The linear interplay of intrinsic and extrinsic noises ensures a high accuracy of cell fate selection in budding yeast

Effect of color cross-correlated noise on the growth characteristics of tumor cells under immune surveillance

Based on the Michaelis-Menten reaction model with catalytic effects, a more comprehensive one-dimensional stochastic Langevin equation with immune surveillance for a tumor cell growth system is obtained by considering the fluctuations in growth rate and mortality rate. To explore the impact of environmental fluctuations on the growth of tumor cells, the analytical solution of the steady-state probability distribution function of the system is derived using the Liouville equation and Novikov theory, and the influence of noise intensity and correlation intensity on the steady-state probability distributional function are discussed. The results show that the three extreme values of the steady-state probability distribution function exhibit a structure of two peaks and one valley. Variations of the noise intensity, cross-correlation intensity and correlation time can modulate the probability distribution of the number of tumor cells, which provides theoretical guidance for determining treatment plans in clinical treatment. Furthermore, the increase of noise intensity will inhibit the growth of tumor cells when the number of tumor cells is relatively small, while the increase in noise intensity will further promote the growth of tumor cells when the number of tumor cells is relatively large. The color cross-correlated strength and cross-correlated time between noise also have a certain impact on tumor cell proliferation. The results help people understand the growth kinetics of tumor cells, which can a provide theoretical basis for clinical research on tumor cell growth.

Forecasting sensitive targets of the kynurenine pathway in pancreatic adenocarcinoma using mathematical modeling

In this study, a new mathematical model was established and validated to forecast and define sensitive targets in the kynurenine pathway (Kynp) in pancreatic adenocarcinoma (PDAC). Using the Panc-1 cell line, genetic profiles of Kynp molecules were tested. qPCR data were implemented in the algorithm programming (fmincon and lsqnonlin function) to estimate 35 parameters of Kynp variables by Matlab 2017b. All tested parameters were defined as non-negative and bounded. Then, based on experimental data, the function of the fmincon equation was employed to estimate the approximate range of each parameter. These calculations were confirmed by qPCR and Western blot. The correlation coefficient (R) between model simulation and experimental data (72 hours, in intervals of 6 hours) of every variable was >0.988. The analysis of reliability and predictive accuracy depending on qPCR and Western blot data showed high predictive accuracy of the model; R was >0.988. Using the model calculations, kynurenine (x3, a6), GPR35 (x4, a8), NF-kβp105 (x7, a16), and NF-kβp65 (x8, a18) were recognized as sensitive targets in the Kynp. These predicted targets were confirmed by testing gene and protein expression responses. Therefore, this study provides new interdisciplinary evidence for Kynp-sensitive targets in the treatment of PDAC.

Likelihood for transcriptions in a genetic regulatory system under asymmetric stable Lévy noise

This work is devoted to investigating the evolution of concentration in a genetic regulation system, when the synthesis reaction rate is under additive and multiplicative asymmetric stable Lévy fluctuations. By focusing on the impact of skewness (i.e., non-symmetry) in the probability distributions of noise, we find that via examining the mean first exit time (MFET) and the first escape probability (FEP), the asymmetric fluctuations, interacting with nonlinearity in the system, lead to peculiar likelihood for transcription. This includes, in the additive noise case, realizing higher likelihood of transcription for larger positive skewness (i.e., asymmetry) index β, causing a stochastic bifurcation at the non-Gaussianity index value α = 1 (i.e., it is a separating point or line for the likelihood for transcription), and achieving a turning point at the threshold value β≈-0.5 (i.e., beyond which the likelihood for transcription suddenly reversed for α values). The stochastic bifurcation and turning point phenomena do not occur in the symmetric noise case (β = 0). While in the multiplicative noise case, non-Gaussianity index value α = 1 is a separating point or line for both the MFET and the FEP. We also investigate the noise enhanced stability phenomenon. Additionally, we are able to specify the regions in the whole parameter space for the asymmetric noise, in which we attain desired likelihood for transcription. We have conducted a series of numerical experiments in "regulating" the likelihood of gene transcription by tuning asymmetric stable Lévy noise indexes. This work offers insights for possible ways of achieving gene regulation in experimental research.

