Negative interactions and feedback regulations are required for transient cellular response

ABSTRACT Signal transduction is a process required to conduct information from a receptor to the nucleus. This process is vital for the control of cellular function and fate. The dynamics of

signaling activation and inhibition determine processes such as apoptosis, proliferation and differentiation. Thus, it is important to understand the factors modulating transient and

sustained response. To address this question, by applying mathematical approach we have studied the factors which can alter the activation nature of downstream signaling molecules. The

factors which we have investigated are loops (feed forward and feedback loops), cross-talk of signal transduction pathways and the change in the concentration of the signaling molecules.

Based on our results we conclude that among these factors feedback loop and the cross-talks which directly inhibit the target protein dominantly controls the transient cellular response.

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Open access 20 June 2024 INTRODUCTION Cells transmit and receive information through signal transduction process by controling the dynamics of the intracellullar signaling molecules

(SMs)1,2,3,4,5. The temporal dynamics of SMs plays critical roles in making cellular decisions5,6,7,8,9. For example, PC-12 cells after NGF treatment causes sustained Erk activation leads to

differentiation of the PC-12 cells, whereas transient Erk activation induces proliferation10. From the previous published data11,12,13,14,15, it appears that there are many important

diseases which arise due to aberrations in the signal transduction process. The critical point is the cellular response duration (nature) which seems to be directly linked to the cell-fate

decision10,16,17,18,19,20. Based on the nature of the cellular response (transient or sustained or partially adapted), the cells undergo apoptosis, proliferation, or differentiation10,18,19.

Thus, it is an important step in signal transduction process to understand the interaction of the signaling pathways resulting in transient or sustained cellular response. In the past, many

research groups have focused on the signal transduction pathways and investigated different factors which may play critical roles in controling the cellular response nature and finally the

cell-fate (or cell-fate decision)9,21,22,23. The factors which have been investigated so far are the rate of reactions24,25, network topology25, concentration of the SM26,27, feed forward

loops (FFLs), feedback loops (FBLs)21,22, or the cross-talk of the signal transduction pathways28,29,30,31,32,33,34,35. In biological systems, mainly four different types of cross-talks ((i)

concomitant signaling, (ii) collaborative signaling, (iii) direct signaling and (iv) amplification of signaling), have been reported31. Unlike to these previous works, we have started the

investigation of a minimal cascade to the complex signaling regulation by adding all the possible interactions in one model. Some of the FBLs22, FFLs36 and cross-talks28,29,31,37,38,39 have

been investigated in biological signaling. In addition to these previously studied possible regulations, we have included more possible FFLs (both positive and negative), FBLs (both positive

and negative), the combination of FFLs and FBLs and increased more cross-talk possibilities (both the cross-interactions between the cascades i.e., inhibition and activation) between the

linear cascades in one model and investigated their impact in controling the cellular response nature. From our results, we conclude that FBL and cross-talk plays critical role in

determining transient cellular response. This model will help to understand the cellular response nature, to further reveal the new interactions based on the desired output response and to

perturb the output response by targeting the specific SM. RESULTS As mentioned in the previous section, some of the FBLs, FFLs and cross-talks have been investigated in biological signaling.

In addition to these previously studied possible regulations, we have included more possible FFLs (both positive and negative), FBLs (both positive and negative), the combination of FFLs

and FBLs and increased more cross-talk possibilities (both the cross-interactions between the cascades i.e., inhibition and activation) between the linear cascades in one model (Figure 1 a,

b, c, d, e, f and g) and investigated their impact in controling the cellular response nature. The major difference between the previous works and our work is the investigation of the

combinations of different kinds of FFLs and FBLs and more cross-interactions between the signaling cascades in the presence and absence of FFLs and FBLs than the four positive cross-talks

(Figure 1g) reported by Ivaska J and Heino J28,29,30,31,34,40,41,42,43,44,45. In this model, the complex signaling networks have been simplified and represented as receptor level (R),

intracellular signaling level (ISM) and target level (TP). So that the effect of different kinds of interactions at different levels on the final cellular response nature can be studied. A

LINEAR CASCADE ALWAYS PRODUCES SUSTAINED CELLULAR RESPONSE Here, we have investigated the kinetics of the signaling molecules for linear cascade (a cascade without feed forward loop,

feedback loop and cross-talk between a pair of linear cascades) and linear cascades with feed forward loop and feedback loop (Figure 1 a, b, c and d). For this purpose, we have generated

linear cascades with different sets of kinetic parameters (_k__par_). In case of signaling networks, the unit of _k__par_ can be second−1 or minute−146. It is known that in general, the

signal transduction process is fast and can function on the timescale of seconds to minutes47. Throughout our work, we have written time instead of second or minute. Initially, _k__par_ were

randomly generated between 0.001 to 0.1. So, all the cascades have response kinetics close to zero (Figure 2a). Then, we have applied an evolutionary algorithm (EA)24,48 to evolve the

cascades. During the evolutionary period, we allowed the change in _k__par_ and the concentration level of SMs. In this period, the signaling cascade adapts the improved kinetic parameters

to produce better response. After analyzing the kinetics of the evolved networks, we observe that in a linear signaling cascade (without any FFL/FBL), the change in the kinetic parameters or

the concentration does not produce any transient response (Figure 2b, c and d). Increase in the concentration (SMs) or the kinetic parameter values leads to improved sustained response

