Jinzhi Lei

Burst synchronization transitions in a neuronal network of subnetworks

In this paper, the transitions of burst synchronization are explored in a neuronal network consisting of subnetworks. The studied network is composed of electrically coupled bursting Hindmarsh-Rose neurons. Numerical results show that two types of burst synchronization transitions can be induced not only by the variations of intra- and intercoupling strengths but also by changing the probability of random links between different subnetworks and the number of subnetworks. Furthermore, we find that the underlying mechanisms for these two bursting synchronization transitions are different: one is due to the change of spike numbers per burst, while the other is caused by the change of the bursting type. Considering that changes in the coupling strengths and neuronal connections are closely interlaced with brain plasticity, the presented results could have important implications for the role of the brain plasticity in some functional behavior that are associated with synchronization.

Stochasticity in single gene expression with both intrinsic noise and fluctuation in kinetic parameters

Stochasticity is one of the most important properties in gene expression. Noise originates from two sources: thermal fluctuation inherent in the system (intrinsic noise) and variabilities in factors external to the system that usually result to the fluctuation in the kinetic parameters (extrinsic noise). This paper studies analytically the stationary fluctuation of the number of protein molecules through a mathematical model involving both sources of noises. The results in this paper show that the two sources of noises interlock to each other to generate total fluctuation in protein numbers. In particular, the extrinsic noises effect the total fluctuation in multiple ways, including the extrinsic fluctuation, the correlation with intrinsic noise, the alternation of the time averaging of transcription and translation, and the amplification of the total fluctuation by an impact factor. The impact factor is pronounced when the fluctuations in the degradation rates of mRNA or protein are large. Moreover, the extrinsic noise to the translational rate generates large fluctuation when the translational efficiency is too low, which is contrast to the translational bursting in high translational efficiency because of intrinsic noise. These results suggest that it is important to control the mRNA and protein degradation rate as well as the translational efficiency in order to attenuate the fluctuation in gene expression in the present of both intrinsic and extrinsic noises.

Stochastic Differential Delay Equation, Moment Stability, and Application to Hematopoietic Stem Cell Regulation System

We study the moment stability of the trivial solution of a linear differential delay equation in the presence of additive and multiplicative white noise. The results established here are applied to examining the local stability of the hematopoietic stem cell (HSC) regulation system in the presence of noise. The stability of the first moment for the solutions of a linear differential delay equation under stochastic perturbation is identical to that of the unperturbed system. However, the stability of the second moment is altered by the perturbation. We obtain, using Laplace transform techniques, necessary and sufficient conditions for the second moment to be bounded. In applying the results to the HSC system, we find that the system stability is sensitive to perturbations in the stem cell differentiation and death rates, but insensitive to perturbations in the proliferation rate.

Neutrophil dynamics in response to chemotherapy and G-CSF.

We have used a mathematical model of the combined dynamics of the hematopoietic stem cells and the differentiated neutrophil progeny to examine the effects of periodic chemotherapy in generating neutropenia, and the corresponding response of this system to granulocyte colony stimulating factor given to counteract the neutropenia. We find that there is a significant period of chemotherapy delivery that induces resonance in the system (at a period twice the average neutrophil lifespan from commitment to death) and a corresponding neutropenia suggesting that myelosuppressive protocols should avoid this period to minimize hematopoietic damage. The response to G-CSF is highly variable.

Adiabatic reduction of a model of stochastic gene expression with jump Markov process

This paper considers adiabatic reduction in a model of stochastic gene expression with bursting transcription considered as a jump Markov process. In this model, the process of gene expression with auto-regulation is described by fast/slow dynamics. The production of mRNA is assumed to follow a compound Poisson process occurring at a rate depending on protein levels (the phenomena called bursting in molecular biology) and the production of protein is a linear function of mRNA numbers. When the dynamics of mRNA is assumed to be a fast process (due to faster mRNA degradation than that of protein) we prove that, with appropriate scalings in the burst rate, jump size or translational rate, the bursting phenomena can be transmitted to the slow variable. We show that, depending on the scaling, the reduced equation is either a stochastic differential equation with a jump Poisson process or a deterministic ordinary differential equation. These results are significant because adiabatic reduction techniques seem to have not been rigorously justified for a stochastic differential system containing a jump Markov process. We expect that the results can be generalized to adiabatic methods in more general stochastic hybrid systems.

