Geometry parameters for the XCN (X=Cl, Br) molecules as used in equations (25) and (27)

<p><strong>Figure 1.</strong> Geometry parameters for the XCN (X=Cl, Br) molecules as used in equations (<a href="http://iopscience.iop.org/0953-4075/46/12/125101/article#jpb469975eqn25" target="_blank">25</a>) and (<a href="http://iopscience.iop.org/0953-4075/46/12/125101/article#jpb469975eqn27" target="_blank">27</a>).</p> <p><strong>Abstract</strong></p> <p>In this work, we present the four-component quadratic vibronic coupling model for the description of the Renner–Teller effect (RTE) in the presence of the spin–orbit coupling. The interaction of the two potential energy surfaces emerging from the cationic ²Π states of singly ionized linear triatomic molecules is described by the quadratic coupling constant <em>c</em> for the genuine RT repulsion and the second parameter, <em>d</em>, for a nonconstant spin–orbit coupling varying with the bond angle of the triatomic. The emergence of a linear RT constant in the presence of the spin–orbit operator was originally shown by Poluyanov and Domcke (2004 <em>Chem. Phys.</em> <strong>301</strong> 111–27) and is based on the application of the Breit–Pauli Hamiltonian in combination with nonrelativistic wavefunctions. In contrast to this methodology, we generate the diabatic RT Hamiltonian in a 4-spinor basis where the symmetry transformation properties of the electronic and vibrational wavefunctions completely determine the RT matrix structure. Explicit access to highly correlated wavefunctions is not required in our approach. In addition, the four-component vibronic coupling model takes into account the full spatial orbital relaxation upon the inclusion of the spin–orbit coupling and is therefore well suited for heavy systems. The third parameter, <em>p</em>, accounting for a possible pseudo-Jahn–Teller interaction is not considered here, but it does not introduce a principal difficulty. As the initial systems for this study, we considered the BrCN⁺ and ClCN⁺ cations and determined the <em>c</em> and <em>d</em> parameters by a numerical fit to accurate adiabatic potential energy surfaces obtained by the relativistic Fock-space coupled-cluster method. New values for the computed linear RT parameter <em>d</em> amount to 14.7 ± 0.5 cm⁻¹ for ClCN⁺ and 73.2 ± 0.7 cm⁻¹ for BrCN⁺.</p

Split upper (<em>V</em>₊) and lower (<em>V</em>₋) PECs of the BrCN⁺²Π state determined by applying FSCC in combination with an NR Hamiltonian

<p><strong>Figure 2.</strong> Split upper (<em>V</em>₊) and lower (<em>V</em>₋) PECs of the BrCN⁺²Π state determined by applying FSCC in combination with an NR Hamiltonian. The SF curves look almost identical and are not plotted separately.</p> <p><strong>Abstract</strong></p> <p>In this work, we present the four-component quadratic vibronic coupling model for the description of the Renner–Teller effect (RTE) in the presence of the spin–orbit coupling. The interaction of the two potential energy surfaces emerging from the cationic ²Π states of singly ionized linear triatomic molecules is described by the quadratic coupling constant <em>c</em> for the genuine RT repulsion and the second parameter, <em>d</em>, for a nonconstant spin–orbit coupling varying with the bond angle of the triatomic. The emergence of a linear RT constant in the presence of the spin–orbit operator was originally shown by Poluyanov and Domcke (2004 <em>Chem. Phys.</em> <strong>301</strong> 111–27) and is based on the application of the Breit–Pauli Hamiltonian in combination with nonrelativistic wavefunctions. In contrast to this methodology, we generate the diabatic RT Hamiltonian in a 4-spinor basis where the symmetry transformation properties of the electronic and vibrational wavefunctions completely determine the RT matrix structure. Explicit access to highly correlated wavefunctions is not required in our approach. In addition, the four-component vibronic coupling model takes into account the full spatial orbital relaxation upon the inclusion of the spin–orbit coupling and is therefore well suited for heavy systems. The third parameter, <em>p</em>, accounting for a possible pseudo-Jahn–Teller interaction is not considered here, but it does not introduce a principal difficulty. As the initial systems for this study, we considered the BrCN⁺ and ClCN⁺ cations and determined the <em>c</em> and <em>d</em> parameters by a numerical fit to accurate adiabatic potential energy surfaces obtained by the relativistic Fock-space coupled-cluster method. New values for the computed linear RT parameter <em>d</em> amount to 14.7 ± 0.5 cm⁻¹ for ClCN⁺ and 73.2 ± 0.7 cm⁻¹ for BrCN⁺.</p

