Singular values, <i>σ_i</i>, obtained from singular value decomposition of the glycan class process gain matrices for three operating ranges.

<p>Output modes associated with singular values, <i>σ_i</i>><i>σ_*</i> = 1, are considered controllable.</p

Heat maps representing the significant elements of the process gain matrices for specific glycoforms typically found in biologics in operating (a) Range 1, (b) Range 2, and (c) Range 3.

<p>Visual inspection suggests that significant process gains are associated with 8 of the 18 glycoforms when the process is operated in Range 1 and 11 of the 18 glycoforms when operated in Range 2, indicating that the relative percentage of glycoforms can be changed in these operating ranges. As with the glycan classes, there are no significant process gains for any glycoforms in operating Range 3, suggesting that the relative percentage of glycoforms cannot be affected or controlled at all when the process is operated in Range 3.</p

Graphical representation of the coefficients associated with each enzyme and sugar nucleotide donor in input modes, µ<i>_i</i>, associated with the controllable output modes for glycoforms, <i>η_i,</i> shown in Figure 6.

<p>Each column shows the glycosylation enzymes and sugar nucleotides of each input modes in each operating range (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0087973#pone-0087973-t001" target="_blank">Table 1</a>). No input modes are shown for operating Range 3 since no controllable modes were found in this range. Coefficients were obtained using eq. 10 following singular value decomposition of the process gain matrix corresponding to the glycoform distribution as described in section “Assessing Controllability from the Process Gain Matrix”. How much the enzyme or sugar nucleotide contributes to an input mode is reflected in the coefficient associated with that variable in the linear combination. A dominant contributor to a mode (where one exists) is identified by the variable with the largest coefficient in the weighted sum. The enzyme(s) and/or sugar nucleotide(s) that are dominant contributors of the input mode affect the glycoforms of the associated output mode the most.</p

Graphical representation of the coefficients associated with each glycan class in the controllable output modes, <i>η_i.</i>

<p>Modes that were not controllable (i.e. associated with singular values, <b><i>σ_i</i></b><<b><i>σ_*</i></b> = 1) are not shown. Each column shows the glycan classes (output modes) that are controllable in each operating range (See <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0087973#pone-0087973-t001" target="_blank">Table 1</a>). No output modes are shown for operating Range 3 since no controllable modes were found in this range. Coefficients were obtained using eq. 9 following singular value decomposition of the glycan class process gain matrix as described in section “Assessing Controllability from the Process Gain Matrix”. How much the glycan class contributes to an output mode is reflected in the coefficient associated with that variable in the linear combination. A dominant contributor to a mode (where one exists) is identified by the variable with the largest coefficient in the weighted sum. Any glycan classes associated with a non-zero coefficient can be affected by perturbations in the associated input mode; however the dominant glycan class will be affected the most.</p

Heat maps representing the significant elements of the process gain matrices for the glycan classes in operating (a) Range 1, (b) Range 2, and (c) Range 3.

<p>Visual inspection suggests that significant process gains are associated with 10 of the 12 glycan classes when the process is operated in Range 1 or 2 indicating that the relative percentage of glycan classes can be changed in these operating ranges. There are no significant process gains for any glycan class in operating Range 3, suggesting that the relative percentage of glycan classes cannot be affected or controlled at all when the process is operated in Range 3.</p

Graphical representation of the coefficients associated with each enzyme and sugar nucleotide donor in input modes, <i>µ_i</i>, associated with the controllable output modes for glycan classes, <i>η_i,</i> shown in Figure 2.

<p>Each column shows the coefficients associated with the enzymes and sugar nucleotides of each input mode in each operating range (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0087973#pone-0087973-t001" target="_blank">Table 1</a>). No input modes are shown for operating Range 3 since no controllable modes were found in this range. Coefficients were obtained using eq. 10 following singular value decomposition the process gain matrix for the glycan classes as described in section “Assessing Controllability from the Process Gain Matrix”. How much the enzyme or sugar nucleotide contributes to an input mode is reflected in the coefficient associated with that variable in the linear combination. A dominant contributor to a mode (where one exists) is identified by the variable with the largest coefficient in the weighted sum. The enzyme(s) and/or sugar nucleotide(s) that are dominant contributors of the input mode affect the glycan classes of the associated output mode the most.</p

Operating ranges of input factors used in controllability analysis (i.e., µM concentrations used for each glycosylation enzyme and sugar nucleotide donor investigated as factors in DoE).

<p>Operating ranges of input factors used in controllability analysis (i.e., µM concentrations used for each glycosylation enzyme and sugar nucleotide donor investigated as factors in DoE).</p

Singular values, <i>σ_i</i>, obtained from singular value decomposition of the glycoform process gain matrix for three operating ranges.

<p>Output modes associated with singular values, <i>σ_i</i>><i>σ_*</i> = 1, are considered controllable.</p

List of responses and inputs used for controllability analysis.

†<p>Note: The naming convention of the glycan classes is as follows: S# is the number of sialic acid molecules present in the glycoform, G#, galactose, and F#, fucose; where A represents anternarity. For example, the S0 class includes those glycoforms of the 7,565 that are possible with no sialic acid molecules present. The numbers in the glycoform nomenclature represent the number of each sugar molecule attached to the core glycan structure (i.e., three mannose and two n-acetyl glucosamine molecules). For example, the A2G2S2 glycoform has 2 branches each with a galactose and a sialic acid molecule attached to the core glycan structure, as shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0087973#pone-0087973-g005" target="_blank">Figure 5</a>.</p