Deducing Underlying Mechanisms from Protein Recruitment Data

Abstract

By using fluorescent labelling techniques, the distribution and dynamics of proteins can be measured within living cells, allowing to study in vivo the response of cells to a triggering event, such as DNA damage. In order to evaluate the reaction rate constants and to identify the proteins and reactions that are essential for the investigated process, mechanistic models are used, which often contain many proteins and associated parameters and are therefore underdetermined by the data. In order to establish criteria for assessing the significance of a model, we present here a systematic investigation of the information that can be reliably deduced from protein recruitment data, assuming that the complete set of reactions that affect the data of the considered protein species is not known. To this purpose, we study in detail models where one or two proteins that influence each other are recruited to a substrate. We show that in many cases the kind of interaction between the proteins can be deduced by analyzing the shape of the recruitment curves of one protein. Furthermore, we discuss in general in which cases it is possible to discriminate between different models and in which cases it is impossible based on the data. Finally, we argue that if different models fit experimental data equally well, conducting experiments with different protein concentrations would allow discrimination between the alternative models in many cases.

Figure 1. Effect of a variation of on the one protein one substrate model with dissociation.

Coloured lines: Exact analytical solution (eq. (9)) normalized to (eq. (13)) with , , . The value of decreases from the lowest (blue) curve () to the the highest (green) curve ( = 500). Grey line: QCA solution (eq. (15)) with and . The inset shows the section in which the blue curve and the green curve cross, amplified by a factor of . The dashed lines illustrate the parameter estimation described in the main text.

Figure 2. Model in which protein increases the association rate of protein . and from bottom to top curve.

A) . Solid lines are for protein , the dotted line is for protein , and the dashed lines are used for estimating the order of magnitude of the rate constants from the curves, giving for the steepest curve, and and for the slowest curve. Depending on the parameters the curves show an increasing slope at the beginning. B) same parameters as in A) except . The curves always show an increasing slope at the beginning, which helps distinguishing this case from the one shown in Figure 2A. Additionally, for large values of the recruitment curves of resemble the recruitment curve of , which is not the case if .

Figure 3. Model in which protein decreases the association rate of protein . and from bottom to top curve.

A) . Solid lines are for protein , the dotted line is for protein . The grey line is a monoexponential fit. The dashed lines are used for estimating the rate constants from the curves, giving . After has risen to a high level, recruitment of becomes much slower, and the slope of the recruitment curve of (purple curve) decreases faster than would be expected from a monoexponential curve that has a similar initial slope (grey curve). B) same parameters as in A) except . The curves always resemble a monoexponential function.

Figure 4. Model in which decreases the association rate of and in which dissociation is relevant. and from green to blue curve; and .

The curves are normalized to their asymptotic value at . In contrast to the previous models, the recruitment curves of this model have a maximum that is larger than the plateau value if and .

Figure 5. Model in which protein decreases the dissociation rate of protein .

A) , from bottom to top curve, , . Grey curves: Fits of the model in which protein decreases the association rate of protein . Orange curves: Monoexponential fit with an intercept. Decreasing leads to a new feature, which is characterized by a decline of the slope followed by an increase. Since this feature can not occur in the model in which protein decreases the association rate, it allows distinguishing between the model in which protein decreases the association rate and the model in which it decreases the dissociation rate. B) same parameters as in subfigure A, but from bottom to top and . Despite of the variation in , the time at which the bend occurs is the same for all curves.

Figure 6. Model in which protein increases the dissociation rate of . , from green to blue curve, and .

Grey curves: Fits of the model in which protein decreases the association rate of and in which dissociation is relevant (section B1.3).

Figure 7. Comparison of the models.