Upper (<em>V</em>₊) and lower (<em>V</em>₋) PECs for the BrCN⁺^2Pi _{frac{1}{2}} and ^2Pi _{frac{3}{2}} states determined by applying the FSCC method in combination with the Dirac–Coulomb Hamiltonian (DC-FSCC)

<p><strong>Figure 3.</strong> Upper (<em>V</em>₊) and lower (<em>V</em>₋) PECs for the BrCN⁺^2\Pi _{\frac{1}{2}} and ^2\Pi _{\frac{3}{2}} states determined by applying the FSCC method in combination with the Dirac–Coulomb Hamiltonian (DC-FSCC).</p> <p><strong>Abstract</strong></p> <p>In this work, we present the four-component quadratic vibronic coupling model for the description of the Renner–Teller effect (RTE) in the presence of the spin–orbit coupling. The interaction of the two potential energy surfaces emerging from the cationic ²Π states of singly ionized linear triatomic molecules is described by the quadratic coupling constant <em>c</em> for the genuine RT repulsion and the second parameter, <em>d</em>, for a nonconstant spin–orbit coupling varying with the bond angle of the triatomic. The emergence of a linear RT constant in the presence of the spin–orbit operator was originally shown by Poluyanov and Domcke (2004 <em>Chem. Phys.</em> <strong>301</strong> 111–27) and is based on the application of the Breit–Pauli Hamiltonian in combination with nonrelativistic wavefunctions. In contrast to this methodology, we generate the diabatic RT Hamiltonian in a 4-spinor basis where the symmetry transformation properties of the electronic and vibrational wavefunctions completely determine the RT matrix structure. Explicit access to highly correlated wavefunctions is not required in our approach. In addition, the four-component vibronic coupling model takes into account the full spatial orbital relaxation upon the inclusion of the spin–orbit coupling and is therefore well suited for heavy systems. The third parameter, <em>p</em>, accounting for a possible pseudo-Jahn–Teller interaction is not considered here, but it does not introduce a principal difficulty. As the initial systems for this study, we considered the BrCN⁺ and ClCN⁺ cations and determined the <em>c</em> and <em>d</em> parameters by a numerical fit to accurate adiabatic potential energy surfaces obtained by the relativistic Fock-space coupled-cluster method. New values for the computed linear RT parameter <em>d</em> amount to 14.7 ± 0.5 cm⁻¹ for ClCN⁺ and 73.2 ± 0.7 cm⁻¹ for BrCN⁺.</p

Geometry parameters, vibrational frequencies and RT parameters for the BrCN⁺ cation

