Data analysis and simulations

I. Hill equation

The data were fit to a Hill equation of the form (M0- Mf) [1 - AH / (AH+ K1/2H)] + Mf, where M0 is the pre-stimulus kinase activity in absence of attractant, Mf is the residual kinase activity upon addition of saturating amount of attractant, A is concentration of added attractant, H is Hill coefficient, and K1/2 is the concentration of attractant resulting in a half-maximal response.

Summary of the best-fit values obtained using the Hill equation (by figure):

Figure 1 a, Tar+ Tsr+ Tap+ cells (circles): M0= 0.08, Mf= 0.044, K1/2 = 0.16 mM, H = 1; Tar+ Tap+ cells (triangles): M0= 0.056, Mf= 0, K1/2 = 0.019 mM, H = 3; Tar+ cells (inverted triangles): M0= 0.035, Mf= 0, K1/2 = 0.0056 mM, H = 2.7. c, 0.6-times the native level of Tar (diamonds): M0= 1, Mf= 0.937, K1/2 = 0.13 mM, H = 1.3; the native level of Tar (circles): M0= 1, Mf= 0.687, K1/2 = 0.13 mM, H = 1.3; 2-times the native level of Tar (squares): M0= 1, Mf= 0.29, K1/2 = 0.079 mM, H = 1.6; 6-times the native level of Tar (triangles): M0= 1, Mf= 0.013, K1/2 = 0.044 mM, H = 3.8. d, No Tar (open circles): M0= 1, Mf= 0, K1/2 = 0.027 mM, H = 9; 0.6-times the native level of Tar (diamonds): M0= 1, Mf= 0, K1/2 = 0.029 mM, H = 5.3; the native level of Tar (circles): M0= 1, Mf= 0, K1/2 = 0.044 mM, H = 3.8; 2-times the native level of Tar (squares): M0= 1, Mf= 0.124, K1/2 = 0.053 mM, H = 2.6; 6-times the native level of Tar (triangles): M0= 1, Mf= 0.21, K1/2 = 0.16 mM, H = 1.3.

Figure 2a, The native level of Tar (filled circles): M0= 0.018, Mf= 0, K1/2 = 0.011 mM, H = 2; 2-times the native level of Tar (filled squares): M0= 0.061, Mf= 0, K1/2 = 0.013 mM, H = 3.7; 6-times the native level of Tar (open diamonds): M0= 0.086, Mf= 0, K1/2 = 0.021 mM, H = 11. b, 0.3-times the native level of Tsr (filled circles): M0= 0.009, Mf= 0, K1/2 = 0.012 mM, H = 2.7; 0.7-times the native level of Tsr (filled squares): M0= 0.036, Mf= 0, K1/2 = 0.02 mM, H = 3.2; 5-times the native level of Tsr (open diamonds): M0= 0.094, Mf= 0, K1/2 = 0.036 mM, H = 10. c, 0.01-times the native level of CheW (filled circles): M0= 0.0058, Mf= 0, K1/2 = 0.021 mM, H = 3; 0.1-times the native level of CheW (filled squares): M0= 0.036, Mf= 0, K1/2 = 0.034 mM, H = 5; 0.7-times the native level of CheW (open diamonds): M0= 0.044, Mf= 0, K1/2 = 0.043 mM, H = 9.6. d, 0.25-times the native level of CheA (filled circles): M0= 0.022, Mf= 0, K1/2 = 0.05 mM, H = 5; 0.3-times the native level of CheA (filled squares): M0= 0.026, Mf= 0, K1/2 = 0.044 mM, H = 5; 8-times the native level of CheA (open diamonds): M0= 0.031, Mf= 0, K1/2 = 0.033 mM, H = 2.

Figure 3 a, Tar[QEEE] (filled squares): M0= 0.007, Mf= 0, K1/2 = 0.0011 mM, H = 1.2; Tar[QEQQ] (filled circles): M0= 0.04, Mf= 0, K1/2 = 0.013 mM, H = 3.8; Tar[QEEE] Tar[QEQQ] (open circles): M0= 0.068, Mf= 0, K1/2 = 0.0054 mM, H = 2.5. b, Tsr+ Tar[EEEE] (circles): M0= 0.067, Mf= 0, K1/2 = 0.018 mM, H = 3.4; Tsr+ Tar[QEQQ] (squares): M0= 0.106, Mf= 0.029, K1/2 = 0.059 mM, H = 2.4. c, Tsr+ Tar[QEQE] + 0.07 mM serine (squares): M0= 0.062, Mf= 0, K1/2 = 0.021 mM, H = 2; Tsr+ Tar[QEQE] no serine (circles): M0= 0.103, Mf= 0.041, K1/2 = 0.093 mM, H = 1.6.

