Analysis of single-molecule diffusion movement in cell membrance based on unsupervised learning methods: Different effects of cholesterol on flowability of model membrane and living cell membrane

Tan Jin-Peng; Zhang Wan-Ting; Xu Cheng; Lu Xue-Mei; Zhu Wen-Sheng; Yang Kai; Yuan Bing

doi:10.7498/aps.73.20240915

Abstract

Single molecular tracking is a valuable approach to investigate the dynamic processes and molecular interactions in soft matter systems, particularly in biological systems. However, understanding the complexity of single molecule motion behaviors in biological systems remains a significant challenge. To address this issue, we propose a two-step classification method based on unsupervised learning to efficiently identify and classify single molecule trajectories. Firstly, we employ an entropy-constrained least square method to distinguish between confined (e.g., immobile) and unconfined diffusion trajectories. Subsequently, statistical tests are utilized to categorize the unconfined trajectories into different diffusion modes such as sub-diffusion, normal diffusion, and super-diffusion.By applying this method, we analyze the diffusion motion of single molecules in both DOPC model cell membranes and living cell membranes while uncovering their distinct responses to cholesterol composition. Our findings demonstrate that both model membranes and living cell membranes exhibit diverse molecular diffusion modes. Specifically, in the DOPC model membrane system, the presence of cholesterol components impedes lipid diffusion within the membrane. The degree of inhibition is positively correlated with the amount of cholesterol present. For instance, as the cholesterol content in the membrane increases from 0 to 20% (DOPC:Chol = 4∶1) and 50% (DOPC:Chol = 1∶1), there is an increase in the proportion of molecules, exhibiting confined diffusion and sub-diffusion (from 55% to 45%), while there is a decrease in the proportion of molecules, displaying normal diffusion and super-diffusion (from 45% to 35%). The ensemble diffusion coefficient of molecules in the membrane significantly decreases, which can be attributed to both a decrease in velocity among fast-moving molecules. Interestingly, after using MeβCD to remove cholesterol, the single-molecule mobility within the DOPC/Chol composite membrane system is restored to a level similar to that of the pure DOPC membrane.Conversely, in the living cell membrane system, the diffusion coefficient values of molecules are significantly lower than those observed in the model membrane system; furthermore, the removal of cholesterol further slows down the molecular diffusion rate. This study contributes to understanding the intricacies of biomolecular motility and its dependence on environmental factors from a perspective of single molecular motion.

Keywords:

Authors and contacts

1.
School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
2.
Songshan Lake Materials Laboratory, Dongguan 523808, China
3.
Center for Soft Condensed Matter Physics and Interdisciplinary Research, School of Physical Science and Technology, Soochow University, Suzhou 215006, China
4.
School of Optical and Electronic Information, Suzhou City University, Suzhou 215104, China
5.
Jiangsu Key Laboratory of Frontier Material Physics and Devices, Suzhou City University, Suzhou 215006, China

Corresponding author: Yang Kai, yangkai@suda.edu.cn ; Yuan Bing, yuanbing@sslab.org.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12274307, 32230063, 12347102, 22307090, 22203059), the Basic and Applied Basic Research Foundation of Guangdong Province, China (Grant No. 2023A1515011610), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20210100), and the Program of Jiangsu Key Laboratory of Frontier Material Physics and Devices, China (Grant No. KJS2131).

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2024年73卷188702补充材料-模型膜和活细胞膜内单分子运动轨迹的扩散系数、异常指数、位移的三维分布视频.gif

References

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Cited By

图 1 单分子扩散运动的不同模式　(a)模拟运动模型的MSD曲线, 即定向扩散(蓝色)、正常扩散(红色)、异常扩散(绿色)和受限扩散(黑色), 横坐标为滞后时间(lag time); (b)采用“两步归类法”对单分子轨迹进行识别和分类的步骤, 第一步区分受限扩散与非受限扩散, 第二步将非受限扩散进一步区分

Figure 1. Different modes of single-molecule diffusion. (a) Simulated mean square displacement (MSD) curves depicting directed diffusion (blue), normal diffusion (red), anomalous diffusion (green), and confined diffusion (black). (b) The “two-step classification method” employed to identify and classify single-molecule trajectories: the first step involves distinguishing between confined and unconfined diffusion, followed by further differentiation of unconfined diffusion in the second step.