<p><b>Table 1.</b> Geometry parameters, vibrational frequencies and RT parameters for the BrCN⁺ cation. Hereby, bond lengths are given in Å, vibrational frequencies (ω) and RT parameters <em>c</em> and <em>d</em> are given in wavenumbers for the NR, scalar relativistic (SF) and four-component (DC) treatment. For the DC case the distances for the lower and (upper) surface are both listed, where ε is dimensionless. <em>c</em>_calc and <em>c</em>_fit denote the values obtained by equations (<a href="http://iopscience.iop.org/0953-4075/46/12/125101/article#jpb469975eqn28" target="_blank">28</a>), (<a href="http://iopscience.iop.org/0953-4075/46/12/125101/article#jpb469975eqn29" target="_blank">29</a>) and via the fit. The parameter <em>d</em> does not apply in the absence of the SO coupling.</p> <p><strong>Abstract</strong></p> <p>In this work, we present the four-component quadratic vibronic coupling model for the description of the Renner–Teller effect (RTE) in the presence of the spin–orbit coupling. The interaction of the two potential energy surfaces emerging from the cationic ²Π states of singly ionized linear triatomic molecules is described by the quadratic coupling constant <em>c</em> for the genuine RT repulsion and the second parameter, <em>d</em>, for a nonconstant spin–orbit coupling varying with the bond angle of the triatomic. The emergence of a linear RT constant in the presence of the spin–orbit operator was originally shown by Poluyanov and Domcke (2004 <em>Chem. Phys.</em> <strong>301</strong> 111–27) and is based on the application of the Breit–Pauli Hamiltonian in combination with nonrelativistic wavefunctions. In contrast to this methodology, we generate the diabatic RT Hamiltonian in a 4-spinor basis where the symmetry transformation properties of the electronic and vibrational wavefunctions completely determine the RT matrix structure. Explicit access to highly correlated wavefunctions is not required in our approach. In addition, the four-component vibronic coupling model takes into account the full spatial orbital relaxation upon the inclusion of the spin–orbit coupling and is therefore well suited for heavy systems. The third parameter, <em>p</em>, accounting for a possible pseudo-Jahn–Teller interaction is not considered here, but it does not introduce a principal difficulty. As the initial systems for this study, we considered the BrCN⁺ and ClCN⁺ cations and determined the <em>c</em> and <em>d</em> parameters by a numerical fit to accurate adiabatic potential energy surfaces obtained by the relativistic Fock-space coupled-cluster method. New values for the computed linear RT parameter <em>d</em> amount to 14.7 ± 0.5 cm⁻¹ for ClCN⁺ and 73.2 ± 0.7 cm⁻¹ for BrCN⁺.</p

Model selection.

<p>The model trajectories for a selection of key pathway components are shown for CFU-E, H838 and H838-HA-hEPOR cells. This includes expression of the EPOR targets <i>CISH</i> mRNA and <i>SOCS3</i> mRNA measured by qRT-PCR as well as pEPOR, pJAK2 and cytoplasmic STAT5 data measured by quantitative immunoblotting. The amount of pSTAT5 was determined by either mass spectrometry or quantitative immunoblotting. The closed circles represent experimentally measured data in H838 and H838-HA-hEPOR cells. CFU-E data previously published [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005049#pcbi.1005049.ref019" target="_blank">19</a>] are shown as circles. The lines depict the three applied model strategies: dashed green (only cell type-specific parameters), dashed blue (no cell type-specific parameters) and solid red (parsimonious model, only relevant cell type-specific parameters). The parsimonious model describes the data similarly to the model with only cell type-specific parameters, whereas the trajectories of the model without cell type-specific parameters are not in line with the experimental data, e.g. for <i>SOCS3</i> mRNA in CFU-E and for pSTAT5 in H838. All data sets, replicates and trajectories of the parsimonious model are shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005049#pcbi.1005049.s010" target="_blank">S8</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005049#pcbi.1005049.s011" target="_blank">S9</a> Figs.</p

Identification of Cell Type-Specific Differences in Erythropoietin Receptor Signaling in Primary Erythroid and Lung Cancer Cells