(Figure 2b, c and d). Addition of a positive FFL in a signaling cascade (Figure 1c) does not change the cascade response and it remains sustained (Figure 2e, left) while the addition of a

negative FFL disturbs the output response. The addition of a negative FFL produces mixed response either as transient, or sustained, or complete blocking of the response (Figure 2e, right)

which means the activation pattern is not robust. Addition of FBL (positive or negative) leads to transient response (Figure 2f). Presence of one positive FFL and a positive FBL leads to

sustained response (Figure 2g, left), presence of one negative FFL and a negative FBL and one negative FFL and a positive FBL leads to transient response (Figure 2 g and h) and presence of

one positive FFL and a negative FBL does not change the sustained response to transient nature (Figure 2i). These FFL (positive or negative) and FBL (positive or negative) are from R to TP

or TP to R (Figure 1d). When we apply the FBL (positive or negative) and/or FFL (positive or negative) from R to ISM or ISM to R in a cascade, we always observe sustained output response

(Figure 2j). CONCOMITANT INHIBITION BETWEEN CASCADES DOMINANTLY PRODUCE TRANSIENT RESPONSE After analyzing the kinetics of signaling cascade response, we investigated the change in the

kinetics of the TP of the signaling cascade in the presence of different kinds of cross-talks known from biological system31. We have investigated their inhibitory forms (in biological

cross-talks the links between the cascades are activation) also for all the four cross-talks. We found that concomitant signaling (activation link between two cascade) leads to sustained

response (Figure 3a) and its inhibitory form produces transient response (Figure 3b). While all the three other kinds of cross-talks (collaborative, direct and signal amplification) between

the cascades help in producing stable sustained response (Figure 3 c, d, e, f, g and h) irrespective the nature (activation or inhibition) of the links between the cascade. In case of direct

signaling, inhibitory interaction between the two cascades leads to only one output response in cascade 1 and complete blockage of the output response of cascade 2 (Figure 3f) because here

input signal (S2) is blocked. INCREASE IN THE NUMBER OF INHIBITORY LINKS LEADS TO TRANSIENT RESPONSE OR COMPLETE BLOCKAGE OF THE OUTPUT RESPONSE Finally, we have investigated the effect of

all the possible interactions (FFL, FBL and cross-talks) in a single model. Here, we have two linear cascades in parallel without any cross-interaction. We have generated 200 sets of

parallel cascades and evolved them in parallel until 100 generations by allowing the rate of reactions (_k__par_) to change during evolutionary period to adapt new _k__par_ in order to

produce improved kinetic response. After 100 generations, all the new interactions were added one-by-one in a linear signaling cascade (Figure 1a) in each generation. In this work, first we

have started addition of negative interactions between two cascades, then FFL and FBL and finally the positive interactions between cascades. We observe that all the minimal cascades produce

sustained output response for all the six different (strength) input signals (Figure 4 a and b). In contrast, addition of new inhibitory interactions between the two cascades, FFL and FBL

leads to transient response which can be seen between generation 100 and 165 in Figure 4 a and b. The response nature has been shown in Figure 4c (for a linear cascade – where both the

cascades produce sustained output response before generation 100 (left – pathway 1 and right – pathway 2)). Since, in the beginning we add the interactions through which pathway 2 inhibits

pathway 1 so the output response of pathway 1 is transient and pathway 2 remains sustained (Figure 4d). When we add the interactions (inhibitory) between both the pathways then both the

pathways produce transient response or completely block the output response of both the pathways (Figure 4e). Addition of positive interactions between the cascades lead to the sustained

output response which can be seen in Figure 4 a and b after generation 165 and the kinetics of the output appears similar to Figure 4c. As far as the fitness of the cascades is concerned, as

long as the cascades are free from additional interactions, the fitness remain stable and stays at maximum (Figure 4f (left)) because the kinetics of all the cascades for all the input

signals easily crosses the threshold level and remain sustained. While addition of new inhibitory interactions between the cascades and the FFL and FBL shows fluctuation in the fitness

because the output response becomes either transient or does not crosses the threshold. We further investigated the change in the _k__par_. In linear cascade which has comparatively less

number of reactions so the mean of the _k__par_ is comparatively lower than the cascade with new interactions and the addition of new interactions in each generation leads to the gradual

increase in the _k__par_ (Figure 4f (right)). So, we conclude that the irrespective the response nature (sustained or transient) the _k__par_ increases but it does not affect the cellular

response nature. BISTABLE BEHAVIOR After analyzing the kinetics of the output response, we have also analyzed the bistable behavior49,50,51 for the output response (TPpp) of linear cascade

