Quarterly Biology Report, 1956, Vol. 8 no. 4

Reporting on fishing to waterfowl of the state of Iowa is in this quarter biology report. Reports include census of fish in lakes, ponds, streams in Iowa. Also a count of upland birds, raccoons and waterfowl is included in this report

Random Parameter Sampling of a Generic Three-Tier MAPK Cascade Model Reveals Major Factors Affecting Its Versatile Dynamics

<div><p>The mitogen-activated protein kinase (MAPK) pathway is considered to be a central block in many biological signaling networks. Despite the common core cascade structure, the activation of MAPK in different biological systems can exhibit different types of dynamic behaviors. Computer modeling may help to reveal the mechanisms underlying such variations. However, so far most computational models of the MAPK cascade have been system-specific, or to reflect a particular type among the wide spectrum of possible dynamics. To obtain a general and integrated view of the relationship between the dynamics of MAPK activation and the structures and parameters of the MAPK cascade, we constructed a generic model by comparing previous models covering different specific biological systems. We assumed that reliable qualitative results could be predicted through a qualitative model with pseudo parameters. We used randomly sampled parameters instead of a specific set of “best-fit” parameters to avoid biases towards any particular systems. A range of dynamics behaviors for MAPK activation, including ultrasensitivity, bistability, transient activation and oscillation, were successfully predicted by the generic model. The results indicated that the steady state dynamics (ultrasensitivity and bistability) was jointly determined by the three-tiered structure of the MAPK cascade and the competitive substrate binding in the dual-phosphorylation processes of the central components, while the temporal dynamics (transient activation and oscillation) was mainly affected by the upstream signaling pathway and feedbacks. Moreover, MAPK kinase (MAPKK) played more important roles than the other two components in determining the dynamics of MAPK activation. We hypothesize that this is an important and advantageous property for the regulation and for the functional diversity of MAPK pathways in real cells. Finally, to assist developing generic models for signaling motifs through model comparisons, we proposed a reaction-based database to make the model data more flexible and interoperable.</p> </div

Correlation coefficients between [MAPKK]_total and <i>Gradient</i>/Signal Range.

a<p><i>Gradient</i> is an indicator for ultrasensitivity (see text).</p>b<p>Signal range from the beginning to the end (maximum) of MAPKK activation.</p>c<p>Sample sets grouped by <i>Gradients.</i><b>Low</b>: samples having <i>Gradients</i> between (1.0, 10.0), representing “low ultrasensitivity”; <b>Medium</b>: samples having <i>Gradients</i> between (10.0, 100.0), representing “medium ultrasensitivity”; <b>High</b>: samples having <i>Gradients</i> larger than 100.0, representing “high ultrasensitivity”.</p>d<p>Correlation coefficients between [MAPKK]_total (total concentration of MAPKK) and <i>Gradient</i> or Signal range.</p

A schematic drawing summarizing the topologies of the MAPK activation network studied by previous models.

<p>The numbers are numeric IDs of the models as they are referred in the text and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0054441#pone-0054441-t001" target="_blank">Table 1</a>. The prefix ‘p-’ means phosphorylated and ‘pp-’ means dual-phosphorylated.</p

Number of (absolutely) bistable models obtained with different concentration vectors under different network topologies.

<p>Number of (absolutely) bistable models obtained with different concentration vectors under different network topologies.</p

Case Study on Temperature-Accelerated Molecular Dynamics Simulation of Ligand Dissociation: Inducer Dissociation from the Lac Repressor Protein

We studied ligand dissociation from the inducer-binding domain of the Lac repressor protein using temperature-accelerated molecular dynamics (TAMD) simulations. With TAMD, ligand dissociation could be observed within relatively short simulation time. This allowed many dissociation trajectories to be sampled. Under the adiabatic approximation of TAMD, all but one degree of freedom of the system were sampled from usual canonical ensembles at room temperature. Thus, meaningful statistical analyses could be carried out on the trajectories. A systematic approach was proposed to analyze possible correlations between ligand dissociation and fluctuations of various protein conformational coordinates. These analyses employed relative entropies, allowing both linear and nonlinear correlations to be considered. Applying the simulation and analysis methods to the inducer binding domain of the Lac repressor protein, we found that ligand dissociation from this protein correlated mainly with fluctuations of side-chain conformations of a few residues that surround the binding pocket. In addition, the two binding sites of the dimeric protein were dynamically coupled: occupation of one site by an inducer molecule could significantly reduce or slow down conformational dynamics around the other binding pocket

The topology of the generic model for MAPK activation.

<p>The presence or absence of the two probable feedbacks depends on the chosen kinetic parameters. In choosing the parameters, we applied the constraints that a particular parameter set can lead to either no feedback or the presence of only one of the feedbacks, but not the simultaneous presence of both feedbacks. In the Figure, the prefix p- means phosphorylated and pp- means dual-phosphorylated.</p

Number of kinetic parameter vectors (vertical axis) that, when combined with 36 concentration vectors, lead to responsive models in more than 30 cases.

<p>The total 160 kinetic parameter vectors are grouped by different ratios (horizontal axis) of (a) various association rates (kbN and kb-N) over the corresponding dissociation rates (kdN and kd-N), and (b) various activation rates (kN) over the corresponding deactivation rate (k-N).</p

The numbers of bistable models obtained for different phosphorylation rates (horizontal axis).

<p>(a) Absolutely bistable models (<i>Bistability</i>>9.5); (b) Bistable models (<i>Bistability</i>>1.5).</p

Number of kinetic parameter vectors (vertical axis) that lead to large <i>Gradient</i> (<i>Gradient</i>>400) for MAPK activation (see text).

<p>As in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0054441#pone-0054441-g003" target="_blank">Figure 3</a>, the numbers are shown for different ratios (horizontal axis) of (a) various association rates (kbN and kb-N) over the respective dissociation rates (kdN and kd-N), and (b) various activation rates (kN) over the respective deactivation rate (k-N).</p