These chemicals can come from distant locations in the body (endocrine signaling by hormones), from nearby cells (paracrine signaling) or can even be secreted by the same cell (autocrine signaling). Funded by the U.S. Department of Education, CollegeCost Reduction and Access(CCRAA) grant award# P031C080096. In this model, induction of the output species E is a two-step process: An input u increases the amount of species R, which in turn influences E as E=gR. Importantly, upregulation of membrane synthesis restored the slow rate of nuclear growth resulting from loss of ndc1 but not from loss of nup53.
Recombinant human Wnt3A was purchased from Fisher Scientific (5036WN), and recombinant human EGF was purchased from Sigma (E9644). Finally, the analytical expressions we derived in this study not only reveal linear signal transmission, but also the mechanisms by which it arises. To avoid this confusion, we now described it more clearly in the manuscript that we considered how the analytical solutions behaved in a physiologically relevant parameter regime i.e., the values of parameters that have been measured or estimated in specific biological contexts. This means that relates to the amount of unphosphorylated Smad2 in the same sense that u relates to nuclear Smad complex. Indeed, for the signaling pathways studied here, it has been shown experimentally that the robust outcome of ligand stimulation is the fold-change in the level of transcriptional regulator (Goentoro and Kirschner, 2009; Cohen-Saidon et al., 2009; Lee et al., 2014; Frick et al., 2017). 2008 (Richard et al., 2008) identified negative feedback by Fus3 acting on Sst2, a yeast GAP protein. The authors used modeling and then experiment to show linear input-output relations in several model signaling pathways, which were the canonical Wnt, ERK, and Tgf- pathways. Testing the results experimentally, we present direct measurements of linear input-output behavior in the Wnt and ERK pathways.
Once bound and activated by the signal molecule, the activated receptor can initiate a cellular response, such as a change in gene expression. The relative magnitudes of , , , and indicate how the Raf pool partitions during signaling (Equations A21, A29A31). (D) As in (B), but measurements were performed in H1299 cells expressing mutant Raf S289/296/301A.
This includes the models having sufficient accuracy over both the parameter and time ranges that are considered. In the Tgf pathway (D), the output is regulated through continual nucleocytoplasmic shuttling. As illustrated in Figure 2A, Kis are equilibrium dissociation constants, kis are rate constants, and vis are synthesis rates. Cells encountering stressful situations activate the integrated stress response (ISR) pathway to limit protein synthesis and redirect translation to better cope.
Each relay molecule in the signal transduction pathway changes the next molecule in the pathway. To derive an analytical expression for the ERK pathway, we used a variable elimination technique developed for networks of mass action kinetics (Feliu and Wiuf, 2012). 3D-EM tomography of reforming and expanded NEs establishes that Ndc1 determines NPC density. Indeed, in the Wnt pathway, we not only observed linearity, but also that it is unexpectedly more strongly maintained in the cells than the model predicts. To confirm the effects reported, we verified that quantitation of the same sample loaded in multiple lanes in a gel gives CV<10%, and quantitation of the same sample across multiple independent gels gives CV<10% (Figure 3figure supplement 7).
As long as the model operates in the regime of linear signal transmission (i.e. Switch-like response in the ERK model could be achieved by decreasing or increasing , both amount to weakening the negative feedback. by inhibiting the destruction complex) will break the futile cycle (grey line, Figure 2D). Assessing the dynamic range of the input as before (04 ng/mL EGF), we now found that dpERK responds nonlinearly to EGF dose (blue circles, Figure 3D), consistent with model predictions (grey line, Figure 3D). We have now revised the misleading phrase into measured parameters in (the name of the specific systems), physiologically relevant parameter ranges, or some physiological contexts. For each gel, we normalize the unstimulated sample (i.e. However, we know that natural pathways can convey inputs varying across multiple orders of magnitude, forexample, vision. We agree with the editor and reviewers that this gives a misleading impression that we have information about the parameter ranges across all biological contexts.
In fact, not only can the linear dose response be observed, it appears rather robust to perturbations until you exceed some critical value.
