Separating Fusion from Rivalry

Visual fusion is the process in which differing but compatible binocular information is transformed into a unified percept. Even though this is at the basis of binocular vision, the underlying neural processes are, as yet, poorly understood. In our study we therefore aimed to investigate neural correlates of visual fusion. To this end, we presented binocularly compatible, fusible (BF),and incompatible, rivaling (BR) stimuli, as well as an intermediate stimulus type containing both binocularly fusible and monocular, incompatible elements (BFR). Comparing BFR stimuli with BF and BR stimuli, respectively, we were able to disentangle brain responses associated with either visual fusion or rivalry. By means of functional magnetic resonance imaging, we measured brain responses to these stimulus classes in the visual cortex, and investigated them in detail at various retinal eccentricities. Compared with BF stimuli, the response to BFR stimuli was elevated in visual cortical areas V1 and V2, but not in V3 and V4 - implying that the response to monocular stimulus features decreased from V1 to V4. Compared to BR stimuli, the response to BFR stimuli decreased with increasing eccentricity, specifically within V3 and V4. Taken together, it seems that although the processing of exclusively monocular information decreases from V1 to V4, the processing of binocularly fused information increases from earlier to later visual areas. Our findings suggest the presence of an inhibitory neural mechanism which, depending on the presence of fusion, acts differently on the processing of monocular information

Correlated receptor transport processes buffer single-cell heterogeneity

<div><p>Cells typically vary in their response to extracellular ligands. Receptor transport processes modulate ligand-receptor induced signal transduction and impact the variability in cellular responses. Here, we quantitatively characterized cellular variability in erythropoietin receptor (EpoR) trafficking at the single-cell level based on live-cell imaging and mathematical modeling. Using ensembles of single-cell mathematical models reduced parameter uncertainties and showed that rapid EpoR turnover, transport of internalized EpoR back to the plasma membrane, and degradation of Epo-EpoR complexes were essential for receptor trafficking. EpoR trafficking dynamics in adherent H838 lung cancer cells closely resembled the dynamics previously characterized by mathematical modeling in suspension cells, indicating that dynamic properties of the EpoR system are widely conserved. Receptor transport processes differed by one order of magnitude between individual cells. However, the concentration of activated Epo-EpoR complexes was less variable due to the correlated kinetics of opposing transport processes acting as a buffering system.</p></div

Quantitative characterization of single-cell EpoR transport dynamics.

<p><b>(A)</b> Predicted single-cell EpoR concentration trajectories. Predictions were plotted for means of the best 0.5% of 1000 ACD model fits. Shaded areas indicate 1σ-confidence intervals. (EpoR_m, membrane bound EpoR; EpoR_i, intracellular EpoR; EpoR*_m, membrane bound Epo-EpoR complexes; EpoR*_RE, intracellular Epo-EpoR within the “recycling endosomal” compartment). Average fluxes are shown in red together with shaded areas indicating 1σ-confidence intervals, which are in most cases negligibly small. <b>(B)</b> Predicted reaction fluxes for EpoR traffic and Epo binding reactions. Lines represent means of the best 0.5% of 1000 ACD model fits, and shaded areas indicate 1σ-confidence intervals. Average fluxes are shown in red together with shaded areas indicating 1σ-confidence intervals (F_deg, EpoR degradation; F_ItoM and F_MtoI, transport from the intracellular compartment to the plasma membrane or in the opposite direction; F_Epo,on and F_Epo,off, Epo binding and unbinding; F_EpoR*,MtoI, endocytosis of Epo-EpoR; F_EpoR*,REtoM, recycling to plasma membrane; F_{EpoR*,deg,REtoEx}, degradation with exocytosis of Epo; F_{EpoR*,deg,REtoI}, degradation with intracellular accumulation of degraded Epo). <b>(C)</b> Average single-cell EpoR reaction fluxes close to steady state at t = 300’, illustrated by arrow widths, show the important involvement of rapid exchange between intracellular and membrane compartments, Epo-EpoR internalization and transport back to the plasma membrane.</p

Identifiability of single-cell parameters after using different datasets for model fitting.