DownLoad: Full-Size Img PowerPoint

图 2 不同模型膜体系内单分子扩散运动分析, 即利用“两步归类法”将其分为受限扩散(Confined diffusion)、亚扩散(Sub-diffusion)、正常扩散(Normal diffusion)、超扩散(Super-diffusion) 4个子群, 分别计算其单分子轨迹的时间平均MSD并作出其分布. 轨迹数目见表1

Figure 2. Analysis of single lipid diffusion in various model membrane systems using the “two-step classification method”. Trajectories were categorized into four subgroups, namely confined diffusion, sub-diffusion, normal diffusion, and super-diffusion. The time-averaged MSD of individual trajectories was calculated to obtain the distribution. The number of trajectories is presented in Table 1.

DownLoad: Full-Size Img PowerPoint

图 3 B16活细胞膜(MeβCD处理前或处理后)内单分子扩散运动分析, 即利用“两步归类法”将其分为受限扩散(Confined diffusion)、亚扩散(Sub-diffusion)、正常扩散(Normal diffusion) 3个子群, 分别计算其单分子轨迹的时间平均MSD并作出其分布, 轨迹数目见表2

Figure 3. Analysis of single-molecule diffusion in live cell membranes (before or after MeβCD treatment). This analysis employs a two-step classification method to divide the data into subgroups of confined diffusion, sub-diffusion, and normal diffusion. The time-averaged MSD is calculated for individual trajectories and its distribution is plotted. The number of trajectories analyzed is provided in Table 2.

DownLoad: Full-Size Img PowerPoint

图 4 不同体系内D_L和α值分布, 包括纯DOPC膜(包含1324条轨迹)、DOPC∶Chol = 1∶1混合膜(2347条轨迹)、活细胞膜经MeβCD处理之前(1436条轨迹)和之后(784条轨迹), 其中插图中横坐标以对数形式显示

Figure 4. Distribution of D_L and α values in different systems: pure DOPC membrane (1324 trajectories), DOPC∶Chol = 1∶1 mixed membrane (2347 trajectories), living cell membrane before MeβCD treatment (1436 trajectories), and after MeβCD treatment (784 trajectories). The horizontal coordinate is presented logarithmically in the inset.

DownLoad: Full-Size Img PowerPoint

表 1 不同模型膜体系内单脂质分子轨迹分类及相应的系综扩散系数和异常指数数值, 其中轨迹长度为60帧

Table 1. Classification of single lipid trajectories in different model membrane systems and corresponding ensemble diffusion coefficient and anomaly index values. The trajectory length is 60 frames.

	Subgroup	Control			+MeβCD
	Subgroup	DOPC	DOPC:CHOL = 4∶1	DOPC:CHOL = 1∶1	DOPC	DOPC:CHOL = 4∶1	DOPC:CHOL = 1∶1
Trajectory number	Confined	282	383	497	293	334	330
	Sub-diffusion	943	1143	1036	947	799	811
	Normal diffusion	318	294	290	305	200	207
	Super-diffusion	667	577	524	647	448	449
Proportion/%	Confined	12.76	15.98	21.18	13.37	18.75	18.36
	Sub-diffusion	42.67	47.68	44.14	43.20	44.86	45.13
	Normal diffusion	14.39	12.27	12.36	13.91	11.23	11.52
	Super-diffusion	30.18	24.07	22.33	29.52	25.15	24.99
Diffusion coefficient D_L/(μm²·s^–1)	Confined	0.045	0.032	0.029	0.064	0.034	0.061
	Sub-diffusion	1.086	0.582	0.308	0.805	0.784	0.717
	Normal diffusion	2.421	1.581	0.870	2.100	2.051	1.781
	Super-diffusion	4.149	3.211	1.444	3.908	3.650	3.381
Anomaly index (α)	Confined	0.116	0.094	0.068	0.207	0.099	0.171
	Sub-diffusion	0.709	0.629	0.512	0.629	0.635	0.614
	Normal diffusion	0.909	0.869	0.916	0.948	0.910	0.874
	Super-diffusion	1.133	1.103	1.178	1.141	1.132	1.132

DownLoad: CSV

表 2 经MeβCD去除胆固醇前后活细胞膜内单分子轨迹分类及相应的系综扩散系数和异常指数数值, 其中轨迹长度为20帧

Table 2. Classification of single-molecule trajectory in living cell membranes before and after cholesterol depletion by MeβCD, along with corresponding ensemble-averaged diffusion coefficient and anomaly index values. The trajectory length is 20 frames.