Here we utilize a toy model to illustrate how ultrasensitivity and strong negative feedback combine to generate input-output linearity. We utilize the fact that the differential equations for A, B, and C are first-order and homogenous with respect to our cut, and rewrite them in matrix form. Using the variable elimination techniques in section Variable Elimination, we identify the following cut set: This allows us to express the steady-state concentration of pRaf as a function of parameters, and the remaining species in the ERK pathway. It would be interesting to further probe the generality of linear signal transmission. Finally, for each antibody used in the study, we did careful characterization of the linear range, and verified that our measurement conditions were within the linear range of the antibody. Below, we describe our analysis of each pathway and the unifying behavior that emerges from all three pathways. Source codes for the numerical simulations in Figure 2DF (grey and black lines) are available in Figure 2source code 1. Why evolve complexity in signaling pathways only to produce seemingly simple behavior? Membrane receptorsfunction by binding the signal molecule (ligand) and causing the production of a second signal (also known as a second messenger) that then causes a cellular response. Shaded in purple is the region of the response with L1-norm < 0.1. To score the validity of nonlinear model fits for Figure 3D, we used the bias-corrected Akaike Information Criterion as described in ref. We therefore would love to have the manuscript reconsidered, as we believe eLife would provide a good home for reaching the suitable audience for the work. Numerical simulations of a well-established NF-B model (50) over the range of nuclear NF-B translocation observed in human epithelial cells (51) reveal that the peak of the nuclear NF-B pulse correlates linearly with ligand concentration (Figure 2figure supplement 7).. Shown in the subplot are the same least squares regression line (solid line), overlaid with the model prediction (dashed line). We have now made this more obvious in Figure 3 and the legend. Nevertheless, we would like to understand the physical significance of the parameter groups.
While quantitative assessment of single-cell dynamics is now increasingly done, double quantitation of input-output in single cells is still technically challenging.
The modeling started with established ODE-based models and reduced them to simplified analytical expressions that related output to input; these expressions did not show linear relationships in general but did in physiologically relevant parameter regimes. We began our analysis using established models of the Wnt (Lee et al., 2003), ERK (Sturm et al., 2010), and Tgf (Schmierer et al., 2008) pathways. Accurate information transmission through dynamic biochemical signaling networks, An evaluation of R2 as an inadequate measure for nonlinear models in pharmacological and biochemical research: a Monte Carlo approach, Cis-interactions between Notch and Delta generate mutually exclusive signalling states, https://doi.org/10.1101/cshperspect.a007898, Cell-specific responses to the cytokine TGF are determined by variability in protein levels, The mammalian MAPK/ERK pathway exhibits properties of a negative feedback amplifier, https://doi.org/10.1126/scisignal.2001212, Localization of planarian -CATENIN-1 reveals multiple roles during anterior-posterior regeneration and organogenesis, A mechanism for Wnt coreceptor activation, https://doi.org/10.1016/S1097-2765(03)00484-2, Reliable encoding of stimulus intensities within random sequences of intracellular Ca2+ spikes, https://doi.org/10.1126/scisignal.2005237, Using optogenetics to interrogate the dynamic control of signal transmission by the Ras/Erk module, https://doi.org/10.1016/j.cell.2013.11.004, Controlling long-term signaling: receptor dynamics determine attenuation and refractory behavior of the TGF- pathway, https://doi.org/10.1126/scisignal.2004416, Information transfer by leaky, heterogeneous, protein kinase signaling systems, The self-limiting dynamics of TGF- signaling in silico and in vitro, with negative feedback through PPM1A upregulation, https://doi.org/10.1371/journal.pcbi.1003573, Dynamics of TGF- signaling reveal adaptive and pulsatile behaviors reflected in the nuclear localization of transcription factor Smad4, Stimulus-coupled spatial restriction of extracellular signal-regulated kinase 1/2 activity contributes to the specificity of signal-response pathways, https://doi.org/10.1128/MCB.24.23.10145-10150.2004, An ancient role for nuclear -catenin in the evolution of axial polarity and germ layer segregation, Nucleocytoplasmic shuttling of signal transducers, The extracellular signal-regulated kinase: multiple substrates regulate diverse cellular functions, https://doi.org/10.1080/02699050500284218, Negative feedback that improves information transmission in yeast signalling, A dual-kinase mechanism for Wnt co-receptor phosphorylation and