Fig 1.
Signaling motifs determine how upstream signals are converted into downstream responses.
(A) The same upstream signal, X, can produce different downstream responses, Z, depending on the signaling motif. Positive feedback leads to rapid amplification of Z following a delay in its induction. An incoherent feedforward loop (IFFL) allows Z to adapt to changes in X by first activating then dampening the downstream response. Coupled positive and negative feedback can lead to oscillations of Z. Signaling motifs often involve an intermediate signaling factor, Y, that is necessary to achieve the appropriate downstream response. Ordinary differential equations for each signaling motif are provided in the S1 Text. (B) In response to a given stimulus, individual cells show heterogeneous signaling patterns. For many cellular signaling pathways, the variability of the upstream signal, X, is correlated with the downstream response, Z. (C) Hypothetical model for a common signaling motif that explains the correlation between upstream signaling and downstream responses. Differences in upstream signal are mapped onto the downstream response. Under this model, it may be possible to infer the underlying structure by observing many examples of the upstream and downstream signaling patterns.
Fig 2.
A single signaling motif can explain the correlation between upstream signals and downstream responses in single cells.
(A) Experimentally measured values for cell-to-cell variation in signal height and delay were used to generate a large number of simulated signaling patterns. Each trace represents a unique upstream signal from an individual cell. (B) Average (top) and single-cell (bottom) signaling patterns for upstream signals (left) and downstream responses (right) for 50 simulated cells. While X is generated using the approach in panel A, the downstream responses are calculated using the signaling motif (middle). Here, Z if produced by the incoherent feed forward loop. A single signaling motif translates 50 upstream signals into 50 downstream responses. Each row corresponds to an individual cell. Color represents the fold change. (C) There is a correlation between the upstream and downstream signals that is not present if the cells are shuffled. Black dots are from paired cells and grey dots are from shuffled cells. The red line is a correlation line for the paired cells. The unpaired cells do not have any correlation.
Fig 3.
Inferring the underlying signaling motif from simulated single-cell dynamics.
(A) An incoherent feedforward loop (IFFL) signaling motif was used to generate a synthetic data set for 50 single cells. Individual upstream signals X were generated as shown in Fig 2A. Each signal was then subjected to the IFFL signaling motif using ODEs to calculate a unique downstream response Z for each cell (see S1 Text). The resulting X and Z pairs for all cells were then analyzed to infer the underlying signaling motif. (B) Heat map representation of motif structures for all possible 3-factor signaling motifs. (left) A conventional representation of motif structure consisting of circles and arrows can be represented by (right) a single column of shaded rectangles in which each rectangle denotes a specific interaction within the motif: black, positive regulation; red, negative regulation; white, no regulation. The heat map representation for the IFFL is shown next to the conventional diagram. (Right) All 402 possible unique motif structures are shown for a 3-component network (X, Y, and Z). (C) To infer the mechanism underlying X and Z, a separate downstream response, Z’, is calculated for each possible parameterized signaling motif and compared to the original downstream response, Z. Each motif is assigned an error score that reflects the average difference in fold change between Z and Z’ per cell per unit time. (D) Distribution of error scores. The error scores are distributed such that they approach the asymptote of the worst possible score (i.e., the output of an unconnected graph). The top graphs are defined as those before the “elbow” of the graph and are determined by looking at the first derivative. (E) The top-scoring motifs. The links for the incoherent feed forward loop, as well as its simpler sub-motif structures, are overrepresented among the best-performing motifs. (F) Heat map representation of the consensus motif. Asterisks indicate a greater than 50% confidence in that link being correct. Darker colors mean more confidence and lighter colors mean less confidence. The distance from the consensus motif to the known motif was XX which has a p-value of 9.95x105.
Fig 4.
Validation of MISC with additional biological motifs.
(A) Cascade motif. The cascade motif creates a delay in the output, Z. Upper left, ball and stick model and arrow representation of the motif. Lower Left and Middle, an example of the motif. Right, Known and predicted motif. Asterisks indicate greater than 50% confidence in that connection. (B) Feedback motif. The feedback motif creates a persistence in the response of Z. Upper left, ball and stick model and arrow representation of the motif. Lower Left and Middle, an example of the motif. Right, Known and predicted motif. Asterisks indicate greater than 50% confidence in that connection. (C) Coherent Feed Forward Loop (CFFL) motif. The CFFL creates a delay in the onset of Z, but no delay in the offset. Upper left, ball and stick model and arrow representation of the motif. Lower Left and Middle, an example of the motif. Right, Known and predicted motif. Asterisks indicate greater than 50% confidence in that connection.
Fig 5.
Motif inference for the yeast stress response pathway under different environmental perturbations.
(A) Schematic of the system showing the fluorescent reporter system used. See ref. 21 for experimental details. Experimental data were used with author permission. (B) Oxidative Stress. 58 cells were treated with 0.1 mM H2O2. Far left, heatmap of the individual cell’s Msn2 activation, and a plot of the mean and standard deviation of the cells. Left middle, STRE response as reported by the CFP reporter. Right middle, heatmap and ball and stick representations of the significant sub-motifs. Single asterisks represent 50% confidence and double asterisks represent 80% confidence. Displayed as ball and stick representations are the 80% confidence connections. Far right, Simulated STRE response of the top preforming sub-motif. (C) Nutrient Stress. 60 cells were treated with a 0.1% glucose media. Far left, heatmap of the individual cell’s Msn2 activation, and a plot of the mean and standard deviation of the cells. Left middle, STRE response as reported by the CFP reporter. Right middle, heatmap and ball and stick representations of the significant sub-motifs. Single asterisks represent 50% confidence and double asterisks represent 80% confidence. Displayed as ball and stick representations are the 80% confidence connections. Far right, Simulated STRE response of the top preforming sub-motif. (D) Osmotic Stress. 28 cells were treated with 0.5 M KCl. Far left, heatmap of the individual cell’s Msn2 activation, and a plot of the mean and standard deviation of the cells. Left middle, STRE response as reported by the CFP reporter. Right middle, heatmap and ball and stick representations of the significant sub-motifs. Single asterisks represent 50% confidence and double asterisks represent 80% confidence. Displayed as ball and stick representations are the 80% confidence connections. Far right, Simulated STRE response of the top preforming sub-motif.
Fig 6.
Single-cell dynamics can provide improved certainty or accuracy in motif prediction than population-averaged data.
(A) In order to evaluate motif prediction based on single-cell versus population-averaged time-series traces, we performed MISC on pairs of time-series traces that were either correctly paired (top) or randomly shuffled (bottom). Note that in both cases the average time series trajectory is the same. (B) Shuffled versus paired predictions for the IFFL and yeast stresses. Ten replicates were used for each condition. Note that MISC produces variability in predictions even for paired traces since parameter values on the motifs are randomly chosen.
Fig 7.
Additional single-cell measurement can provide increasingly better predictions about the underlying signaling motif.
MISC was performed on an increasing number of paired single-cell measurements and the accuracy of the prediction (based on the distance to the true motif or the motif calculated by the 80% threshold shown in Fig 5) was calculated. (A) Synthetic Data, (B) Nutrient Stress, (C) Osmotic Stress, (D) Oxidative Stress. The Synthetic Data did not decrease, but all of the natural stress predictions decreased in percentage as the number of cells increased.