. 2019 Mar 18;9:4700. doi: 10.1038/s41598-019-41072-w

Table 2.

Prediction models for selected rheological attributes.

Rheological Attribute	Prediction Formula	PLS factors	VIP	R²Y (%)
Log₁₀(J_max)	$1.598 p w - 48.694 b r + 0.016 a p l - 9.188 l y + 52.705 e p r - 4.874$	4	apl ly	89.65
log₁₀(J_r)	$0.950 p w - 29.975 b r + 0.005 a p l - 6.651 l y + 3.072 e p r - 2.905$	3	apl ly	81.56
J _el	$- 33.843 p w + 689.778 b r - 0.265 a p l + 72.428 l y - 1591.011 e p r + 132.938$	4	pw br apl ly epr	71.85
Log₁₀(η₀)	$57.529 b r - 1.567 p w - 0.018 a p l + 11.776 l y - 54.449 e p r + 6.519$	4	apl ly	89.68
1/G*	$9.275 \cdot 10^{- 5} p w - 2.446 \cdot 10^{- 3} b r + 8.503 \cdot 10^{- 7} a p l - 4.547 \cdot 10^{- 4} l y + 3.391 \cdot 10^{- 3} e p r - 8.588 \cdot 10^{- 5}$	5	br ly	84.26
tanδ	$0.151 p w - 4.067 b r + 7.868 \cdot 10^{- 4} a p l - 1.010 l y + 1.501 e p r + 0.377$	3	aplly	84.83
1/A_f	$9.161 \cdot 10^{- 5} p w - 2.491 \cdot 10^{- 3} b r + 8.597 \cdot 10^{- 7} a p l - 4.586 \cdot 10^{- 4} l y + 3.489 \cdot 10^{- 3} e p r - 8.525 \cdot 10^{- 5}$	5	pw br ly	83.81
z	$2.222 p w + 81.507 b r + - 5.997 \cdot 10^{- 3} a p l + 13.389 l y - 29.568 e p r - 5.274$	4	apl ly	83.26

Equations for rheology prediction were determined by PLS models of the microstructural attributes protein width (pw), branching rate (br), average protein length (apl), lacunarity (ly) and end-point rate (epr). The models’ dominated attributes are given by VIP (variable importance for projection) values greater than 0.8. R²Y describes the percentage explained for cumulative Y.