Information content in data sets for a nucleated-polymerization model

Figures & data

Figure 1. The data sets of interest from [9,25]. The total polymerized mass is measured by Thioflavin T (ThT), which is one of the most common experimental tools for in vitro protein polymerization [25,29]. (available in colour online)

Figure 2. Parametric representation for $k_{\mathrm{on}}$.

Figure 3. Plots with simulated data: (a) correct cost function vs. time $(\gamma =1)$; (b) incorrect cost function vs. time $(\gamma =0)$.

Figure 4. Plots with simulated data: (a) correct cost function vs. model $(\gamma =1)$; (b) incorrect cost function vs. model $(\gamma =0)$.

Figure 5. (a) $M\left(t_k\right)$ (Madim) with OLS; (b) residuals vs. model: OLS.

Figure 6. (a) $M\left(t_k\right)$ with GLS, $\gamma =1$; (b) residuals vs. model: GLS.

Figure 7. Residuals for DS4 using different values of γ.

Figure 8. Residuals for the four experimental data sets using $\gamma =0.6$.

Figure 9. (a) Sensitivity w.r.t. $k_I^{-}$; (b) sensitivity w.r.t. $k_I^{+}$.

Figure 10. (a) Sensitivity w.r.t. $k_{\mathrm{on}}^N$; (b) sensitivity w.r.t. $k_{\mathrm{off}}^N$.

Figure 11. (a) Sensitivity w.r.t. $k_{\mathrm{on}}^{min}$; (b) sensitivity w.r.t. $k_{\mathrm{off}}^{max}$.

Figure 12. (a) Sensitivity w.r.t. $x_1$; (b) sensitivity w.r.t. $x_2$.

Figure 13. (a) Sensitivity w.r.t. $i_{max}$; (b) sensitivity w.r.t. $x_{11}=i_{max}{x}_1$.

Table

$k_{\mathrm{on}}^N$	$k_{\mathrm{off}}^N$	$k_{\mathrm{on}}^{\min }$	$k_{\mathrm{on}}^{\max }$	x1	x2	imax
4616.962	93.332	1684.381	1.5152·10^9	0.0626	0.859	3.542×10^5

Table

	$k_I^{+}$	$k_I^{-}$
q0	2.1600	10.9270

Figure 14. Two parameters estimation ($k_I^{+}$, $k_I^{-}$). Bootstrapping distribution for $k_I^{+}$. We use GLS and $M=1000$ runs.

Figure 15. Two parameters estimation ($k_I^{+}$, $k_I^{-}$). Bootstrapping distribution for $k_I^{-}$. We use GLS and $M=1000$ runs.

Table

	$k_I^{+}$(boot) (GLS)	$k_I^{-}$(boot) (GLS)	$k_I^{+}$(asymp) (GLS)	$k_I^{-}$(asymp) (GLS)
Mean	2.158	10.911	2.157	10.911
SE	0.0044	0.0247	0.00396	0.0225

Table

$k_{\mathrm{off}}^N$	$k_{\mathrm{on}}^{\min }$	$k_{\mathrm{on}}^{\max }$	x1	x2	imax
93.33	1684.38	1.5×10^9	0.062	0.859	3.5×10^5

Table

	$k_I^{+}$	$k_I^{-}$	$k_{\mathrm{on}}^N$
q0	2.1600	10.9270	4616.962

Table

	$k_I^{+}$	$k_I^{-}$	$k_{\mathrm{on}}^N$	SE	σ^2	κ
DS 1	2.26	13.49	4616.96	(0.012, 0.099, 53.925)	8.52×10^−6	8.89×10^10
DS 2	2.99	16.20	4616.96	(0.021, 0.151, 56.691)	9.67×10^−6	4.37×10^10
DS 3	2.18	15.76	9840.31	(0.011, 0.103, 90.466)	6.45×10^−6	3.94×10^11
DS 4	2.16	10.91	4616.96	(0.0089, 0.0649, 45.262)	6.36×10^−6	7.14×10^10

Figure 16. Confidence intervals.

Table

	$k_I^{+}$(boot)	$k_I^{-}$(boot)	$k_{\mathrm{on}}^N$(boot)	$k_I^{+}$(asymp)	$k_I^{-}$(asymp)	$k_{\mathrm{on}}^N$(asymp)
Mean	2.153	10.887	4616.962	2.157	10.910	4616.962
SE	0.0039	0.0219	0.00003	0.0089	0.0649	45.262

Figure 17. Estimation for $k_I^{+}$, $k_I^{-},$ and $k_{\mathrm{on}}^N$: bootstrapping distribution for $k_I^{-}$ for GLS and $M=1000$ runs.