(without FFL, FBL, or cross-talk) and the cascade with FFL, FBL and cross-talk. We found that in case of a linear cascade and a cascade with positive FFL and a linear cascade with negative

FFL, the response is linear (Figure 5a). We observed bistable behavior for a cascade with FBL (positive/negative) and combination of FFL (positive/negative) and FBL (positive/negative)

(Figure 5 b, c, d, e and f). In case of negative cross-interaction between cascades with few exceptions (Figure 5g) the multistable response behavior appears to be dominant (most of the

successful evolved networks show multiple stable states) (Figure 5 h, I and j). DISCUSSION In this study, we have investigated the change in the output response nature (sustained or

transient) of the signaling cascade in the presence and absence of the FFL, FBL and cross-talks between two cascades. The cascade which we have used here, is similar to the MAPK cascade1.

Based on our data, we propose that transient signaling responses result from FBL and/or negative cross-interactions between signaling cascades. If the concentration of the TP is lower than

the concentration of the R and ISM and either FBL or negative cross-talks are present then all the cascade produce consistently transient output response. Irrespective of the concentration

of the signaling molecules, FFL and all the positive interactions (cross-talks) between the cascades lead to stable and sustained output response. The evolved networks in a stationary

population show stable activation pattern against the change in kinetic parameters for both signaling cascades (until generation 100) and addition of the positive interactions between the

signaling cascades (after generation 165 onwards) and the output response as sustained response. This suggests that this type of response is the generic cellular behavior when the presence

of a signal is sufficient information for a cell. While in the presence of inhibitory interactions between the signaling cascades and the cascade with FBL and the simultaneous presence of

FBL and FFL, the kinetics of the output response is always transient (if the concentration of the TP is less than R and ISM). The fitness of the cascades fluctuates significantly. This

suggests the transient response as the generic solution. If the concentration of R, ISM and TP is equal then the cascades with inhibitory cross-talks and the cascade with FBL or with

combination of FFL and FBL also produces the transient response but not all the cascades (with the exceptions of few cascades having sustained response). From previous

works21,22,23,31,52,53, some interesting facts about the effect of variation in the concentration of SMs, FBL, FFL and cross-talk of signaling pathways are known. Here, they have

investigated the role of change in the concentration of an individual molecule and not investigated in comparison to the other molecules involved in signaling. The FBL, FFL, or cross-talk of

pathways have been investigated individually and not in combination of FFL and FBL or cross-talk. Most of the complex and/or common diseases such as cancer, diabetes, obesity and asthma are

caused by defects in multiple genes and pathways. So, it is not surprising that the current one-target-one-compound approach in drug discovery and development has failed to deliver as many

efficacious medicines as expected in the post-genomic era15,37,54. In order to understand such complex diseases and find therapeutic solution, it appears to be promising point to understand

the signal transduction process from a simple linear cascade to a complex regulatory mechanism (a linear cascade with different loops and the cross-interactions of the cascade) of signaling

network. By applying this approach, we can selectively target the signaling molecules to get the desired output response and will help to target multiple signaling molecules. The advantage

of our model is that it will not only help to understand the effect of the variation in the concentration of the receptor molecules but also help to understand the impact of the

concentration of other signaling molecules (such as intermediate and effector molecules) involved in the signal transduction and will give an insight of the different additional regulations

such as FFL, FBL and cross-talk. These models can only be applied to those systems which are known to have such behavior, but often the exact behavior of the STNs is not known. Therefore,

the creation of a fitness function that encodes the task that a cell solves under certain experimental conditions, may be more beneficial in determining possible and likely behavior of the

underlying signaling cascades. CONCLUSION Based on our data, we conclude that the transient response is controlled by the FBL and the negative cross-interactions between the cascades. If the

concentration of the TP is lower than the concentration of the R and ISM and either FBL or negative cross-talks are present then all the cascade produce consistently transient output

response. Irrespective of the concentration of the signaling molecules, FFL and all the positive interactions (cross-talks) between the cascades lead to stable and sustained output response.