Mathematical modeling and quantitative analysis of HIV-1 Gag trafficking and polymerization

Gag, as the major structural protein of HIV-1, is necessary for the assembly of the HIV-1 sphere shell. An in-depth understanding of its trafficking and polymerization is important for gaining further insights into the mechanisms of HIV-1 replication and the design of antiviral drugs. We developed a mathematical model to simulate two biophysical processes, specifically Gag monomer and dimer transport in the cytoplasm and the polymerization of monomers to form a hexamer underneath the plasma membrane. Using experimental data, an optimization approach was utilized to identify the model parameters, and the identifiability and sensitivity of these parameters were then analyzed. Using our model, we analyzed the weight of the pathways involved in the polymerization reactions and concluded that the predominant pathways for the formation of a hexamer might be the polymerization of two monomers to form a dimer, the polymerization of a dimer and a monomer to form a trimer, and the polymerization of two trimers to form a hexamer. We then deduced that the dimer and trimer intermediates might be crucial in hexamer formation. We also explored four theoretical combined methods for Gag suppression, and hypothesized that the N-terminal glycine residue of the MA domain of Gag might be a promising drug target. This work serves as a guide for future theoretical and experimental efforts aiming to understand HIV-1 Gag trafficking and polymerization, and might help accelerate the efficiency of anti-AIDS drug design.

The human immunodeficiency virus (HIV-1) is a retrovirus that causes acquired immunodeficiency syndrome (AIDS), an infectious disease with high annual mortality. Gag protein is the major structural protein of HIV-1 and can self-assemble into the HIV-1 sphere shell. Therefore, an in-depth understanding of Gag protein trafficking and polymerization is important for gaining further insights into the mechanisms of HIV-1 replication and the design of antiviral drugs. Through mathematical modeling, optimization and quantitative analysis, we hypothesized the budding and release time of virus-like particles and revealed that the dimer and trimer intermediates might be crucial in hexamer formation. We also concluded that the predominant pathways in hexamer formation might be the polymerization of two monomers to form a dimer, the polymerization of a dimer and a monomer to form a trimer, and the polymerization of two trimers to form a hexamer. Our analysis also suggested that the N-terminal glycine residue of the MA domain of Gag might be a promising drug target. These results serve as a guide for further theoretical and experimental efforts aiming to understand HIV-1 Gag trafficking and polymerization and could aid anti-AIDS drug design.

Several Indicators of Critical Transitions for Complex Diseases Based on Stochastic Analysis

Many complex diseases (chronic disease onset, development and differentiation, self-assembly, etc.) are reminiscent of phase transitions in a dynamical system: quantitative changes accumulate largely unnoticed until a critical threshold is reached, which causes abrupt qualitative changes of the system. Understanding such nonlinear behaviors is critical to dissect the multiple genetic/environmental factors that together shape the genetic and physiological landscape underlying basic biological functions and to identify the key driving molecules. Based on stochastic differential equation (SDE) model, we theoretically derive three statistical indicators, that is, coefficient of variation (CV), transformed Pearson's correlation coefficient (TPC), and transformed probability distribution (TPD), to identify critical transitions and detect the early-warning signals of the phase transition in complex diseases. To verify the effectiveness of these early-warning indexes, we use high-throughput data for three complex diseases, including influenza caused by either H3N2 or H1N1 and acute lung injury, to extract the dynamical network biomarkers (DNBs) responsible for catastrophic transition into the disease state from predisease state. The numerical results indicate that the derived indicators provide a data-based quantitative analysis for early-warning signals for critical transitions in complex diseases or other dynamical systems.

Noise Decomposition Principle in a Coherent Feed-Forward Transcriptional Regulatory Loop

Coherent feed-forward loops exist extensively in realistic biological regulatory systems, and are common signaling motifs. Here, we study the characteristics and the propagation mechanism of the output noise in a coherent feed-forward transcriptional regulatory loop that can be divided into a main road and branch. Using the linear noise approximation, we derive analytical formulae for the total noise of the full loop, the noise of the branch, and the noise of the main road, which are verified by the Gillespie algorithm. Importantly, we find that (i) compared with the branch motif or the main road motif, the full motif can effectively attenuate the output noise level; (ii) there is a transition point of system state such that the noise of the main road is dominated when the underlying system is below this point, whereas the noise of the branch is dominated when the system is beyond the point. The entire analysis reveals the mechanism of how the noise is generated and propagated in a simple yet representative signaling module.

Transitions in a genetic transcriptional regulatory system under Lévy motion

Based on a stochastic differential equation model for a single genetic regulatory system, we examine the dynamical effects of noisy fluctuations, arising in the synthesis reaction, on the evolution of the transcription factor activator in terms of its concentration. The fluctuations are modeled by Brownian motion and α-stable Lévy motion. Two deterministic quantities, the mean first exit time (MFET) and the first escape probability (FEP), are used to analyse the transitions from the low to high concentration states. A shorter MFET or higher FEP in the low concentration region facilitates such a transition. We have observed that higher noise intensities and larger jumps of the Lévy motion shortens the MFET and thus benefits transitions. The Lévy motion activates a transition from the low concentration region to the non-adjacent high concentration region, while Brownian motion can not induce this phenomenon. There are optimal proportions of Gaussian and non-Gaussian noises, which maximise the quantities MFET and FEP for each concentration, when the total sum of noise intensities are kept constant. Because a weaker stability indicates a higher transition probability, a new geometric concept is introduced to quantify the basin stability of the low concentration region, characterised by the escaping behaviour.