<p><b>(A)</b> Relative parameter 1σ-confidence intervals (C. I.) from PLE for four exemplary cells (c1 to c4) at four different conditions for model fitting. These cells were either part of cell ensemble models (Epo internalizing + bleached + CHX treated cells, Epo internalizing + bleached cells, Epo internalizing cells only) or independent single-cell models of the variant ACD. Colors indicate the percentage of the parameter C. I. sizes relative to the value of the best fit parameters from 1000 fits for all single-cell parameters (grey color, C. I. larger than 200% of the best fit parameter; white color, C. I. of infinite size; upper or lower triangle, upper limit is infinity or lower limit is zero). While some parameters were identifiable for all four model fitting conditions, identifiability was best for including the complete dataset. <b>(B)</b> Best fit values and error bars indicating C. I. sizes from PLE for the exemplary parameter k_EpoR*,REtoM that describes EpoR recycling back to the plasma membrane.</p

Fits of the optimal cell ensemble model variant to the complete dataset.

<p><b>(A)</b> Fits of the model variant ACD to 16 Epo-Cy5.5 internalizing cells (circles, experimental data; lines, model fits; EpoR-GFP_mem, membrane EpoR; EpoR-GFP_ves, EpoR in vesicles without Epo; EpoR-GFP_Cy5.5,ves, EpoR in Epo-Cy5.5 vesicles; Epo-Cy5.5_mem, Epo-Cy5.5 bound to membrane EpoR; Epo-Cy5.5_cpl, cytosolic Epo-Cy5.5). <b>(B)</b> ACD model fits to data from 10 cells newly synthesizing EpoR-GFP after bleaching at t = 5’ (EpoR-GFP_mem, membrane EpoR; EpoR-GFP_ves, Epo in vesicles). <b>(C)</b> ACD model fits to data from 7 cells degrading EpoR-GFP after inhibiting synthesis with CHX as in (B).</p

Quantitative characterization of single-cell EpoR transport dynamics.

<p><b>(A)</b> Predicted single-cell EpoR concentration trajectories. Predictions were plotted for means of the best 0.5% of 1000 ACD model fits. Shaded areas indicate 1σ-confidence intervals. (EpoR_m, membrane bound EpoR; EpoR_i, intracellular EpoR; EpoR*_m, membrane bound Epo-EpoR complexes; EpoR*_RE, intracellular Epo-EpoR within the “recycling endosomal” compartment). Average fluxes are shown in red together with shaded areas indicating 1σ-confidence intervals, which are in most cases negligibly small. <b>(B)</b> Predicted reaction fluxes for EpoR traffic and Epo binding reactions. Lines represent means of the best 0.5% of 1000 ACD model fits, and shaded areas indicate 1σ-confidence intervals. Average fluxes are shown in red together with shaded areas indicating 1σ-confidence intervals (F_deg, EpoR degradation; F_ItoM and F_MtoI, transport from the intracellular compartment to the plasma membrane or in the opposite direction; F_Epo,on and F_Epo,off, Epo binding and unbinding; F_EpoR*,MtoI, endocytosis of Epo-EpoR; F_EpoR*,REtoM, recycling to plasma membrane; F_{EpoR*,deg,REtoEx}, degradation with exocytosis of Epo; F_{EpoR*,deg,REtoI}, degradation with intracellular accumulation of degraded Epo). <b>(C)</b> Average single-cell EpoR reaction fluxes close to steady state at t = 300’, illustrated by arrow widths, show the important involvement of rapid exchange between intracellular and membrane compartments, Epo-EpoR internalization and transport back to the plasma membrane.</p

Correlations of single-cell parameters.

