The Modeling And Reconstruction Of Complex Immune And Dynamic Networks

In the real world,complex systems are ubiquitous,such as a series of complex systems involving many fields,including biological systems,economic systems,atmospheric systems,and so on.These systems,dominated by highdimensional nonlinear dynamics,have complex and variable spatio-temporal structures,so it is difficult to predict and control them.In the study of complex systems,Researchers usually describe them as complex networks according to the special properties of complex systems,and contemplate the structure and evolution of complex networks in order to understand and appreciate the dynamics,functions and regulation laws of their corresponding complex systems.In recent years,experimental and information technologies have flourished,and a large number of experimental observations in various fields are publicly available for scientific research.These experimental data often contain information on the structure and dynamics of the system,which can be used to reconstruct the system,and this is very valuable in academic research or engineering applications.In this paper,we try to establish a complex biological regulatory network model from the data,analyze the constructed model,and draw a conclusion from it,which can be used to guide the experiment.In the whole process,we first analyze the existing network reconstruction algorithms and propose a corresponding time-series-based network reconstruction algorithm for the shortcomings in current complex network reconstruction algorithms,such as noise interference,missing data,and other problems.These methods make up for the lack of nonlinear time series reconstruction to some extent.On the basis of sufficient data and some understanding of the data,these algorithms are expected to be applied to the reconstruction of complex biological networks.After the outbreak of COVID-19,according to the public data,this thesis built a phenomenological mesoscopic infection model of COVID-19 to analyze the relationship between microscopic human immunity and the COVID-19 infection process in macroscopic confined space,which provides a bridge for the joint statistics of epidemic spread and individual physiological parameters and can explain some of the observed phenomena.Because this model is not discussed in depth in the micro-immunity part,we select the germinal center in the immune tissue as the modeling goal of the complex biological regulatory network.Through microscopic experimental observations and less data,we successfully constructed a stochastic spatio-temporal model about the germinal center,and through the quantitative analysis of the model,we have a better understanding of the complex network structure and operating mechanism of the germinal center.In the future,with the support of more abundant data,the topology and dynamics of the regulatory network can be reconstructed based on the previous algorithms to achieve data-driven modeling of complex networks,which can be better used to understand and regulate complex systems for our production,life,and research.The main research contents as well as the innovation points of the thesis are as follows.1.Reconstructing the equations of motion and network topology of a system from time series is a very important problem,and many methods exist.However,in practice,Researchers are faced with the situation that the system is likely to be polluted by noise,and affected by objective conditions,only part of the information in the system is available,these two problems make reconstruction very difficult,so we propose some simple and effective methods to solve these problems and realize the reconstruction of system dynamics and network topology.In the face of strong noise intensity,we build a fitting model based on the invariance of the evolution equation of an autonomous system during time translation,by which a globally valid local approximation of the trajectory is determined,which could be reliably used for the reconstruction of the vector fields with unknown parameters or functional forms.Moreover,the noise interference with nonlinearity is computed to the leading order,which together with the global consideration bestows exceptional robustness and extra accuracy to the technique.The new method only needs to calculate the solution of the linear equation,so the computational efficiency is very high,which is well demonstrated in the analysis under different conditions.On the other hand,for the problem of hidden variables,we propose a novel variational method that transforms the determination of both the unknown variable orbits and the unknown coefficients of the equations into parameter learning.Using their different properties,the hidden variables and equation coefficients can be accurately inferred when only some of the variables are observed,even in the presence of noisy disturbances.This simple and effective method modifies the system equation we want to reconstruct in the process of dynamic evolution,until the reconstructed data is consistent with the real data,indicating that our reconstruction is complete,then the corresponding dynamical equations and network topology are obtained.2.Based on the publicly available data,we construct a stochastic model of COVID-19 transmission and infection in confined space and explain in detail the interaction between virus transmission and infection among mobile individuals.The model involves different aspects of mesoscopic interaction,such as human movement,virus shedding and transmission,virus invasion,and human immune system response.and their relative importance in the whole process of infection was evaluated.The model provides a bridge for studying the relationship between epidemiological statistics and individual physiological parameters and can be used as a theoretical guidance for epidemic prevention and control.3.Given the deficiency of immune response details of the COVID-19 mesoscopic infection model,we constructed a more complex biological regulatory network-Germinal center model.The germinal center(GC)is a selforganizing structure produced in the lymphoid follicle during the T-dependent immune response and is an important component of the humoral immune system,mainly composed of rapidly proliferating and hyper-mutated B cells,Follicular Dendritic Cell(FDC)for antigen presentation,Follicular Helper T cells(Tfh),Memory B cells(MBC)and Plasma cells(PC).However,the impact of the special structure of GC on antibody production is not clear.According to the latest biological experiments,we establish a spatiotemporal stochastic model to simulate the whole self-organization process of the GC including the appearance of two specific zones:the dark zone(DZ)and the light zone(LZ),the development of which serves to maintain an effective competition among different cells and promote affinity maturation.On the other hand,there is a phase transition in the affinity of memory or plasma cells,which determines a critical GC volume for affinity maturation in both the stochastic and the deterministic model.Further increase of the volume does not make much improvement on the performance.Through analysis,we find that the critical volume is determined by the shape space distance between the activated B Cell Receptor(BCR)and the target epitope of an antigen.The conclusion is confirmed in both 2D and 3D simulations and explains partly the variability of the observed GC size.