P06-06

Development of RNA velocity method using numerical integration of ordinary differential equations

Yuki KOBAYASHI *, Tomonari MATSUDA

Department of Environmental Engineering, Graduate School of Engineering, Kyoto University
( * E-mail: kobayashi.yuki.58w@st.kyoto-u.ac.jp )

RNA velocity is one of the trajectory inference methods of single-cell transcriptome analysis, which uses the number of mature/immature mRNA and kinetics about transcription/splicing/degradation of mRNA. RNA velocity method has the potential to recover real time series by describing the dynamics with differential equations. However, any current methods have their own challenges in dealing with the differential equations: requirement of analytical solutions, machine learning of the differential equations and so on. To solve the problems, we develop a method using numerical integration of ordinary differential equations. It is expected that more realistic dynamics can be used even when analytical solutions are difficult to obtain. In addition, simulations also use numerical integration but have often been performed qualitatively. However, our method enables quantitative evaluation and modification of simulations, and it is expected to promote knowledge-based in silico analysis.

Integration of observations and numerical simulations is named as data assimilation, which has been developed in geosciences. In this study, we formulated the method using the four-dimensional variational method (4D Var), which can integrate observations from multiple times at once. Here, we derive 4D Var using maximum likelihood estimation of normal distribution for observation errors.

In this study, we assume that the gene expression kinetics is the same as current RNA velocity methods and use pseudo data generated from the kinetics of a single gene. The kinetics of mRNA are described by the parameters of transcription rate, degradation rate, expected number of mature/immature mRNA, and time interval for each cell. Applying 4D Var, we should decide numerical integration method, observation operator, and optimization method according to the experimental setting. The numerical integration method is used as the fourth order Runge–Kutta scheme. The observation operator is a matrix that returned the number of mature/immature mRNA. In addition, Observation data are generated by adding a normally distributed random number into the true values of mature/immature mRNA. Optimization is performed by increment method and conjugate gradient method. As a result, the curve fitting on the gene expression space stretched by mature/immature mRNA was successful, and it was confirmed that the other unobservable parameters could be successfully estimated like current methods.

One of the current issues of our methods is the high initial value dependence of the analytical results. Therefore, optimization methods and initial value setting using the analytical solution will be developed. In addition, mRNA dynamics assumed in this study are very simple, but the superiority of our method is to handle complex dynamics. Therefore, we will model the dynamics of gene expression in more detail and our methods can be performed more accurately than with current RNA velocity methods.