Figure 4 a, 0.6-times the native level of Tar (diamonds): M0= 0.0026, Mf= 0, K1/2 = 0.0043 mM, H = 2; native level of Tar (filled circles): M0= 0.0038, Mf= 0, K1/2 = 0.0034 mM, H = 2.3; 2-times the native level of Tar (filled squares): M0= 0.013, Mf= 0, K1/2 = 0.0015 mM, H = 2.5; 6-times the native level of Tar (open diamonds): M0= 0.013, Mf= 0, K1/2 = 0.00087 mM, H = 2. b, 0.25-times the native level of CheA (filled circles): M0= 0.0046, Mf= 0, K1/2 = 0.0035 mM, H = 1.9; 8-times the native level of CheA (open diamonds): M0= 0.012, Mf= 0, K1/2 = 0.015 mM, H = 1.4.

II.MWC model

Alternatively, data were fit to a Monod-Wyman-Changeux (MWC) model of multi-subunit allosteric proteins27 of the form (M0- Mf) [1 - (1 + A / Ki)N / (L (1 + A / Ka)N+ (1 + A / Ki)N)] + Mf, where M0, Mf, and A are as defined above, and N, L, Ki, and Ka are as defined in Box 1. Although the values of Ki and Ka have not been measured directly, they could be estimated based on the binding affinitites of receptors in unmethylated and fully methylated states to aspartate16 and serine21 measured in vitro, and the sensitivity of response to aspartate and MeAsp measured in a cheR cheB strain22. We assumed Ki = 0.03 mM and Ka = 1 mM for MeAsp, and Ki = 0.01 mM and Ka = 0.02 mM for serine. When modelling the Tar+ Tsr+ Tap+ strain in Fig. 1a we assumed for simplicity that activities of Tar and Tsr are independent.

Summary of the best-fit values obtained using the MWC model (by figure):

Figure 1 a, Tar+ Tsr+ Tap+ cells (circles): M0= 0.08, Mf= 0.044, N = 1.5, L = 9; Tar+ Tap+ cells (triangles): M0= 0.057, Mf= 0, N = 8, L = 46; Tar+ cells (inverted triangles): M0= 0.037, Mf= 0, N = 16, L = 15. Values for Ki and Kaof MeAsp were assumed to be 0.03 mM and 1 mM, respectively.

Figure 2a, The native level of Tar (filled circles): M0= 0.019, Mf= 0, N = 8, L = 8; 2-times the native level of Tar (filled squares): M0= 0.061, Mf= 0, N = 12, L = 72; 6-times the native level of Tar (open diamonds): M0= 0.087, Mf= 0, N = 25, L = 105. b, 0.3-times the native level of Tsr (filled circles): M0= 0.009, Mf= 0, N = 16, L = 150; 0.7-times the native level of Tsr (filled squares): M0= 0.036, Mf= 0, N = 21, L = 4103; 5-times the native level of Tsr (open diamonds): M0= 0.094, Mf= 0, N = 62, L = 1013. Values for Ki and Kaof MeAsp were assumed to be 0.03 mM and 1 mM, respectively; values for Ki and Kaof serine were assumed to be 0.01 mM and 0.02 mM, respectively.

Figure 4 a, The native level of Tar (filled circles): M0= 0.019, Mf= 0, N = 8, L = 0.27; 2-times the native level of Tar (filled squares): M0= 0.061, Mf= 0, N = 19, L = 0.3; 6-times the native level of Tar (open diamonds): M0= 0.087, Mf= 0, N = 29, L = 0.2. Note that M0 values were taken to be the same as in fits to the data in Fig. 2a.

The precision of parameter (N and L) estimations in the MWC model is limited by the precision in estimations of attractant binding affinity to inactive and active states of the receptor that we rely on (see Methods). For comparison, if Kaof MeAsp is assumed to be 0.1 mM instead of 1 mM, the best-fit values for N in Figure 2a change to 12 at the native level of Tar and to 39 at 6-times the native level of Tar; the best-fit values for L change to 9 and 5105, respectively. If Kaof MeAsp is assumed to be 100 mM, the best-fit values for N in Figure 2a change to 7 at the native level of Tar and to 21 at 6-times the native level of Tar; the best-fit values for L change to 7 and 7105, respectively.

III. Simulations

Activity of the MWC-type model of receptor complex was simulated for different values of L and N using the equation 1 - (1 + A / Ki)N / (L (1 + A / Ka)N+ (1 + A / Ki)N), where A, N, L, Ki, and Ka are as defined above, assuming the K values for MeAsp. Receptor occupancy was simulated using the equation [L (A / Ka) (1 + A / Ka)N-1 + (A / Ki) (1 + A / Ki)N-1] / [(L (1 + A / Ka)N+ (1 + A / Ki)N)].