溶酶菌蛋白质结晶的多目标优化与模拟

doi:10.11949/0438-1157.20230757

摘要/Abstract

摘要：

晶体形式的蛋白质药物在活性组分可控释放、生化稳定性等方面有较大优势，但蛋白质结晶的优化控制很复杂。通过基于晶体形貌的群体平衡模型与多目标遗传算法的耦合求解，研究了鸡蛋清溶酶菌冷却结晶的多目标优化问题，目标包括晶体尺寸均一、晶体形状相同、产品收率最大。冷却策略采用十个区间依次降温，但各区间降温速率独立线性变化。Pareto解是三个目标相互平衡的结果，收率目标与形状目标朝极值演化的趋势一致，而晶体尺寸分布目标与上述两者相反。随着不同Pareto解的收率增加，相应结晶过程的各段降温速率总体增加，平均过饱和度也变大且普遍高于常见小分子结晶的过饱和度。由于过饱和度对晶体两个法向距离的增长速度具有不同影响，导致更高收率的Pareto解对应的最终平均晶体尺寸更大，且形状更扁平。

关键词: 结晶, 蛋白质, 数值模拟, 优化, 群体平衡模型, 遗传算法

Abstract:

Crystalline protein drugs have significant advantages in controllable release of active components and biochemical stability, but the optimization and control of protein crystallization are complex. Based on the combined algorithm of morphological population balance (MPB) model and multi-objective genetic algorithm, multi-objective optimization for the cooling crystallization of hen-egg-white (HEW) lysozyme is investigated with the objectives of uniform crystal size distribution (CSD), certain crystal shape, and maximum product yield. The piece-wise cooling strategy with ten sections is adopted, while the cooling rates linearly vary in each section independently. The Pareto-optimal solutions are the trade-off among three objective functions. It is found that the shape objective and yield objective have similar evolution tendency toward their ideal extremes, while the CSD objective evolves toward the opposite direction. With the increase of product yield for different Pareto-optimal solutions, the cooling rates during the crystallization process generally increase, and the relative supersaturation becomes larger, which is also higher than most common small molecules. Due to the different influences of supersaturation on the growth rates of two normal distances, the final protein crystals for those Pareto-optimal solutions with higher yield also have larger dimensions, and their shapes become more plate-like.

Key words: crystallization, protein, numerical simulation, optimization, population balance model, genetic algorithm

中图分类号:

TQ 018

周光正, 王学重, 周浩宇. 溶酶菌蛋白质结晶的多目标优化与模拟[J]. 化工学报, 2023, 74(10): 4191-4200.

Guangzheng ZHOU, Xuezhong WANG, Haoyu ZHOU. Multi-objective optimization and simulation of lysozyme protein crystallization[J]. CIESC Journal, 2023, 74(10): 4191-4200.

图/表 9

图1 溶酶菌晶体的几何结构与两个法向距离

Fig.1 Geometrical structure of lysozyme crystal and its two normal distances

图2 蛋白质结晶多目标优化的求解流程图

Fig.2 Flowchart of multi-objective optimization for protein crystallization

图3 Pareto前沿及其在三个面的投影

Fig.3 Pareto frontier and its projection on three faces

图4 冷却速率与温度的时间演化

Fig.4 Variations of cooling rate and temperature with time

图5 三个目标函数的时间演化

Fig.5 Variations of three objective functions with time

图6 过饱和度的时间演化

Fig.6 Variations of relative supersaturation with time

图7 晶体两个法向距离比值的时间演化

Fig.7 Evolutions of length ratio of two normal distances with time

图8 初始时刻的平均晶体形状以及三个不同收率的平均最终晶体形状

Fig.8 Initial mean crystal shape and the final mean shapes under three different crystal yields

图9 晶体质量的时间演化

Fig.9 Variations of crystal mass with time

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