Gene switching rate determines response to extrinsic perturbations in the self-activation transcriptional network motif

Gene switching dynamics is a major source of randomness in genetic networks, also in the case of large concentrations of the transcription factors. In this work, we consider a common network motif - the positive feedback of a transcription factor on its own synthesis - and assess its response to extrinsic noises perturbing gene deactivation in a variety of settings where the network might operate. These settings are representative of distinct cellular types, abundance of transcription factors and ratio between gene switching and protein synthesis rates. By investigating noise-induced transitions among the different network operative states, our results suggest that gene switching rates are key parameters to shape network response to external perturbations, and that such response depends on the particular biological setting, i.e. the characteristic time scales and protein abundance. These results might have implications on our understanding of irreversible transitions for noise-related phenomena such as cellular differentiation. In addition these evidences suggest to adopt the appropriate mathematical model of the network in order to analyze the system consistently to the reference biological setting.

Crosstalk between pathways enhances the controllability of signalling networks

The control of complex networks is one of the most challenging problems in the fields of biology and engineering. In this study, the authors explored the controllability and control energy of several signalling networks, which consisted of many interconnected pathways, including networks with a bow-tie architecture. On the basis of the theory of structure controllability, they revealed that biological mechanisms, such as cross-pathway interactions, compartmentalisation and so on make the networks easier to fully control. Furthermore, using numerical simulations for two realistic examples, they demonstrated that the control energy of normal networks with crosstalk is lower than in networks without crosstalk. These results indicate that the biological networks are optimally designed to achieve their normal functions from the viewpoint of the control theory. The authors' work provides a comprehensive understanding of the impact of network structures and properties on controllability.

A New Method for Detecting Protein Complexes based on the Three Node Cliques

The identification of protein complexes in protein-protein interaction (PPI) networks is fundamental for understanding biological processes and cellular molecular mechanisms. Many graph computational algorithms have been proposed to identify protein complexes from PPI networks by detecting densely connected groups of proteins. These algorithms assess the density of subgraphs through evaluation of the sum of individual edges or nodes; thus, incomplete and inaccurate measures may miss meaningful biological protein complexes with functional significance. In this study, we propose a novel method for assessing the compactness of local subnetworks by measuring the number of three node cliques. The present method detects each optimal cluster by growing a seed and maximizing the compactness function. To demonstrate the efficacy of the new proposed method, we evaluate its performance using five PPI networks on three reference sets of yeast protein complexes with five different measurements and compare the performance of the proposed method with four state-of-the-art methods. The results show that the protein complexes generated by the proposed method are of better quality than those generated by four classic methods. Therefore, the new proposed method is effective and useful for detecting protein complexes in PPI networks.

Negative feedback contributes to the stochastic expression of the interferon-β gene in virus-triggered type I interferon signaling pathways

Type I interferon (IFN) signaling pathways play an essential role in the defense against early viral infections; however, the diverse and intricate molecular mechanisms of virus-triggered type I IFN responses are still poorly understood. In this study, we analyzed and compared two classes of models i.e., deterministic ordinary differential equations (ODEs) and stochastic models to elucidate the dynamics and stochasticity of type I IFN signaling pathways. Bifurcation analysis based on an ODE model reveals that the system exhibits a bistable switch and a one-way switch at high or low levels when the strengths of the negative and positive feedbacks are tuned. Furthermore, we compared the stochastic simulation results under the Master and Langevin equations. Both of the stochastic equations generate the bistable switch phenomenon, and the distance between two stable states are smaller than normal under the simulation of the Langevin equation. The quantitative computations also show that a moderate ratio between positive and negative feedback strengths is required to ensure a reliable switch between the different IFN concentrations that regulate the immune response. Moreover, we propose a multi-state stochastic model based on the above deterministic model to describe the multi-cellular system coupled with the diffusion of IFNs. The perturbation and inhibition analysis showed that the positive feedback, as well as noises, has little effect on the stochastic expression of IFNs, but the negative feedback of ISG56 on the activation of IRF7 has a great influence on IFN stochastic expression. Together, these results reveal that positive feedback stabilizes IFN gene expression, and negative feedback may be the main contribution to the stochastic expression of the IFN gene in the virus-triggered type I IFN response. These findings will provide new insight into the molecular mechanisms of virus-triggered type I IFN signaling pathways.