METHODS MODEL We have set up a signaling cascade which function in the similar way as MAPK signaling cascade works (Figure S1). This signaling cascade is divided into several different

levels of signaling such as receptor level (represented as R), intracellular signaling level (as ISM) and the target level represented as TP (the target proteins are those proteins which

communicate the information to the nucleus in the form of the output response). Then, we have added different kinds of loops and the cross-interactions (cross-talks) between two signaling

cascades at different levels of signaling. In the next step, we have created mass-action kinetic model by using the ordinary differential equations (ODEs) for all the molecules including the

complexes formed as result of chemical reaction. In simplified form, the temporal change in the concentration of the signaling components (SMs including the complexes formed) can be

represented as: After the calculation of the kinetics of the all the molecules (1), we have calculated the fitness of all the cascades. For all the calculations, we have used six different

input signals (_n__s_ = 6). The six different input signals (different in strength) were 0.0001, 0.001, 0.01, 0.1, 1 and 10. For each input signal (_n_), the kinetics of TP is tested whether

it exceeds the threshold level (_TL_). The threshold ( of the initial concentration of TP) is defined to be the relative fraction of double phosphorylated form of TP. In case of cascade

with or without FBL and FFL, If this double phosphorylated form of TP crosses the threshold level at any time point then the cascade is assigned a value 1.0 called fitness factor

(_F__factor_1) and _F__factor_2 = 0. In case of cross-talk of two cascades, in the similar way we check the kinetics of the double phosphorylated form of TP of both the cascades, if the

kinetics of cascade 1 crosses the threshold at any time point then we assign fitness factor (_F__factor_1) a value of 0.5 and if the kinetics of cascade 2 crosses the threshold at any time

point then we assign fitness factor (_F__factor_2) a value of 0.5 for cascade 2. After evaluating the kinetics for each cascade for all the six input signals (different in strength), we

calculate the fitness (_F_) by taking the mean of the fitness factors (_F__factor_1_and__F__factor_2) which can be represented as: WORK FLOW We have created a set of cascades (total number

of cascades 200) with randomly generated kinetic parameters (_k__par_) between 0.001 and 0.1. EA24,55 has been applied to evolve the signaling cascades. For each cascade, we have _F_. After

calculating _F_ of all the cascades (2), we select the best 50 cascades (successful cascades) based on higher _F_ values. In order to improve the response kinetics, these successful cascades

are allowed to adapt new _k__par_. Four copies of all these 50 cascades with updated _k__par_ are created to keep the total number of cascades equal in each iteration. All these processes

are repeated for 200 iterations. Each iteration is called as a generation. Sets of ODEs have been solved with MATLAB 7.9.0. ADDITIONAL INFORMATION MM and TB were supported in part by grants

from the German Ministry of Education and Research (BMBF FORSYS program) [0313922], the State of Sachsen-Anhalt (Dynamic Systems) [XD3639HP/0306] and the European Union (SYBILLA)

[HEALTH-F4-2008-201106]. No additional external funding received for this study. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of

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PLoS ONE 2, e434 (2007). Article  ADS  PubMed  PubMed Central  CAS  Google Scholar  Download references AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Institute of Molecular and Clinical

Immunology, Otto-von-Guericke University, 39120, Magdeburg, Germany Mohammad Mobashir, Tilo Beyer & Burkhart Schraven * Institute of Clinical Chemistry and Pathobiochemistry,

Otto-von-Guericke University, 39120, Magdeburg, Germany Thati Madhusudhan & Berend Isermann * Department of Immune Control, Helmholtz Centre for Infectious Disease (HZI), Inhoffenstrasse

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author publications You can also search for this author inPubMed Google Scholar * Berend Isermann View author publications You can also search for this author inPubMed Google Scholar * Tilo

Beyer View author publications You can also search for this author inPubMed Google Scholar * Burkhart Schraven View author publications You can also search for this author inPubMed Google

Scholar CONTRIBUTIONS M.M. carried out research design and performed study, data analysis and wrote main manuscript text and prepared figures. M.T. helped in designing research. B.I. helped

in designing research and contributed in manuscript writing. T.B. and B.S. designed research and contributed to write the manuscript. All authors read and approved the final manuscript.

ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing financial interests. ELECTRONIC SUPPLEMENTARY MATERIAL SUPPLEMENTARY INFORMATION S1: Minimal cascade and its reaction

details RIGHTS AND PERMISSIONS This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit

http://creativecommons.org/licenses/by/3.0/ Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE Mobashir, M., Madhusudhan, T., Isermann, B. _et al._ Negative Interactions and

Feedback Regulations Are Required for Transient Cellular Response. _Sci Rep_ 4, 3718 (2014). https://doi.org/10.1038/srep03718 Download citation * Received: 07 November 2013 * Accepted: 19

December 2013 * Published: 16 January 2014 * DOI: https://doi.org/10.1038/srep03718 SHARE THIS ARTICLE Anyone you share the following link with will be able to read this content: Get

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