activation, Initiation of Wnt signaling: control of Wnt coreceptor Lrp6 phosphorylation/activation via frizzled, dishevelled and axin functions, Signaling Systems: Transferring information without distortion, The integrated stress response remodels the microtubule-organizing center to clear unfolded proteins following proteotoxic stress, Ndc1 drives nuclear pore complex assembly independent of membrane biogenesis to promote nuclear formation and growth, Dissociation of destructioncomplex(DC) by active Dvl, Dissociation constant for APC:axin binding, Dissociation constant for -catenin:DC binding, Rate of phosphorylated -catenin release from DC, Degradation rate of phosphorylated -catenin, Dissociation constant for -catenin:TCF binding, Dissociation constant for -catenin:APC binding, Total concentration of adenomatous polyposis coli, Total concentration of glycogen synthase kinase 3, APC*/axin*/GSK3(*denotesphosphorylated), Hyper-phosphorylation rate of Raf by ppERK, Hyper-phosphorylation rate of phosphorylated Raf by dpERK, Phosphorylated Raf bound to its phosphatase, Doubly-phosphorylated MEK bound to its phosphatase, Phosphorylated MEK bound to its phosphatase, Phosphorylated ERK bound to its phosphatase, Doubly-phosphorylated ERK bound to its phosphatase, Phosphorylated Raf bound to doubly-phosphorylated ERK, Hyper-phosphorylated Raf bound to its phosphatase, Algebraic Equations for conserved species, Aviv Regev, Broad Institute of MIT and Harvard, United States, Wenying Shou, Fred Hutchinson Cancer Research Center, United States, Steven S Andrews, Fred Hutchinson Cancer Research Center, United States. 10) What ranges on the theoretical plots do the experimental results correspond to? While we can tightly control technical variability, there are inevitable biologic differences, e.g., each plate of cells may have slightly different cell confluency, cell contact, cell cycle state and therefore slightly different receptivity to ligands. However, there are rigorous ways to measure linearity, based on the L1-norm, as described in PMID:19279212 and PMID:23385595, which should be cited.
Our results support the model requirement that strong negative feedback is critical to linear signal transmission in the ERK pathway.
flies have one EGF receptor whereas humans have four [Citri et al., 2003]), we focused on the conserved core pathway (Figure 1A). Parameters that do not appear in the parameter groups either drop out due to irreversible reaction steps (such as k10 and k11 in the Wnt pathway) or negligible (as indicated by ellipses). We also revised the legend to explain why certain parameters are not in the parameter groups (e.g., k11 describes an irreversible degradation of phosphorylated -catenin, and therefore does not affect the level of unphosphorylated -catenin we are solving for).
Recombinant human Wnt3A was purchased from Fisher Scientific (5036WN), and recombinant human EGF was purchased from Sigma (E9644). Finally, the analytical expressions we derived in this study not only reveal linear signal transmission, but also the mechanisms by which it arises. To avoid this confusion, we now described it more clearly in the manuscript that we considered how the analytical solutions behaved in a physiologically relevant parameter regime i.e., the values of parameters that have been measured or estimated in specific biological contexts. This means that relates to the amount of unphosphorylated Smad2 in the same sense that u relates to nuclear Smad complex. Indeed, for the signaling pathways studied here, it has been shown experimentally that the robust outcome of ligand stimulation is the fold-change in the level of transcriptional regulator (Goentoro and Kirschner, 2009; Cohen-Saidon et al., 2009; Lee et al., 2014; Frick et al., 2017). 2008 (Richard et al., 2008) identified negative feedback by Fus3 acting on Sst2, a yeast GAP protein. The authors used modeling and then experiment to show linear input-output relations in several model signaling pathways, which were the canonical Wnt, ERK, and Tgf- pathways. Testing the results experimentally, we present direct measurements of linear input-output behavior in the Wnt and ERK pathways.
Once bound and activated by the signal molecule, the activated receptor can initiate a cellular response, such as a change in gene expression. The relative magnitudes of , , , and indicate how the Raf pool partitions during signaling (Equations A21, A29A31). (D) As in (B), but measurements were performed in H1299 cells expressing mutant Raf S289/296/301A.
This includes the models having sufficient accuracy over both the parameter and time ranges that are considered. In the Tgf pathway (D), the output is regulated through continual nucleocytoplasmic shuttling. As illustrated in Figure 2A, Kis are equilibrium dissociation constants, kis are rate constants, and vis are synthesis rates. Cells encountering stressful situations activate the integrated stress response (ISR) pathway to limit protein synthesis and redirect translation to better cope.