Optimal control strategy for abnormal innate immune response

Innate immune response plays an important role in control and clearance of pathogens following viral infection. However, in the majority of virus-infected individuals, the response is insufficient because viruses are known to use different evasion strategies to escape immune response. In this study, we use optimal control theory to investigate how to control the innate immune response. We present an optimal control model based on an ordinary-differential-equation system from a previous study, which investigated the dynamics and regulation of virus-triggered innate immune signaling pathways, and we prove the existence of a solution to the optimal control problem involving antiviral treatment or/and interferon therapy. We conduct numerical experiments to investigate the treatment effects of different control strategies through varying the cost function and control efficiency. The results show that a separate treatment, that is, only inhibiting viral replication (u₁(t)) or enhancing interferon activity (u₂(t)), has more advantages for controlling viral infection than a mixed treatment, that is, controlling both (u₁(t)) and (u₂(t)) simultaneously, including the smallest cost and operability. These findings would provide new insight for developing effective strategies for treatment of viral infectious diseases.

A new asynchronous parallel algorithm for inferring large-scale gene regulatory networks

The reconstruction of gene regulatory networks (GRNs) from high-throughput experimental data has been considered one of the most important issues in systems biology research. With the development of high-throughput technology and the complexity of biological problems, we need to reconstruct GRNs that contain thousands of genes. However, when many existing algorithms are used to handle these large-scale problems, they will encounter two important issues: low accuracy and high computational cost. To overcome these difficulties, the main goal of this study is to design an effective parallel algorithm to infer large-scale GRNs based on high-performance parallel computing environments. In this study, we proposed a novel asynchronous parallel framework to improve the accuracy and lower the time complexity of large-scale GRN inference by combining splitting technology and ordinary differential equation (ODE)-based optimization. The presented algorithm uses the sparsity and modularity of GRNs to split whole large-scale GRNs into many small-scale modular subnetworks. Through the ODE-based optimization of all subnetworks in parallel and their asynchronous communications, we can easily obtain the parameters of the whole network. To test the performance of the proposed approach, we used well-known benchmark datasets from Dialogue for Reverse Engineering Assessments and Methods challenge (DREAM), experimentally determined GRN of Escherichia coli and one published dataset that contains more than 10 thousand genes to compare the proposed approach with several popular algorithms on the same high-performance computing environments in terms of both accuracy and time complexity. The numerical results demonstrate that our parallel algorithm exhibits obvious superiority in inferring large-scale GRNs.

Deciphering deterioration mechanisms of complex diseases based on the construction of dynamic networks and systems analysis

The early diagnosis and investigation of the pathogenic mechanisms of complex diseases are the most challenging problems in the fields of biology and medicine. Network-based systems biology is an important technique for the study of complex diseases. The present study constructed dynamic protein-protein interaction (PPI) networks to identify dynamical network biomarkers (DNBs) and analyze the underlying mechanisms of complex diseases from a systems level. We developed a model-based framework for the construction of a series of time-sequenced networks by integrating high-throughput gene expression data into PPI data. By combining the dynamic networks and molecular modules, we identified significant DNBs for four complex diseases, including influenza caused by either H3N2 or H1N1, acute lung injury and type 2 diabetes mellitus, which can serve as warning signals for disease deterioration. Function and pathway analyses revealed that the identified DNBs were significantly enriched during key events in early disease development. Correlation and information flow analyses revealed that DNBs effectively discriminated between different disease processes and that dysfunctional regulation and disproportional information flow may contribute to the increased disease severity. This study provides a general paradigm for revealing the deterioration mechanisms of complex diseases and offers new insights into their early diagnoses.

Mathematical modeling for intracellular transport and binding of HIV-1 Gag proteins

This paper presents a modeling study for the intracellular trafficking and trimerization of the HIV-1 Gag proteins. A set of differential equations including initial and boundary conditions is used to characterize the transport, diffusion, association and dissociation of Gag monomers and trimers for the time period from the initial production of Gag protein monomers to the initial appearance of immature HIV-1 virions near the cell membrane (the time duration Ta). The existence and stability of the steady-state solution of the initial boundary value problems provide a quantitative characterization of the tendency and equilibrium of Gag protein movement. The numerical simulation results further demonstrate Gag trimerization near the cell membrane. Our calculations of Ta are in good agreement with published experimental data. Sensitivity analysis of Ta to the model parameters indicates that the timing of the initial appearance of HIV-1 virions on the cell membrane is affected by the diffusion and transport processes. These results provide important information and insight into the Gag protein transport and binding and HIV-1 virion formation.