Neutrophil dynamics after chemotherapy and G-CSF: The role of pharmacokinetics in shaping the response

Chemotherapy has profound effects on the hematopoietic system, most notably leading to neutropenia. Granulocyte colony stimulating factor (G-CSF) is often used to deal with this neutropenia, but the response is highly variable. In this paper we examine the role of pharmacokinetics and delivery protocols in shaping the neutrophil responses to chemotherapy and G-CSF. Neutrophil responses to different protocols of chemotherapy administration with varying dosages, infusion times, and schedules are studied through a mathematical model. We find that a single dose of chemotherapy produces a damped oscillation in neutrophil levels, and short-term applications of chemotherapy can induce permanent oscillations in neutrophil level if there is a bistability in the system. In addition, we confirm previous findings [Zhuge et al., J. Theor. Biol., 293(2012), 111-120] that when periodic chemotherapy is given, there is a significant period of delivery that induces resonance in the system and exacerbates the corresponding neutropenia. The width of this resonant period peak increases with the recovery rate after a single chemotherapy, which is given by the real part of the dominant eigenvalue pair at the steady state, and both are determined by a single cooperativity coefficient in the feedback function for the neutrophils. Our numerical studies show that the neutropenia caused by chemotherapy can be overcome if G-CSF is given early after chemotherapy but can actually be worsened if G-CSF is given later, consistent with results reported in Zhuge et al. (2012). The nadir in neutrophil level is found to be more sensitive to the dosage of chemotherapy than that of the G-CSF. Furthermore, dependence of our results with changes in key pharmacokinetic parameters as well as initial functions are studied. Thus, this study illuminates the potential for destructive resonance leading to neutropenia in response to periodic chemotherapy, and explores and explains why the timing of G-CSF is so crucial for successful reversal of chemotherapy induced neutropenia.

PDCD5-Regulated Cell Fate Decision after Ultraviolet-Irradiation-Induced DNA Damage

Programmed cell death 5 (PDCD5) is a human apoptosis-related molecule that is involved in both the cytoplasmic caspase-3 activity pathway (by regulating Bax translocation from cytoplasm to mitochondria) and the nuclear pathway (by interacting with Tip60). In this study, we developed a mathematical model of the PDCD5-regulated switching of the cell response from DNA repair to apoptosis after ultraviolet irradiation-induced DNA damage. We established the model by combining several hypotheses with experimental observations. Our simulations indicate that the ultimate cell response to DNA damage is dependent on a signal threshold mechanism, and the PDCD5 promotion of Bax translocation plays an essential role in PDCD5-regulated cell apoptosis. Furthermore, the model simulations revealed that PDCD5 nuclear translocation can attenuate cell apoptosis, and PDCD5 interactions with Tip60 can accelerate DNA damage-induced apoptosis, but the final cell fate decision is insensitive to the PDCD5-Tip60 interaction. These results are consistent with experimental observations. The effect of recombinant human PDCD5 was also investigated and shown to sensitize cells to DNA damage by promoting caspase-3 activity.

Understanding and Treating Cytopenia Through Mathematical Modeling

Here, we briefly review how the study of dynamic hematological diseases with mathematical modeling tools has led to a better understanding of the origin of some types of neutropenia and thrombocytopenia and to improved treatment strategies. In addition, we have briefly discussed how these models suggest improved ways to minimize and/or treat cytopenia induced by chemotherapy.

PDCD5 functions as a regulator of p53 dynamics in the DNA damage response.

The tumor suppressor p53 plays a central role in cell fate decisions after DNA damage. Programmed Cell Death 5 (PDCD5) interacts with the p53 pathway to promote cell apoptosis. Recombinant human PDCD5 can significantly sensitize different cancers to chemotherapies. In the present paper, we construct a computational model that includes PDCD5 interactions in the p53 signaling network and study the effects of PDCD5 on p53-mediated cell fate decisions during the DNA damage response. Our results revealed that PDCD5 functions as a co-activator of p53 and regulates p53-dependent cell fate decisions via the mediation of p53 dynamics. The effects of PDCD5 are dose-dependent, such that p53 activity exhibits sustained low level, pulsed oscillations, or sustained high level dynamics depending on the PDCD5 level following DNA damage. Moreover, PDCD5 regulates caspase-3 activation via two mechanisms during the two phases of sustained and pulsed p53 dynamics. This study provides insights regarding how PDCD5 functions as a regulator of the p53 pathway and might be helpful for increasing our understanding of the molecular mechanisms by which PDCD5 can be used to treat cancers.

On positive solutions and the Omega limit set for a class of delay differential equations

This paper studies positive solutions of a class of delay differential equations of two delays that are originated from a mathematical model of hematopoietic dynamics. We give an optimal condition on initial conditions for