Each relay molecule in the signal transduction pathway changes the next molecule in the pathway. To derive an analytical expression for the ERK pathway, we used a variable elimination technique developed for networks of mass action kinetics (Feliu and Wiuf, 2012). 3D-EM tomography of reforming and expanded NEs establishes that Ndc1 determines NPC density. Indeed, in the Wnt pathway, we not only observed linearity, but also that it is unexpectedly more strongly maintained in the cells than the model predicts. To confirm the effects reported, we verified that quantitation of the same sample loaded in multiple lanes in a gel gives CV<10%, and quantitation of the same sample across multiple independent gels gives CV<10% (Figure 3figure supplement 7).
As long as the model operates in the regime of linear signal transmission (i.e. Switch-like response in the ERK model could be achieved by decreasing or increasing , both amount to weakening the negative feedback. by inhibiting the destruction complex) will break the futile cycle (grey line, Figure 2D). Assessing the dynamic range of the input as before (04 ng/mL EGF), we now found that dpERK responds nonlinearly to EGF dose (blue circles, Figure 3D), consistent with model predictions (grey line, Figure 3D). We have now revised the misleading phrase into measured parameters in (the name of the specific systems), physiologically relevant parameter ranges, or some physiological contexts. For each gel, we normalize the unstimulated sample (i.e. However, we know that natural pathways can convey inputs varying across multiple orders of magnitude, forexample, vision. We agree with the editor and reviewers that this gives a misleading impression that we have information about the parameter ranges across all biological contexts.
In fact, not only can the linear dose response be observed, it appears rather robust to perturbations until you exceed some critical value.
Here we utilize a toy model to illustrate how ultrasensitivity and strong negative feedback combine to generate input-output linearity. We utilize the fact that the differential equations for A, B, and C are first-order and homogenous with respect to our cut, and rewrite them in matrix form. Using the variable elimination techniques in section Variable Elimination, we identify the following cut set: This allows us to express the steady-state concentration of pRaf as a function of parameters, and the remaining species in the ERK pathway. It would be interesting to further probe the generality of linear signal transmission. Finally, for each antibody used in the study, we did careful characterization of the linear range, and verified that our measurement conditions were within the linear range of the antibody. Below, we describe our analysis of each pathway and the unifying behavior that emerges from all three pathways. Source codes for the numerical simulations in Figure 2DF (grey and black lines) are available in Figure 2source code 1. Why evolve complexity in signaling pathways only to produce seemingly simple behavior? Membrane receptorsfunction by binding the signal molecule (ligand) and causing the production of a second signal (also known as a second messenger) that then causes a cellular response. Shaded in purple is the region of the response with L1-norm < 0.1. To score the validity of nonlinear model fits for Figure 3D, we used the bias-corrected Akaike Information Criterion as described in ref. We therefore would love to have the manuscript reconsidered, as we believe eLife would provide a good home for reaching the suitable audience for the work. Numerical simulations of a well-established NF-B model (50) over the range of nuclear NF-B translocation observed in human epithelial cells (51) reveal that the peak of the nuclear NF-B pulse correlates linearly with ligand concentration (Figure 2figure supplement 7).. Shown in the subplot are the same least squares regression line (solid line), overlaid with the model prediction (dashed line). We have now made this more obvious in Figure 3 and the legend. Nevertheless, we would like to understand the physical significance of the parameter groups.
While quantitative assessment of single-cell dynamics is now increasingly done, double quantitation of input-output in single cells is still technically challenging.
