Sarma U and Ghosh I (2012). Design of kinase-phosphatase interactions and phosphatase sequestration shape MAPK cascade robustness and signal flow.
One of the major developments in network biology is the study of the topological properties of systems . The topology of a graph is determined by the manner in which its components are connected. Linking the same set of nodes in different ways can lead to the network behaving differently, hence it is important to understand the topological properties of biological networks. Sarma and Ghosh  computationally analyse different architectures of kinase-phosphatase interactions and assess the impact topology has on a network's ability to maintain function under perturbations, a characteristic known as network robustness. The authors conclude that the design of kinase-phosphate interactions and phosphatases' sequestration influence the robustness profile of the system. In addition, this study identifies an implicit system-level negative feedback loop (BIOMD0000000433), from the phosphatase Dual specificity protein phosphatase 6 (DUSP6, MKP3 or Phos2) to the top layer kinase MKKKK, RAF proto-oncogene serine/threonine-protein kinase (RAF1 or Raf-1). Thus, enhancement or reduction in the concentration of Phos2 reciprocally modulates the amplitude of phosphorylated MKKK. The robustness provided by a strong phosphatase sequestration is suggested as a plausible cellular strategy for sustained signal response upon perturbation.
As a starting point, four systems representing the MAPK cascade are described here. These models (BIOMD0000000430 to BIOMD0000000433) have the same kinase-kinase interactions but different kinases-phosphatases interactions. Moreover, they come from different species such as Xenopus oocytes , Chines hamster Ovary expressing ErbB-4 , NIH-3 T mouse fibroblasts [5, and B cells .
Figure 1. Model 1 to 4, corresponding to BIOMD0000000430 to BIOMD0000000433, of the same MAPK cascade signaling. Phos-n are the different phosphorylases participating in the MAPK kinases signaling. Figures adapted from .
Two types of modelling techniques were used to investigate the robustness of MAPK cascade output: Michaelis-Menten type kinetics (K1) and elementary mass action kinetics (K2). For K1, the different interaction designs of models BIOMD0000000430 to BIOMD0000000433 assume steady-state in the various enzyme-substrate complexes. K1 requires the derivation of flux equations for phosphorylation and de-phosphorylation which capture the system specific flow of signal. On the other hand, no assumptions are made while capturing the dynamics of the systems in Model 1 to Model 4 (BIOMD0000000430 to BIOMD0000000433) when K2 is used. For K2, derivation of the flux equations is required and the signal flow is from the interactions among the kinases and phosphatases. The authors highlight that BIOMD0000000431, BIOMD0000000432 and BIOMD0000000433 systems have two phosphatases whereas BIOMD0000000430 has three (Figure 1).
Independent parameter sets were adopted for models K1 and K2. Despite parametric differences, the MAPK cascade's robustness and signal response behavior depend on the designs of interactions among its kinases and phosphatases. Furthermore, the K2 models are compared with another K2 model which assumes a quasi-steady state (K2_QSS), showing that the signal response behavior and robustness are preserved in both cases. Finally, the perturbations of these systems were applied as global changes where a set of values of all perturbed parameters were randomly selected from the sample space chosen. The robustness coefficient was obtained after running 5000 simulations for each individual case study.
Figure 2. Figure 2.A to 2.D. - Implicit negative feedback loop from DUSP6 (Phos2) to MKKK layer in the system BIOMD0000000433 K2 and BIOMD0000000433 K2_QSS (Quasi steady-state). (A) Kinetics of MKKK-P in BIOMD0000000433 K2 for a low (5 nM) and a high (1000 nM) Phos2 concentration is shown for unsequestrated (USEQ) condition. (B) Kinetics of MKKK-P in BIOMD0000000433 K2 for a low (5 nM) and a high (1000 nM) Phos2 concentration is shown for phosphatase sequestrated (PSEQ) condition. (C) Kinetics of MKKK-P in BIOMD0000000433 K2_QSS for a low (5 nM) and a high (1000 nM) Phos2 concentration is shown for unsequestrated (USEQ) condition. (D) Kinetics of MKKK-P in BIOMD0000000433 K2_ QSS for a low (5 nM) and a high (1000 nM) Phos2 concentration is shown for phosphatase sequestrated (PSEQ) condition. Figures adapted from .
Under un-sequestrated phosphatase conditions, the systems BIOMD0000000430 to BIOMD0000000433 maintain the robustness of the MAPK cascade. This is demonstrated by a comparison of the significance of rewiring connections between the kinases and phosphatases. An implicit negative feedback loop from Phos2 controls the amplitude of MKKK-P in the MAPK cascade (BIOMD0000000433). In general terms, the effect of phosphatase sequestration shields the negative regulation of MKKK-P by Phos2 (Figure 2: A to D shows the behavior over time of different concentrations of kinases at different conditions in models K2). Additionally, the strength of this implicit negative feedback loop is reciprocally controlled by the strength of phosphatases sequestration. Furthermore, the authors propose an experimental verification of this loop by building a synthetic MAPK cascade. They predict that inhibition and overexpression of DUSP6 should minimally alter the RAF-1-P amplitude if the in vivo system is strongly sequestrated. In addition to all the analyses mentioned above, which consider the signal duration as a sustained quantity, another comparison is established using stimuli of transient type. The different architecture of interactions between kinase-phosphatases differentially defines the memory of an input signal. Memory of a signalling pathway is defined as the time taken by the cascade output to reach its unstimulated level after the removal of the signal. The system with minimum memory in the un-sequestered condition (USEQ) has minimum memory in the phosphatase sequestered condition (PSEQ) and vice-versa. Additionally, a difference in the relative changes in the MK-PP duration between USEQ and PSEQ conditions is noticeable between K1 and K2 models. K2 models exhibit longer output memory than the K1 models for both conditions. These differences primarily arise due to a lesser number of steps travelled by the signal from the input to the output layer in the K1 model compared to the K2 models. In both USEQ and PSEQ conditions signal amplitude increases in similar directions in K1 and K2 models, until it reaches a saturation concentration. More phosphatases are sequestrated in fractions for lower input signal doses than for higher doses.
By merging computational models of four experimentally observed systems of interactions between kinases and phosphatases of the MAPK cascade, the authors define the robustness and signal response behavior associated with each of the designs. Results from models under K1 and K2 are not directly comparable, so the comparison is established between the four systems using one or other type of kinetics. First, the robustness of the output of MAPK cascades is a function of the design of interactions among the kinases and phosphatases and phosphatases' sequestration, with the latter enhancing the robustness in all the system types. It also reveals an implicit negative loop. The strength of this loop is evaluated in different conditions, USEQ and PSEQ. The authors suggest strategies to validate this experimentally. A system with high robustness, such as BIOMD0000000431 or BIOMD0000000433, in USEQ and PSEQ conditions also exhibits long signal memory, where PSEQ leads to enhanced output amplitude and memory compared to USEQ. Finally, the authors highlight that PSEQ conditions come with noisy signals but the strength of phosphatase sequestration, adopted by a cascade, would contribute towards adjusting its activation threshold and discriminate the noise from the signal in a context-dependent manner.
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