Quorum sensing (QS) refers to the cell communication through signaling molecules that regulate many important biological functions of bacteria by monitoring their population density. Although a wide spectrum of studies on the QS system mechanisms have been carried out in experiments, mathematical modeling to explore the QS system has become a powerful approach as well. In this paper, we review the research progress of network modeling in bacterial QS to capture the system’s underlying mechanisms. There are four types of QS system models for bacteria: the Gram-negative QS system model, the Gram-positive QS system model, the model for both Gram-negative and Gram-positive QS system, and the synthetic QS system model. These QS system models are mostly described by the ordinary differential equations (ODE) or partial differential equations (PDE) to study the changes of signaling molecule dynamics in time and space and the cell population density variations. Besides the deterministic simulations, the stochastic modeling approaches have also been introduced to discuss the noise effects on kinetics in QS systems. Taken together, these current modeling efforts advance our understanding of the QS system by providing systematic and quantitative dynamics description, which can hardly be obtained in experiments.
RNAs carry out diverse biological functions, partly because different conformations of the same RNA sequence can play different roles in cellular activities. To fully understand the biological functions of RNAs requires a conceptual framework to investigate the folding kinetics of RNA molecules, instead of native structures alone. Over the past several decades, many experimental and theoretical methods have been developed to address RNA folding. The helix-based RNA folding theory is the one which uses helices as building blocks, to calculate folding kinetics of secondary structures with pseudoknots of long RNA in two different folding scenarios. Here, we will briefly review the helix-based RNA folding theory and its application in exploring regulation mechanisms of several riboswitches and self-cleavage activities of the hepatitis delta virus (HDV) ribozyme.
RNAs play crucial and versatile roles in biological processes. Computational prediction approaches can help to understand RNA structures and their stabilizing factors, thus providing information on their functions, and facilitating the design of new RNAs. Machine learning (ML) techniques have made tremendous progress in many fields in the past few years. Although their usage in protein-related fields has a long history, the use of ML methods in predicting RNA tertiary structures is new and rare. Here, we review the recent advances of using ML methods on RNA structure predictions and discuss the advantages and limitation, the difficulties and potentials of these approaches when applied in the field.
Proteins are important biological molecules whose structures are closely related to their specific functions. Understanding how the protein folds under physical principles, known as the protein folding problem, is one of the main tasks in modern biophysics. Coarse-grained methods play an increasingly important role in the simulation of protein folding, especially for large proteins. In recent years, we proposed a novel coarse-grained method derived from the topological soliton model, in terms of the backbone Cα chain. In this review, we will first systematically address the theoretical method of topological soliton. Then some successful applications will be displayed, including the thermodynamics simulation of protein folding, the property analysis of dynamic conformations, and the multi-scale simulation scheme. Finally, we will give a perspective on the development and application of topological soliton.
It is a central issue to find the slow dynamic modes of biological macromolecules via analyzing the large-scale data of molecular dynamics simulation (MD). While the MD data are high-dimensional time-successive series involving all-atomic details and sub-picosecond time resolution, a few collective variables which characterizing the motions in longer than nanoseconds are needed to be chosen for an intuitive understanding of the dynamics of the system. The trajectory map (TM) was presented in our previous works to provide an efficient method to find the low-dimensional slow dynamic collective-motion modes from high-dimensional time series. In this paper, we present a more straight understanding about the principle of TM via the slow-mode linear space of the conformational probability distribution functions of MD trajectories and more clearly discuss the relation between the TM and the current other similar methods in finding slow modes.