Figure 18. Estimation for $k_I^{+}$, $k_I^{-}$, and $k_{\mathrm{on}}^N$: bootstrapping distribution for $k_I^{+}$ for GLS and $M=1000$ runs.

Figure 19. Estimation for $k_I^{+}$, $k_I^{-}$, and $k_{\mathrm{on}}^N$: bootstrapping distribution for $k_{\mathrm{on}}^N$ for GLS and $M=1000$ runs.

Table

$k_{\mathrm{on}}^N$	$k_{\mathrm{on}}^{\min }$	$k_{\mathrm{on}}^{\max }$	x1	x2	imax
4616.962	1684.381	1.5152×10^9	0.0626	0.859	3.542×10^5

Table

	$k_I^{+}$	$k_I^{-}$	$k_{\mathrm{off}}^N$
q0	2.1600	10.9270	108.256

Table

	$k_I^{+}$	$k_I^{-}$	$k_{\mathrm{off}}^N$	SE	σ^2	κ
DS 1	2.203	12.997	99.861	(0.011, 0.091, 1.208)	8.165×10^−6	4.912×10^7
DS 2	2.893	15.474	100.019	(0.019, 0.137, 1.279)	9.323×10^−6	2.486×10^7
DS 3	2.168	15.631	41.935	(0.011, 0.102, 0.424)	6.435×10^−6	9.125×10^6
DS 4	2.181	11.090	90.536	(0.009, 0.066 , 0.936)	6.289×10^−6	3.043×10^7

Figure 20. Three parameters estimation ($k_I^{+}$, $k_I^{-},$ and $k_{\mathrm{off}}^N$): bootstrapping distribution for $k_I^{+}$. We used GLS and $M=1000$ runs.

Figure 21. Three parameters estimation ($k_I^{+}$, $k_I^{-},$ and $k_{\mathrm{off}}^N$): bootstrapping distribution for $k_I^{-}$. We used GLS and $M=1000$ runs.

Figure 22. Three parameters estimation ($k_I^{+}$, $k_I^{-}$ and $k_{\mathrm{off}}^N$): bootstrapping distribution for $k_{\mathrm{off}}^N$. We used GLS and $M=1000$ runs.

Table

	$k_I^{+}$(boot)	$k_I^{-}$(boot)	$k_{\mathrm{off}}^N$(boot)	$k_I^{+}$(asymp)	$k_I^{-}$(asymp)	$k_{\mathrm{off}}^N$(asymp)
Mean	2.169	11.013	91.254	2.181	11.090	90.536
SE	0.0094	0.0699	1.0392	0.009	0.066	0.936

Table

$k_{\mathrm{on}}^{\min }$	$k_{\mathrm{on}}^{\max }$	x1	x2	imax
1684	1.5×10^9	0.062	0.859	3.5×10^5

Table

	$k_I^{+}$	$k_I^{+}$	$k_{\mathrm{on}}^N$	$k_{\mathrm{off}}^N$	σ^2	κ
DS 1	2.1431	12.4751	4616.962	108.259	8.7219×10^−6	6.1226×10^19
DS 2	2.7995	14.7630	4616.957	108.4308	9.8694×10^−6	1.4442×10^19
DS 3	2.180	15.757	4618.599	41.369	6.4622×10^−6	1.881×10^17
DS 4	2.161	10.9278	4617.3316	93.3265	6.374×10^−6	2.144×10^18

Table

α	τ	Confidence level
.25	1.32	75%
.1	2.71	90%
.05	3.84	95%
.01	6.63	99%
.001	10.83	99.9%

H.T. Banks, M. Doumic, and C. Kruse, Efficient numerical schemes for nucleation-aggregation models: Early steps, CRSC-TR14-01, N.C. State University, Raleigh, NC, March, 2014.

 Google Scholar

S. Prigent, A. Ballesta, F. Charles, N. Lenuzza, P. Gabriel, L.M. Tine, H. Rezaei, and M. Doumic, An efficient kinetic model for assemblies of amyloid fibrils and its application to polyglutamine aggregation, PLoS ONE 7 (2012), e43273. DOI:10.1371/journal.pone.0043273.

 Google Scholar

W.-F. Xue, S.W. Homans, and S.E. Radford, Systematic analysis of nucleation-dependent polymerization reveals new insights into the mechanism of amyloid self-assembly, Proc. Natl. Acad. Sci. USA 105 (2008), pp. 8926–8931. doi: 10.1073/pnas.0711664105

 PubMed Web of Science ®Google Scholar