*3.8. Thermodynamic Parameter of the rPsLeuDH*

The *k*cat parameter is the reaction rate constant for the enzymatic-substrate complex chemical conversion into the enzyme and the product. *k*cat was calculated based on kinetics experiments, and the thermodynamic related parameters were assayed by the modification method of Feller [27] as follows:

$$k\_{\text{cat}} = A e^{\frac{-E\_{\text{a}}}{RT}} \tag{1}$$

$$
\Delta H = E\_\text{a} - RT\tag{2}
$$

$$
\Delta S = R \left( I n k\_{\rm cat} - 24.76 - I n T + \frac{E\_{\rm a}}{RT} \right) \tag{3}
$$

$$
\Delta G = \Delta H - T\Delta S \tag{4}
$$

where *A* is the constant, *E*<sup>a</sup> is the activation energy of the reaction, *R* is the gas constant (8.314 J mol−<sup>1</sup> K−1), Δ*H* is the enthalpy of activation, Δ*S* is the entropy of activation, and Δ*G* is the free energy of activation.

#### **4. Conclusions**

A novel cold-adapted leucine dehydrogenase gene (*psleudh*) was cloned from Antarctic sea-ice bacterium and expressed in *E. coli* (DE3). Through homology modeling and comparison with its homologous enzyme (BsLeuDH), it was suggested that more glycine residues, reduced proline residues and arginine residues might be responsible for its catalytic efficiency at low temperature. rPsLeuDH was purified and characterized with higher activity at 30 ◦C, high salt (3.0 M), remarkable pH stability (pH 6.0–10.0), and higher specific activity (275.13 U/mg). These unique properties of rPsLeuDH make it a promising candidate as a biocatalyst in the enzymatic production of L-*tert*-leucine at room temperature.

**Author Contributions:** Y.W., Y.H. and Q.W. took charge of the research and designed the experiments; Y.W., L.Z., X.X., K.P., R.L., Y.W. and Y.H. performed the experiments and analyzed the data; Y.W. and Q.W. wrote the paper.

**Funding:** This research was funded by the National Natural Science Foundation of China (41876149), the Natural Science Foundation of Shandong Province (ZR2017MC046) and the Key Research and Development Plan of Shandong Province (2018GHY115021).

**Conflicts of Interest:** The authors declare no conflict of interest.
