How the Number of Alleles Influences Gene Expression

The higher organisms, eukaryotes, are diploid and most of their genes have two homological copies (alleles). However, the number of alleles in a cell is not constant. In the S phase of the cell cycle all the genome is duplicated and then in the G2 phase and mitosis, which together last for several hours, most of the genes have four copies instead of two. Cancer development is, in many cases, associated with a change in allele number. Several genetic diseases are caused by haploinsufficiency: Lack of one of the alleles or its improper functioning. In the paper we consider the stochastic expression of a gene having a variable number of copies. We applied our previously developed method in which the reaction channels are split into slow (connected with change of gene state) and fast (connected with mRNA/protein synthesis/decay), the later being approximated by deterministic reaction rate equations. As a result we represent gene expression as a piecewise deterministic time-continuous Markov process, which is further related with a system of partial differential hyperbolic equations for probability density functions (pdfs) of protein distribution. The stationary pdfs are calculated analytically for haploidal gene or numerically for diploidal and tetraploidal ones. We distinguished nine classes of simultaneous activation of haploid, diploid and tetraploid genes. This allows for analysis of potential consequences of gene duplication or allele loss. We show that when gene activity is autoregulated by a positive feedback, the change in number of gene alleles may have dramatic consequences for its regulation and may not be compensated by the change of efficiency of mRNA synthesis per allele.     

Distribution and regulation of stochasticity and plasticity in Saccharomyces cerevisiae

Stochasticity is an inherent feature of complex systems with nanoscale structure. In such systems information is represented by small collections of elements (e.g., a few electrons on a quantum dot), and small variations in the populations of these elements may lead to big uncertainties in the information. Unfortunately, little is known about how to work within this inherently noisy environment to design robust functionality into complex nanoscale systems. Here, we look to the biological cell as an intriguing model system where evolution has mediated the trade-offs between fluctuations and function, and in particular we look at the relationships and trade-offs between stochastic and deterministic responses in the gene expression of budding yeast (Saccharomyces cerevisiae). We find gene regulatory arrangements that control the stochastic and deterministic components of expression, and show that genes that have evolved to respond to stimuli (stress) in the most strongly deterministic way exhibit the most noise in the absence of the stimuli. We show that this relationship is consistent with a bursty two-state model of gene expression, and demonstrate that this regulatory motif generates the most uncertainty in gene expression when there is the greatest uncertainty in the optimal level of gene expression.     

Enhanced nigrostriatal neuron-specific,long-term expression by using neural-specific promoters in combination with targeted gene transfer by modified helper virus-free HSV-1 vector particles

Background  

Direct gene transfer into neurons has potential for developing gene therapy treatments for specific neurological conditions, and for elucidating neuronal physiology. Due to the complex cellular composition of specific brain areas, neuronal type-specific recombinant gene expression is required for many potential applications of neuronal gene transfer. One approach is to target gene transfer to a specific type of neuron. We developed modified Herpes Simplex Virus (HSV-1) particles that contain chimeric glycoprotein C (gC) – glial cell line-derived neurotrophic factor (GDNF) or brain-derived neurotrophic factor (BDNF) proteins. HSV-1 vector particles containing either gC – GDNF or gC – BDNF target gene transfer to nigrostriatal neurons, which contain specific receptors for GDNF or BDNF. A second approach to achieve neuronal type-specific expression is to use a cell type-specific promoter, and we have used the tyrosine hydroxylase (TH) promoter to restrict expression to catecholaminergic neurons or a modified neurofilament heavy gene promoter to restrict expression to neurons, and both of these promoters support long-term expression from HSV-1 vectors. To both improve nigrostriatal-neuron specific expression, and to establish that targeted gene transfer can be followed by long-term expression, we performed targeted gene transfer with vectors that support long-term, neuronal-specific expression.     

Circadian rhythms and molecular noise

Circadian rhythms, characterized by a period of about 24 h, are the most widespread biological rhythms generated autonomously at the molecular level. The core molecular mechanism responsible for circadian oscillations relies on the negative regulation exerted by a protein on the expression of its own gene. Deterministic models account for the occurrence of autonomous circadian oscillations, for their entrainment by light-dark cycles, and for their phase shifting by light pulses. Stochastic versions of these models take into consideration the molecular fluctuations that arise when the number of molecules involved in the regulatory mechanism is low. Numerical simulations of the stochastic models show that robust circadian oscillations can already occur with a limited number of mRNA and protein molecules, in the range of a few tens and hundreds, respectively. Various factors affect the robustness of circadian oscillations with respect to molecular noise. Besides an increase in the number of molecules, entrainment by light-dark cycles, and cooperativity in repression enhance robustness, whereas the proximity of a bifurcation point leads to less robust oscillations. Another parameter that appears to be crucial for the coherence of circadian rhythms is the binding/unbinding rate of the inhibitory protein to the promoter of the clock gene. Intercellular coupling further increases the robustness of circadian oscillations.     

Theory for serial correlations of interevent intervals

We consider stochastic systems with m internal states in which discrete events (e.g. hopping events between metastable states or firing events of neurons) occur at a state-dependent rate. Transitions between states are possible with certain fixed rates. Because the state immediately after an event depends in general on the history of the process, the intervals between two consecutive events (“residence times”) are correlated among each other, i.e. the residence time sequence constitutes a nonrenewal process. We construct a general kinetic scheme that accounts for the number of events at a given time. The count statistics is used to derive a general expression for the correlation coefficient of residence times with a certain lag. We apply the theoretical result to a simple neuron model with discrete threshold states leading to negative interspike interval correlations.     

