Computational prediction and analysis of impact of the cross‐talks between JNK and P38 kinase cascades

Signal transduction is a complex protein signaling process with a rich network of multifunctional interactions that occur in a non‐linear fashion. Mitogen‐activated protein kinase (MAPK) signal transduction pathways regulate diverse cellular processes ranging from proliferation and differentiation to apoptosis. In mammals, out of five, there are three well characterized subfamilies of MAPKs ‐ ERKs (Extracellular signal‐regulated kinases), JNKs (c‐Jun N‐terminal kinases), and P38 kinases, and their activators, are implicated in human diseases and are targets for drug development. Kinase cascades in MAPK pathways mediate the sensing and processing of stimuli. To understand how cells makes decisions, the dynamic interactions of components of signaling cascades are important rather than just creating static maps. Based on enzyme kinetic reactions, we have developed a mathematical model to analyze the impact of the cross‐talks between JNK and P38 kinase cascades. Cross‐talks between JNK and P38 kinase cascades influence the activities of P38 kinases. Responses of the signals should be studied for network of kinase cascades by considering cross‐talks.


Background:
All cells receive and respond to signals from their environment, whether they live freely or are part of a tissue. Network of signaling pathways detect, amplify, and integrate diverse external signals to generate responses such as changes in enzyme activity, gene expression, or ion-channel activity to regulate virtually all aspects of cell behavior, including metabolism, movement, proliferation, survival, and differentiation.   The c-Jun N-terminal Kinases consist of three isoforms. JNK1 and JNK2 are the products of alternative splicing of a single gene and are expressed in many tissues, but JNK3 is specifically expressed in neuronal tissue brain. Members of the JNK family play crucial roles in regulating responses to environmental stress, radiation, and growth factors, and in neural development, inflammation, and apoptosis [5]. Four isoforms of P38 MAP kinase, P38α, P38β, P38γ and P38δ have been identified. The P38 MAPKs play an important role in asthma and autoimmunity in humans and are activated by numerous physical and chemical stresses, including hormones, UV irradiation, ischemia, cytokines including interleukin-1 and tumor necrosis factor, osmotic shock and heat shock [6].
In the processes of cellular signaling, protein-protein interactions play a central role. Protein kinases are enzymes that covalently attach phosphate to the side chain of serine, threonine, or tyrosine of specific proteins inside cells and protein phosphatases remove the phosphates that were transferred to the protein substrate by the kinase. In this manner, the action of MAPKs and protein phosphatases reciprocally and rapidly alter the behavior of cells as they respond to changes in their environment [6]. A MAPKKK that is activated by extra cellular stimuli phosphorylates a MAPKK on its serine and threonine residues, and then this MAPKK activates a MAPK through phosphorylation on its threonine and tyrosine residues and then this MAPKs phosphorylate specific serines of target protein substrates and regulate cellular activities ranging from gene expression, mitosis, movement, metabolism, and programmed cell death [6].

Methodology: Systems approach
Cataloguing and classification of signaling molecules will ultimately not suffice to reason out the function of signaling networks or functioning of cells [7], but by the integration of this information through mathematical modeling and subsequent simulation of "networks" of "pathways" composed of interacting (macro-) molecules. We depicts a set of structural relationships among its components of JNK and P38 Kinase cascades ( Figure 2) and therefore, demands to be converted into a set of mathematical equations that describe the temporal and spatial evolution of the system.

Dynamic pathway modeling
Differential equation models are well defined encodings of molecular interactions contributing towards the synthesis and degradation of a protein in the context of cell signaling. A basic assumption of this approach is that the cell presents a well-stirred biochemical reactor. It is known that, as the signal transfer between the cell surface and the nucleus occurs in a stepwise manner, a systems biologist will also think of a step by step biochemical reaction of the whole pathway with network systems of interacting signaling substances receiving inputs and engendering outputs We have used Adams-Bashforth numerical algorithm and MATLAB programming to simulate the system of differential equations. Availability of quantitative values for molar concentrations and reaction rate constants has been a bottleneck for the researchers who are interested to study the dynamic behavior of the signaling pathways for which pathway diagram alone deposited in the databases. Since the molar concentrations and reaction rate constants are not same in the cell types and organisms, we have assumed reasonable values for the parameters representing them in concurrence with the values used in the other MAPK pathway modeling works published in the journals. In this work, for the sack of analysis, we have considered only the plots which represent molar concentrations of the activated JNK and P38 kinases. The plots in (Figure 3) are obtained by simulating the system of equations (3a-3e under supplementary material) without cross-talk terms, which represents the dynamic model of JNK cascade. The plots in (Figure 4) are obtained by simulating the system of equations (3f-3l, see supplementary material) without cross-talk terms, which represents the dynamic model of P38 kinase cascade responses to unit-step input signals. The plots in (Figure 5) are obtained by simulating the system of equations (3a-3l, under supplementary material), which represents the dynamic model of JNK and P38 Kinase cascades with cross-talks, responses to unit-step input signals. We have observed that, the system representing the JNK and P38 Kinase cascades with cross -talks is robust in nature. For the range of input signals (1nM-5nM), the range of reaction rate constants (0.001nM/s -3nM/s), and the range of molar concentrations of kinases (100nM -300nM), the ultra sensitive / sustained / transient manner JNK and P38 Kinases activation doest not vary, only the time taken by the activated JNK's and P38's to reach the saturation is varying. Also, we have observed that, ultra sensitive and sustained manner of JNK2 and JNK3 activation and the transient manner of JNK1 activation does not get affected due to cross -talks. But, it is due to cross -talks, P38α kinases become inactivated, transiently activated P38β kinases reaches saturation earlier, and transiently activated P38γ kinases are activated in ultra sensitive and sustainable manner. In general, the sustained JNK2 and JNK3 activation might associate with apoptosis and the transient JNK1 activation might associate with survival [12]. Specifically, the sustained JNK2 and JNK3 activation in fibroblasts may result in a pro-apoptotic function and the transient JNK1 activation may result in proliferation [13]. The sustained P38γ kinases activation due to the cross -talks might mediate process like mitogenesis, cell fate induction [14], and may result in an anti-angiogenic phenotype that contributes to endothelial dysfunction [15]. Also, we have observed that, it is due to cross talks, the P38α kinases lost its functional role by not getting activated and P38β kinases activation become more transient.

Conclusion:
Cross-talks between JNK and P38 kinase cascades influence the activities of P38 kinases. Responses of the signals should be studied for network of kinase cascades by considering cross-talks.

Edited by P. Kangueane
If we assume that the total for all time t, we require only this one differential equation to model a signaling step [10]. In our model we have assumed Michaelis-Menten kinetics [11]. (2)

Modeling JNK and P38 kinase cascades with cross-talks
To model the entire JNK and P38 Kinase cascades with cross-talks (Figure 2), we have the following state variables representing the concentration of each protein involved in the system (Figure 2). Let u = ASK1, = TAB1 (TAK1 (Transforming growth factor-beta-activated kinase 1)binding protein 1), = TAB2 (TAK1 binding protein 2), x t x t x t and y t y t is constant for all t. Based on the reaction schemes described in (FigureS2 (a) -4(l)), a set of differential equations (3a)-(3l) have been developed to form the dynamic system, to analyze the impact of cross talks between the JNK and P38 Kinase cascades ( Figure 2). Km Km 9 1 1 1 10 2 1 1 9 1 10 1 1 9 1 1 1 0 1 1 9 1 1 0 1

dy t k y t y y t c u y y t k y t c y t h dt
Km y y t Cm y y t K m y t C m y t