A Note on Invertases
Invertases (β-fructofuranosidases) are glycoprotein enzymes classified as Glycoside Hydrolases or GHs (under the GH-family) BRENDA, n.d.. Invertase catalyses the hydrolysis of Sucrose into D-fructose and D-glucose through cleavage of the terminal non-reducing beta-fructofuranoside residues, a reaction known as inversion. In nature, Invertase usually exists in various isoforms.
Figure 1: Inversion of Sucrose into Glucose and Fructose catalysed by Invertase
Two of the main invertases found in sugarcane are the neutral invertases and acid invertases, which are spatially differentiated. Sucrose - the end product of photosynthesis, is transported to three different cellular compartments: the cell wall (apoplastic space), the vacuole, and the cytoplasm. There is a specific invertase isoform for each compartment Shivalingamurthy, S. G., et al., 2018:
- Apoplastic space located cell wall invertase (CWI)/ Insoluble acid Invertase;
- A Vacuolar located acid invertase (VAI) also termed a Soluble acid invertase (SAI); and
- A cytoplasmic located Neutral invertase (NI)
These isoforms of plant invertases are classified into 2 different GH families: GH32 and GH100. Cell wall invertases and Vacuolar invertases (Acid invertases) belong to the GH32 family, while Cytoplasmic invertases (alkaline/neutral invertases) belong to the GH100 family. Acid invertase amino acid sequences generally do not share any similarity with sequences of GH100 enzymes, and the members of GH100 remain in need of structure elucidation and exact mechanism of action.
In sugarcane, Invertase mainly regulates the plant metabolism and sucrose accumulation. It is crucial for metabolizing sucrose to provide energy to the cells for respiration, and to provide a carbon source for glycosynthesis of various essential products. Sucrose accumulation begins in the elongating internodes, until maximum elongation is achieved. Ansari, M. I. et al., 2013. In these immature intermodal tissues, it is found that the concentration of invertase is linearly related to the rate of intermodal elongation Batta, S. K. & Singh, R., 1986. Invertase action is triggered by changes in osmotic pressure of cells, thus achieving cell elongation and growth.
During pre- and post-harvest periods, however, Invertase has an undesirable role in continuously degrading sucrose (in the vacuoles and intracellular space) thereby reducing recovery rate and overall sugar yield. Our genetically engineered E. coli tries to to address this issue.
Data Provided by Mr Sunil Kumar Ohri
Figure 2: Time Cycle of Cane Supply
Figure 3: Loss in Recovery due to Staleness of Cane
Figure 4: Business Impact - Extraneous Matter
Figure 5: Loss of Sugar and Weight due to Delay
Radau Methods
The system of ODEs we obtained for the kill switch were stiff ~ A system of ODEs for which solvers are numerically unstable in nature. Explicit Runge-Kutta methods (like RK45) are unsuitable for solving such differential equations because of their small and bounded region of absolute stability.
For an initial value problem $$ \frac{dy}{dt} = f(t, y), \quad y(t_0) = y_0 $$
An implicit Runge–Kutta method has the form
$$ y_{n+1} = y_n + h\sum_{i=1}^{s}b_ik_i $$ $$\text{where }k_i = f\left(t_n + c_i h, y_n + h\sum_{j=1}^{s}a_{ij}k_j \right) \quad i = 1, 2, \dots, s$$
Owing to the stiffness of the equations, we had to solve our kill switch model using the fifth-order Radau IIA method, which is an implicit Runge-Kutta method where the coefficients \(c_i\) are given by the zeros of the polynomial \( \frac{d^4}{dx^4}(x^4(x-1)^5) \)