	Subgroup	Control	+MeβCD
Trajectory number	Confined	452	304
	Sub-diffusion	645	377
	Normal diffusion	339	103
Proportion/%	Confined	31.48	38.78
	Sub-diffusion	44.92	48.09
	Normal diffusion	23.61	13.14
Diffusion coefficient D_L/(μm²·s^–1)	Confined	0.017	0.011
	Sub-diffusion	0.069	0.040
	Normal diffusion	0.465	0.260
Anomaly index (α)	Confined	0.146	0.095
	Sub-diffusion	0.437	0.461
	Normal diffusion	0.983	0.861

DownLoad: CSV

[1]	Jacobson K, Liu P, Lagerholm B C 2019 Cell 177 806 Google Scholar
[2]	He W, Song H, Su Y, et al. 2016 Nat. Commun. 7 11701 Google Scholar
[3]	Golan Y, Sherman E 2017 Nat. Commun. 8 15851 Google Scholar
[4]	Subczynski W K, Pasenkiewicz-Gierula M, Widomska J, Mainali L, Raguz M 2017 Cell Biochem. Biophys. 75 369 Google Scholar
[5]	van Meer G, Voelker D R, Feigenson G W 2008 Nat. Rev. Mol. Cell Biol. 9 112 Google Scholar
[6]	Liu Y, Zheng X, Guan D, Jiang X, Hu G 2022 ACS Nano 16 16054 Google Scholar
[7]	Lyman E 2021 Biophys. J. 120 1777 Google Scholar
[8]	Zhang X, Barraza K M, Beauchamp J L 2018 P. Natl. Acad. Sci. USA 115 3255 Google Scholar
[9]	Chakraborty S, Doktorova M, Molugu T R, et al. 2020 P. Natl. Acad. Sci. USA 117 21896 Google Scholar
[10]	Pohnl M, Trollmann M F W, Bockmann R A 2023 Nat. Commun. 14 8038 Google Scholar
[11]	Fernandez-Perez E J, Sepulveda F J, Peters C, et al. 2018 Front. Aging Neurosci. 10 226 Google Scholar
[12]	Doole F T, Kumarage T, Ashkar R, Brown M F 2022 J. Membr. Biol. 255 385 Google Scholar
[13]	Byfield F J, Aranda-Espinoza H, Romanenko V G, Rothblat G H, Levitan I 2004 Biophys. J. 87 3336 Google Scholar
[14]	Yang S T, Kreutzberger A J B, Lee J, Kiessling V, Tamm L K 2016 Chem. Phys. Lipids 199 136 Google Scholar
[15]	Norregaard K, Metzler R, Ritter C M, Berg-Sorensen K, Oddershede L B 2017 Chem. Rev. 117 4342 Google Scholar
[16]	Ge F, Du Y, He Y 2022 ACS Nano 16 5325 Google Scholar
[17]	Chen P Y, Yue H, Zhai X B, Huang Z H, Ma G H, Wei W, Yan L T 2019 Sci. Adv. 5 eaaw3192 Google Scholar
[18]	Jeon J H, Javanainen M, Martinez-Seara H, Metzler R, Vattulainen I 2016 Phys. Rev. X 6 021006 Google Scholar
[19]	Xu C, Yang K, Yuan B 2023 J. Phys. Chem. Lett. 14 854 Google Scholar
[20]	Xu C, Ma W, Wang K, He K, Chen Z, Liu J, Yang K, Yuan B 2020 J. Phys. Chem. Lett. 11 4834 Google Scholar
[21]	Pinholt H D, Bohr S S R, Iversen J F, Boomsma W, Hatzakis N S 2021 P. Natl. Acad. Sci. USA 118 e2104624118 Google Scholar
[22]	Muñoz-Gil G, Garcia-March M A, Manzo C, Martín-Guerrero J D, Lewenstein M 2020 New J. Phys. 22 013010 Google Scholar
