Bulletin of Mathematical Biology

, Volume 81, Issue 5, pp 1506–1526 | Cite as

A New Model System for Exploring Assembly Mechanisms of the HIV-1 Immature Capsid In Vivo

  • Yuewu Liu
  • Xiufen ZouEmail author


The assembly of the HIV-1 immature capsid (HIC) is an essential step in the virus life cycle. In vivo, the HIC is composed of \(\sim 420\) hexameric building blocks, and it takes 5–6 min to complete the assembly process. The involvement of numerous building blocks and the rapid timecourse makes it difficult to understand the HIC assembly process. In this work, we study HIC assembly in vivo by using differential equations. We first obtain a full model with 420 differential equations. Then, we reduce six addition reactions for separate building blocks to a single complex reaction. This strategy reduces the full model to 70 equations. Subsequently, the theoretical analysis of the reduced model shows that it might not be an effective way to decrease the HIC concentration at the equilibrium state by decreasing the microscopic on-rate constants. Based on experimental data, we estimate that the nucleating structure is much smaller than the HIC. We also estimate that the microscopic on-rate constant for nucleation reactions is far less than that for elongation reactions. The parametric collinearity investigation testifies the reliability of these two characteristics, which might explain why free building blocks do not readily polymerize into higher-order polymers until their concentration reaches a threshold value. These results can provide further insight into the assembly mechanisms of the HIC in vivo.


HIV-1 immature capsid Assembly model Sixfold symmetry Assembly dynamics Parametric collinearity 



The authors thank the anonymous reviewers for their valuable comments and suggestions. This work was supported by the Key Program of the National Natural Science Foundation of China (No. 11831015) and the Chinese National Natural Science Foundation (No. 61672388).


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Copyright information

© Society for Mathematical Biology 2019

Authors and Affiliations

  1. 1.School of Mathematics and Statistics, Computational Science Hubei Key LaboratoryWuhan UniversityWuhanChina
  2. 2.College of Information Science and TechnologyHunan Agricultural UniversityChangshaChina

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