<div><p>Lung cancer, with its most prevalent form non-small-cell lung carcinoma (NSCLC), is one of the leading causes of cancer-related deaths worldwide, and is commonly treated with chemotherapeutic drugs such as cisplatin. Lung cancer patients frequently suffer from chemotherapy-induced anemia, which can be treated with erythropoietin (EPO). However, studies have indicated that EPO not only promotes erythropoiesis in hematopoietic cells, but may also enhance survival of NSCLC cells. Here, we verified that the NSCLC cell line H838 expresses functional erythropoietin receptors (EPOR) and that treatment with EPO reduces cisplatin-induced apoptosis. To pinpoint differences in EPO-induced survival signaling in erythroid progenitor cells (CFU-E, colony forming unit-erythroid) and H838 cells, we combined mathematical modeling with a method for feature selection, the L₁ regularization. Utilizing an example model and simulated data, we demonstrated that this approach enables the accurate identification and quantification of cell type-specific parameters. We applied our strategy to quantitative time-resolved data of EPO-induced JAK/STAT signaling generated by quantitative immunoblotting, mass spectrometry and quantitative real-time PCR (qRT-PCR) in CFU-E and H838 cells as well as H838 cells overexpressing human EPOR (H838-HA-hEPOR). The established parsimonious mathematical model was able to simultaneously describe the data sets of CFU-E, H838 and H838-HA-hEPOR cells. Seven cell type-specific parameters were identified that included for example parameters for nuclear translocation of STAT5 and target gene induction. Cell type-specific differences in target gene induction were experimentally validated by qRT-PCR experiments. The systematic identification of pathway differences and sensitivities of EPOR signaling in CFU-E and H838 cells revealed potential targets for intervention to selectively inhibit EPO-induced signaling in the tumor cells but leave the responses in erythroid progenitor cells unaffected. Thus, the proposed modeling strategy can be employed as a general procedure to identify cell type-specific parameters and to recommend treatment strategies for the selective targeting of specific cell types.</p></div

Generalized mathematical model structure of the EPO-induced JAK2/STAT5 signaling pathway.

<p>The process diagram of the EPO-induced JAK2/STAT5 signaling pathway model is shown according to Systems Biology Graphical Notation. The binding of the ligand EPO to its cognate receptor results in the phosphorylation of first JAK2 and then of the EPOR (pEPORpJAK2). STAT5 is recruited by pEPOR and phosphorylated by pJAK2 and translocates to the nucleus where it induces the transcription of the negative feedback regulators <i>CISH</i> mRNA and <i>SOCS3</i> mRNA. Protein tyrosine phosphatase (PTP) regulates the dephosphorylation of the EPOR-JAK2 complex.</p

Parameters and identified cell type-specific differences.

<p>Parameters and identified cell type-specific differences.</p

Sensitivity and differences.

<p>The process diagram of the EPO-induced JAK2/STAT5 signaling pathway model is shown according to Systems Biology Graphical Notation. Identified parameter fold-changes between CFU-E and H838 cells are shown in red (higher in CFU-E: JAK2actEPO, EPORactJAK2, CISHRNAturn) or purple (higher in H838: STAT5imp, nSTAT5deact, SOCS3prom, SOCS3RNAdelay). Parameters with a more effective inhibition in H838 cells are shown in light blue (JAK2actEPO, EPORactJAK2, STAT5actJAK2, STAT5actEPOR, STAT5imp, STAT5exp, SOCS3RNAturn). The area-under-curve of npSTAT5 at 60 min after stimulation was used as read-out to calculate the sensitivities.</p

Example model with simulated data for two different cell types.

<p>The process diagram of a two-step phosphorylation reaction (Protein→pProtein→ppProtein) is shown according to Systems Biology Graphical Notation. The ODE was numerically solved over time for two cell types that differ in the initial protein concentration ([Protein]_{t = 0}) and in one kinetic rate (<i>k</i>₃). The initial concentrations of the phosphorylated compounds were set to zero ([pProtein]_{t = 0} = [ppProtein]_{t = 0} = 0). The second phosphorylation step is reversible and the dephosphorylation rate (k₃) was assumed to be cell type-specific. The parameters for the phosphorylation steps (<i>k</i>₁, <i>k</i>₂) are the same for both cell types. Simulated data points are depicted as black dots, and the grey shading indicates the standard deviation (σ = 0.1) of the simulated measurement errors. Model trajectories are displayed as black lines.</p