells, and will require richer modeling languages and tools. A recent paper in BMC Systems Biology represents a signifcant step toward the development of a unified modeling language and software platform for the development of multi-level, multiscale biological models
Kinetic Monte Carlo Method for Rule-based Modeling of Biochemical Networks
We present a kinetic Monte Carlo method for simulating chemical
transformations specified by reaction rules, which can be viewed as generators
of chemical reactions, or equivalently, definitions of reaction classes. A rule
identifies the molecular components involved in a transformation, how these
components change, conditions that affect whether a transformation occurs, and
a rate law. The computational cost of the method, unlike conventional
simulation approaches, is independent of the number of possible reactions,
which need not be specified in advance or explicitly generated in a simulation.
To demonstrate the method, we apply it to study the kinetics of multivalent
ligand-receptor interactions. We expect the method will be useful for studying
cellular signaling systems and other physical systems involving aggregation
phenomena.Comment: 18 pages, 5 figure
ALC: automated reduction of rule-based models
<p>Abstract</p> <p>Background</p> <p>Combinatorial complexity is a challenging problem for the modeling of cellular signal transduction since the association of a few proteins can give rise to an enormous amount of feasible protein complexes. The layer-based approach is an approximative, but accurate method for the mathematical modeling of signaling systems with inherent combinatorial complexity. The number of variables in the simulation equations is highly reduced and the resulting dynamic models show a pronounced modularity. Layer-based modeling allows for the modeling of systems not accessible previously.</p> <p>Results</p> <p>ALC (Automated Layer Construction) is a computer program that highly simplifies the building of reduced modular models, according to the layer-based approach. The model is defined using a simple but powerful rule-based syntax that supports the concepts of modularity and macrostates. ALC performs consistency checks on the model definition and provides the model output in different formats (C MEX, MATLAB, <it>Mathematica </it>and SBML) as ready-to-run simulation files. ALC also provides additional documentation files that simplify the publication or presentation of the models. The tool can be used offline or via a form on the ALC website.</p> <p>Conclusion</p> <p>ALC allows for a simple rule-based generation of layer-based reduced models. The model files are given in different formats as ready-to-run simulation files.</p
Timing molecular motion and production with a synthetic transcriptional clock
The realization of artificial biochemical reaction networks with unique functionality is one of the main challenges for the development of synthetic biology. Due to the reduced number of components, biochemical circuits constructed in vitro promise to be more amenable to systematic design and quantitative assessment than circuits embedded within living organisms. To make good on that promise, effective methods for composing subsystems into larger systems are needed. Here we used an artificial biochemical oscillator based on in vitro transcription and RNA degradation reactions to drive a variety of âloadâ processes such as the operation of a DNA-based nanomechanical device (âDNA tweezersâ) or the production of a functional RNA molecule (an aptamer for malachite green). We implemented several mechanisms for coupling the load processes to the oscillator circuit and compared them based on how much the load affected the frequency and amplitude of the core oscillator, and how much of the load was effectively driven. Based on heuristic insights and computational modeling, an âinsulator circuitâ was developed, which strongly reduced the detrimental influence of the load on the oscillator circuit. Understanding how to design effective insulation between biochemical subsystems will be critical for the synthesis of larger and more complex systems
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