[23]	Cherstvy A G, Thapa S, Wagner C E, Metzler R 2019 Soft Matter 15 2526 Google Scholar
[24]	Granik N, Weiss L E, Nehme E, Levin M, Chein M, Perlson E, Roichman Y, Shechtman Y 2019 Biophys. J. 117 185 Google Scholar
[25]	Janczura J, Kowalek P, Loch-Olszewska H, Szwabinski J, Weron A 2020 Phys. Rev. E 102 032402 Google Scholar
[26]	Barkai E, Garini Y, Metzler R 2012 Phys. Today 65 29 Google Scholar
[27]	Krapf D, Metzler R 2019 Phys. Today 72 48 Google Scholar
[28]	Wu J F, Xu C, Ye Z F, Chen H B, Wang Y P, Yang K, Yuan B 2023 Small 19 2301713 Google Scholar
[29]	Yamamoto E, Akimoto T, Kalli A C, Yasuoka K, Sansom M S P 2017 Sci. Adv. 3 e1601871 Google Scholar
[30]	Feder T J, Brust-Mascher I, Slattery J P, Baird B, Webb W W 1996 Biophys. J. 70 2767 Google Scholar
[31]	Briane V, Kervrann C, Vimond M 2018 Phys. Rev. E 97 062121 Google Scholar
[32]	Lanoiselée Y, Sikora G, Grzesiek A, Grebenkov D S, Wylomanska A 2018 Phys. Rev. E 98 062139 Google Scholar
[33]	Sikora G, Teuerle M, Wylomanska A, Grebenkov D 2017 Phys. Rev. E 96 022132 Google Scholar
[34]	Saxton M J, Jacobson K 1997 Annu. Rev. Biophys. Biomol. Struct. 26 373 Google Scholar
[35]	Kusumi A, Sako Y, Yamamoto M 1993 Biophys. J. 65 2021 Google Scholar
[36]	Saxton M J 1993 Biophys. J. 64 1766 Google Scholar
[37]	Shannon C E 1948 Bell Syst. Tech. J. 27 379 Google Scholar
[38]	Wright S J, Tenny M J 2004 Siam J. Optim. 14 1074 Google Scholar
[39]	Raja M A Z, Ahmed U, Zameer A, Kiani A K, Chaudhary N I 2019 Neural. Comput. Appl. 31 447 Google Scholar
[40]	Zhang Y, Yao F, Iu H H C, Fernando T, Wong K P 2013 J. Mod. Power Syst. Clean Energy 1 231 Google Scholar
[41]	Weron A, Janczura J, Boryczka E, Sungkaworn T, Calebiro D 2019 Phys. Rev. E 99 042149 Google Scholar
[42]	Hubicka K, Janczura J 2020 Phys. Rev. E 101 022107 Google Scholar
[43]	Xu R, Zhang W T, Jin T, Tu W, Xu C, Wei Y, Han W, Yang K, Yuan B 2024 ACS Appl. Mater. Interfaces 16 6813 Google Scholar
[44]	Li L, Ji J, Song F, Hu J 2023 J. Mol. Biol. 435 167787 Google Scholar
[45]	Li L, Hou R H, Shi X H, et al. 2024 Commun. Phys. 7 174 Google Scholar
[46]	Gao J, Hou R, Li L, Hu J 2021 Front. Mol. Biosci. 8 811711 Google Scholar
[47]	陆越, 马建兵, 滕翠娟, 陆颖, 李明, 徐春华 2018 物理学报 67 088201 Google Scholar Lu Y, Ma J B, Teng C J, Lu Y, Li M, Xu C H 2018 Acta Phys. Sin. 67 088201 Google Scholar
[48]	Gao J, Hou R, Hu W, et al. 2024 J. Phys. Chem. B 128 4735 Google Scholar

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2024年73卷188702补充材料.pdf
2024年73卷188702补充材料-模型膜和活细胞膜内单分子运动轨迹的扩散系数、异常指数、位移的三维分布视频.gif

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