The modeling started with established ODE-based models and reduced them to simplified analytical expressions that related output to input; these expressions did not show linear relationships in general but did in physiologically relevant parameter regimes. We began our analysis using established models of the Wnt (Lee et al., 2003), ERK (Sturm et al., 2010), and Tgf (Schmierer et al., 2008) pathways. Accurate information transmission through dynamic biochemical signaling networks, An evaluation of R2 as an inadequate measure for nonlinear models in pharmacological and biochemical research: a Monte Carlo approach, Cis-interactions between Notch and Delta generate mutually exclusive signalling states, https://doi.org/10.1101/cshperspect.a007898, Cell-specific responses to the cytokine TGF are determined by variability in protein levels, The mammalian MAPK/ERK pathway exhibits properties of a negative feedback amplifier, https://doi.org/10.1126/scisignal.2001212, Localization of planarian -CATENIN-1 reveals multiple roles during anterior-posterior regeneration and organogenesis, A mechanism for Wnt coreceptor activation, https://doi.org/10.1016/S1097-2765(03)00484-2, Reliable encoding of stimulus intensities within random sequences of intracellular Ca2+ spikes, https://doi.org/10.1126/scisignal.2005237, Using optogenetics to interrogate the dynamic control of signal transmission by the Ras/Erk module, https://doi.org/10.1016/j.cell.2013.11.004, Controlling long-term signaling: receptor dynamics determine attenuation and refractory behavior of the TGF- pathway, https://doi.org/10.1126/scisignal.2004416, Information transfer by leaky, heterogeneous, protein kinase signaling systems, The self-limiting dynamics of TGF- signaling in silico and in vitro, with negative feedback through PPM1A upregulation, https://doi.org/10.1371/journal.pcbi.1003573, Dynamics of TGF- signaling reveal adaptive and pulsatile behaviors reflected in the nuclear localization of transcription factor Smad4, Stimulus-coupled spatial restriction of extracellular signal-regulated kinase 1/2 activity contributes to the specificity of signal-response pathways, https://doi.org/10.1128/MCB.24.23.10145-10150.2004, An ancient role for nuclear -catenin in the evolution of axial polarity and germ layer segregation, Nucleocytoplasmic shuttling of signal transducers, The extracellular signal-regulated kinase: multiple substrates regulate diverse cellular functions, https://doi.org/10.1080/02699050500284218, Negative feedback that improves information transmission in yeast signalling, A dual-kinase mechanism for Wnt co-receptor phosphorylation and activation, Initiation of Wnt signaling: control of Wnt coreceptor Lrp6 phosphorylation/activation via frizzled, dishevelled and axin functions, Signaling Systems: Transferring information without distortion, The integrated stress response remodels the microtubule-organizing center to clear unfolded proteins following proteotoxic stress, Ndc1 drives nuclear pore complex assembly independent of membrane biogenesis to promote nuclear formation and growth, Dissociation of destructioncomplex(DC) by active Dvl, Dissociation constant for APC:axin binding, Dissociation constant for -catenin:DC binding, Rate of phosphorylated -catenin release from DC, Degradation rate of phosphorylated -catenin, Dissociation constant for -catenin:TCF binding, Dissociation constant for -catenin:APC binding, Total concentration of adenomatous polyposis coli, Total concentration of glycogen synthase kinase 3, APC*/axin*/GSK3(*denotesphosphorylated), Hyper-phosphorylation rate of Raf by ppERK, Hyper-phosphorylation rate of phosphorylated Raf by dpERK, Phosphorylated Raf bound to its phosphatase, Doubly-phosphorylated MEK bound to its phosphatase, Phosphorylated MEK bound to its phosphatase, Phosphorylated ERK bound to its phosphatase, Doubly-phosphorylated ERK bound to its phosphatase, Phosphorylated Raf bound to doubly-phosphorylated ERK, Hyper-phosphorylated Raf bound to its phosphatase, Algebraic Equations for conserved species, Aviv Regev, Broad Institute of MIT and Harvard, United States, Wenying Shou, Fred Hutchinson Cancer Research Center, United States, Steven S Andrews, Fred Hutchinson Cancer Research Center, United States. 10) What ranges on the theoretical plots do the experimental results correspond to? While we can tightly control technical variability, there are inevitable biologic differences, e.g., each plate of cells may have slightly different cell confluency, cell contact, cell cycle state and therefore slightly different receptivity to ligands. However, there are rigorous ways to measure linearity, based on the L1-norm, as described in PMID:19279212 and PMID:23385595, which should be cited.
Our results support the model requirement that strong negative feedback is critical to linear signal transmission in the ERK pathway.
flies have one EGF receptor whereas humans have four [Citri et al., 2003]), we focused on the conserved core pathway (Figure 1A). Parameters that do not appear in the parameter groups either drop out due to irreversible reaction steps (such as k10 and k11 in the Wnt pathway) or negligible (as indicated by ellipses). We also revised the legend to explain why certain parameters are not in the parameter groups (e.g., k11 describes an irreversible degradation of phosphorylated -catenin, and therefore does not affect the level of unphosphorylated -catenin we are solving for).