<p><b>(A)</b> Correlation coefficients between single-cell kinetic parameters (left panel; white to red: positive correlation coefficients; white to blue: negative correlation coefficients) and p-values for significance of correlation coefficients obtained from t-tests (right panel; white to red: values p<0.05; blue to black: values p≥0.05). Essentially, the EpoR trafficking parameters k_EpoR,ItoM, k_EpoR,MtoI, k_EpoR*,REtoM, k_EpoR*,MtoRE were positively correlated (ρ, Pearson correlation coefficient). <b>(B)</b> Correlations of exemplary single-cell parameters, k_EpoR,ItoM and k_EpoR,MtoI, with k_EpoR*,MtoRE. Points represent means and error bars indicate standard errors of the best 0.5% of 1000 fits.</p

Relevance of kinetic parameter variability.

<p><b>(A)</b> Constraining individual single-cell parameters to global parameter values that are equal for all cells lead to increases in ΔAIC_corr relative to the unrestricted ACD model, in which all single-cell parameters were individual. These ΔAIC_corr increases are shown color-coded. After fixing the single-cell parameter with the smallest (left panel) or largest increase in AIC_corr (right panel) to a global value, effects of fixing each of the remaining individual parameters were tested. By iterating this procedure until all parameters, except k_syn, were fixed to global values, parameter rank orders were determined indicating to which degree the variability of different single-cell parameters contributed to explaining the experimental dataset. <b>(B)</b> Sequentially fixing single-cell parameters to global values with smallest AIC_corr increases (lower trajectory) or largest AIC_corr increases (upper trajectory) shows that variability of the parameters k_EpoR,ItoM and k_EpoR,MtoI was most important to explain cellular heterogeneity, while variability of parameters as k_EpoR,deg or k_{EpoR*,deg,REtoEx} was less important. The lower trajectory represents the upper row in the left graph of panel A, the upper trajectory represents the upper row in the right graph of panel A.</p

The optimal model variant contains reactions for EpoR recycling and degradation.

<p><b>(A)</b> Basic model describing transport between membrane and intracellular receptors (EpoR_m, EpoR_i), reversible binding of Epo to EpoR*_m and internalization to recycling endosomal EpoR*_RE (black arrows), extended by variable parts A to D (A, direct EpoR recycling to the plasma membrane; B, recycling to intracellular pool and intracellular accumulation of degraded Epo; C, degradation and transport of degraded Epo_deg,ext to extracellular space; D, degradation and intracellular accumulation of degraded Epo_deg,i). <b>(B)</b> Differences in AIC_corr values to the optimal model variant ACD for all variants, indicated for model fitting to data from only Epo internalizing cells (Epo), additionally bleached cells (Epo+Bleaching), and additionally CHX treated cells (Epo+Bleaching+CHX). The inlay shows that AIC_corr values for the ACD variant were clearly lower than for the next better model variant “ABC”. <b>(C)</b> Differences in AIC_corr to the optimal model variant for model fitting to data from only a single cell at a time, for ten selected cells, indicated by colors (squares, ΔAIC_corr values; black bars, median ΔAIC_corr values for each model variant). Notably, when fitting single-cell models to data from different individual cells, different model variants were optimal. <b>(D)</b> Topology of the optimal variant ACD and indication of kinetic parameters for EpoR trafficking reactions (global parameters: k_on,Epo, k_off,Epo, Epo binding and unbinding; single-cell parameters: k_EpoR,syn, k_EpoR,deg, EpoR turnover; k_EpoR,ItoM, k_EpoR,MtoI, transport between intracellular and plasma membrane compartments; k_EpoR*,MtoI; endocytosis of Epo-ligated EpoR; k_EpoR*,REtoM; recycling to plasma membrane; k_{EpoR*,deg,REtoEx} and k_{EpoR*,deg,REtoI}, EpoR degradation with exocytosis or with intracellular accumulation of degraded Epo).</p