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RaTrav: a tool for calculating mean first-passage times on biochemical networks.

Torchala M, Chelminiak P, Kurzynski M, Bates PA - BMC Syst Biol (2013)

Bottom Line: The RaTrav tool can then be applied in order to compute desired MFPTs.For the provided examples, we were able to find the favourable binding path within a protein-protein docking funnel and to calculate the degree of coupling for two chemical reactions catalysed simultaneously by the same protein enzyme.However, the list of possible applications is much wider.

View Article: PubMed Central - HTML - PubMed

Affiliation: Biomolecular Modelling Laboratory, Cancer Research UK London Research Institute, 44 Lincoln's Inn Fields, London WC2A 3LY, UK. Paul.Bates@cancer.org.uk.

ABSTRACT

Background: The concept of mean first-passage times (MFPTs) occupies an important place in the theory of stochastic processes, with the methods of their calculation being equally important in theoretical physics, chemistry and biology. We present here a software tool designed to support computational biology studies where Markovian dynamics takes place and MFPTs between initial and single or multiple final states in network-like systems are used. Two methods are made available for which their efficiency is strongly dependent on the topology of the defined network: the combinatorial Hill technique and the Monte Carlo simulation method.

Results: After a brief introduction to RaTrav, we highlight the utility of MFPT calculations by providing two examples (accompanied by Additional file 1) where they are deemed to be of importance: analysis of a protein-protein docking funnel and interpretation of the free energy transduction between two coupled enzymatic reactions controlled by the dynamics of transition between enzyme conformational states.

Conclusions: RaTrav is a versatile and easy to use software tool for calculating MFPTs across biochemical networks. The user simply prepares a text file with the structure of a given network, along with some additional basic parameters such as transition probabilities, waiting probabilities (if any) and local times (weights of edges), which define explicitly the stochastic dynamics on the network. The RaTrav tool can then be applied in order to compute desired MFPTs. For the provided examples, we were able to find the favourable binding path within a protein-protein docking funnel and to calculate the degree of coupling for two chemical reactions catalysed simultaneously by the same protein enzyme. However, the list of possible applications is much wider.

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The model network of conformational substates. The model network of stochastic transitions between conformational substates (nodes) corresponding to the shaded box M in Figure 3. Its structure displays both the scale-free topology, as well as the fractality [31]. The distinguished nodes (enlarged dots) symbolizes the gates which have been marked here in accordance with a system of labels used in Figure 3.
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Figure 4: The model network of conformational substates. The model network of stochastic transitions between conformational substates (nodes) corresponding to the shaded box M in Figure 3. Its structure displays both the scale-free topology, as well as the fractality [31]. The distinguished nodes (enlarged dots) symbolizes the gates which have been marked here in accordance with a system of labels used in Figure 3.

Mentions: Let us consider the shaded box shown in Figure 3 which represents the network of conformational substates of a protein macromolecule that catalyses simultaneously two, in general, reversible reactions: the free energy-donating reaction R1 ⇔ P1 and the free energy-accepting reaction R2 ⇔ P2. A model structure of such a network consisting of two hundred nodes is depicted in Figure 4. A set of distinguished transition states, called the gates, underscored by enlarged black nodes, corresponds directly to the system of labels used in Figure 3. For the sake of clarity, we have limited our calculations to a rather simple network of states displaying a tree-like topology, but much more complex networks of states can also be taken into account. In this context, the actual network can be thought of as a spanning tree, a loopless subnetwork consisting of edges with the highest transition probabilities per unit time between conformational substates.


RaTrav: a tool for calculating mean first-passage times on biochemical networks.

Torchala M, Chelminiak P, Kurzynski M, Bates PA - BMC Syst Biol (2013)

The model network of conformational substates. The model network of stochastic transitions between conformational substates (nodes) corresponding to the shaded box M in Figure 3. Its structure displays both the scale-free topology, as well as the fractality [31]. The distinguished nodes (enlarged dots) symbolizes the gates which have been marked here in accordance with a system of labels used in Figure 3.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4222613&req=5

Figure 4: The model network of conformational substates. The model network of stochastic transitions between conformational substates (nodes) corresponding to the shaded box M in Figure 3. Its structure displays both the scale-free topology, as well as the fractality [31]. The distinguished nodes (enlarged dots) symbolizes the gates which have been marked here in accordance with a system of labels used in Figure 3.
Mentions: Let us consider the shaded box shown in Figure 3 which represents the network of conformational substates of a protein macromolecule that catalyses simultaneously two, in general, reversible reactions: the free energy-donating reaction R1 ⇔ P1 and the free energy-accepting reaction R2 ⇔ P2. A model structure of such a network consisting of two hundred nodes is depicted in Figure 4. A set of distinguished transition states, called the gates, underscored by enlarged black nodes, corresponds directly to the system of labels used in Figure 3. For the sake of clarity, we have limited our calculations to a rather simple network of states displaying a tree-like topology, but much more complex networks of states can also be taken into account. In this context, the actual network can be thought of as a spanning tree, a loopless subnetwork consisting of edges with the highest transition probabilities per unit time between conformational substates.

Bottom Line: The RaTrav tool can then be applied in order to compute desired MFPTs.For the provided examples, we were able to find the favourable binding path within a protein-protein docking funnel and to calculate the degree of coupling for two chemical reactions catalysed simultaneously by the same protein enzyme.However, the list of possible applications is much wider.

View Article: PubMed Central - HTML - PubMed

Affiliation: Biomolecular Modelling Laboratory, Cancer Research UK London Research Institute, 44 Lincoln's Inn Fields, London WC2A 3LY, UK. Paul.Bates@cancer.org.uk.

ABSTRACT

Background: The concept of mean first-passage times (MFPTs) occupies an important place in the theory of stochastic processes, with the methods of their calculation being equally important in theoretical physics, chemistry and biology. We present here a software tool designed to support computational biology studies where Markovian dynamics takes place and MFPTs between initial and single or multiple final states in network-like systems are used. Two methods are made available for which their efficiency is strongly dependent on the topology of the defined network: the combinatorial Hill technique and the Monte Carlo simulation method.

Results: After a brief introduction to RaTrav, we highlight the utility of MFPT calculations by providing two examples (accompanied by Additional file 1) where they are deemed to be of importance: analysis of a protein-protein docking funnel and interpretation of the free energy transduction between two coupled enzymatic reactions controlled by the dynamics of transition between enzyme conformational states.

Conclusions: RaTrav is a versatile and easy to use software tool for calculating MFPTs across biochemical networks. The user simply prepares a text file with the structure of a given network, along with some additional basic parameters such as transition probabilities, waiting probabilities (if any) and local times (weights of edges), which define explicitly the stochastic dynamics on the network. The RaTrav tool can then be applied in order to compute desired MFPTs. For the provided examples, we were able to find the favourable binding path within a protein-protein docking funnel and to calculate the degree of coupling for two chemical reactions catalysed simultaneously by the same protein enzyme. However, the list of possible applications is much wider.

Show MeSH
Related in: MedlinePlus