Sensitivity of the power-law exponent in gene expression distribution to mRNA decay rate

Large-scale acquisition technologies in mRNA abundance (gene expression) have provided new opportunities to better understand many complex biological processes. Lately, it has been reported that the observed gene expression data in several organisms significantly deviates from a Poisson distribution and follows a power-law or fat-tailed distribution. Here, we show that a simple stochastic model of gene expression with intrinsic and extrinsic noise derives the stationary power-law distribution using the Stratonovich calculus. Furthermore, we connect the experimental measure of the power-law exponent with the value of the mRNA decay. Finally, we compare the results with other models where stochastic equations were used within the Ito interpretation.     

A mathematical model of the evolution of free radical concentrations in a cell under ionizing radiation

A probabilistic mathematical model that describes the evolution of the free radical concentration in a cell under ionizing radiation is proposed. The model is of a stochastic character and allows one to describe the generation of free radicals in the process of radiolysis, as well as the interaction between the radicals of different types and between the radicals and the cell constituents (the latter is responsible for radiobiological effect). The possibility of the presence in the cell of a certain equilibrium quantity of radicals of nonradiative origin at the moment that the irradiation begins is taken into account. The results thus obtained show that under certain values of the model’s free parameters the total number of free radicals in a cell under radiation may decrease. This effect can explain the “positive” influence of small doses of ionizing radiation.     

Quantum-chemical study of interaction of hydrogen atoms with graphene

The dependence of the binding energy and the activation energy of adsorption of hydrogen atoms on the number of previously adsorbed particles and their position—on one or both sides of a cluster, on nearest or distant neighbors (carbon atoms)—is investigated by quantum-chemical modeling. A hypothesis of the formation of adsorption sites (islands) on graphene at the initial stage of its saturation by hydrogen is discussed.     

Regulatory networks and connected components of the neutral space

The functioning of a living cell is largely determined by the structure of its regulatory network, comprising non-linear interactions between regulatory genes. An important factor for the stability and evolvability of such regulatory systems is neutrality – typically a large number of alternative network structures give rise to the necessary dynamics. Here we study the discretized regulatory dynamics of the yeast cell cycle [Li et al., PNAS, 2004] and the set of networks capable of reproducing it, which we call functional. Among these, the empirical yeast wildtype network is close to optimal with respect to sparse wiring. Under point mutations, which establish or delete single interactions, the neutral space of functional networks is fragmented into ≈ 4.7 × 10⁸ components. One of the smaller ones contains the wildtype network. On average, functional networks reachable from the wildtype by mutations are sparser, have higher noise resilience and fewer fixed point attractors as compared with networks outside of this wildtype component.     

Genetically engineered cardiac pacemaker: Stem cells transfected with HCN2 gene and myocytes—A model

One of the successfully tested methods to design genetically engineered cardiac pacemaker cells consists in transfecting a human mesenchymal stem cell (hMSC) with a HCN2 gene and connecting it to a myocyte. We develop and study a mathematical model, describing a myocyte connected to a hMSC transfected with a HCN2 gene. The cardiac action potential is described both with the simple Beeler-Reuter model, as well as with the elaborate dynamic Luo-Rudy model. The HCN2 channel is described by fitting electrophysiological records, in the spirit of Hodgkin-Huxley. The model shows that oscillations can occur in a pair myocyte-stem cell, that was not observed in the experiments yet. The model predicted that: (1) HCN pacemaker channels can induce oscillations only if the number of expressed IK1 channels is low enough. At too high an expression level of IK1 channels, oscillations cannot be induced, no matter how many pacemaker channels are expressed. (2) At low expression levels of IK1 channels, a large domain of values in the parameter space (n, N) exists, where oscillations should be observed. We denote N the number of expressed pacemaker channels in the stem cell, and n the number of gap junction channels coupling the stem cell and the myocyte. (3) The expression levels of IK1 channels observed in ventricular myocytes, both in the Beeler-Reuter and in the dynamic Luo-Rudy models are too high to allow to observe oscillations. With expression levels below ∼1/4 of the original value, oscillations can be observed. The main consequence of this work is that in order to obtain oscillations in an experiment with a myocyte-stem cell pair, increasing the values of n, N is unlikely to be helpful, unless the expression level of IK1 has been reduced enough. The model also allows us to explore levels of gene expression not yet achieved in experiments, and could be useful to plan new experiments, aimed at improving the robustness of the oscillations.     

Molecular,metabolic, and genetic control: An introduction

The living cell is a miniature, self-reproducing, biochemical machine. Like all machines, it has a power supply, a set of working components that carry out its necessary tasks, and control systems that ensure the proper coordination of these tasks. In this Special Issue, we focus on the molecular regulatory systems that control cell metabolism, gene expression, environmental responses, development, and reproduction. As for the control systems in human-engineered machines, these regulatory networks can be described by nonlinear dynamical equations, for example, ordinary differential equations, reaction-diffusion equations, stochastic differential equations, or cellular automata. The articles collected here illustrate (i) a range of theoretical problems presented by modern concepts of cellular regulation, (ii) some strategies for converting molecular mechanisms into dynamical systems, (iii) some useful mathematical tools for analyzing and simulating these systems, and (iv) the sort of results that derive from serious interplay between theory and experiment. (c) 2001 American Institute of Physics.     

Symmetry and stochastic gene regulation

Lorentz-like noncompact Lie symmetry SO(2,1) is found in a spin-boson stochastic model for gene expression. The invariant of the algebra characterizes the switch decay to equilibrium. The azimuthal eigenvalue describes the affinity between the regulatory protein and the gene operator site. Raising and lowering operators are constructed and their actions increase or decrease the affinity parameter. The classification of the noise regime of the gene arises from the group theoretical numbers.