Functional models for large-scale gene regulation networks: realism and fiction

Merging 1D and 3D genomic information: Challenges in modelling and validation

Genome organization in eukaryotes during interphase stems from the delicate balance between non-random correlations present in the DNA polynucleotide linear sequence and the physico/chemical reactions which shape continuously the form and structure of DNA and chromatin inside the nucleus of the cell. It is now clear that these mechanisms have a key role in important processes like gene regulation, yet the detailed ways they act simultaneously and, eventually, come to influence each other even across very different length-scales remain largely unexplored. In this paper, we recapitulate some of the main results concerning gene regulatory and physical mechanisms, in relation to the information encoded in the 1D sequence and the 3D folding structure of DNA. In particular, we stress how reciprocal crossfeeding between 1D and 3D models may provide original insight into how these complex processes work and influence each other. This article is part of a Special Issue entitled: Transcriptional Profiles and Regulatory Gene Networks edited by Dr. Dr. Federico Manuel Giorgi and Dr. Shaun Mahony.

mRNA function after intracellular delivery and release

Nanocarrier-mediated mRNA delivery and release into the cells with subsequent translation to protein is of interest in the context of the development of a new generation of drugs. In particular, this protein can play a role of a transcription factor and be used as a tool to regulate temporarily the genetic networks. The corresponding transient kinetics of gene expression are expected to depend on the mechanism and duration of mRNA release. Assuming the release to be rapid on the time scale of other steps, the author shows theoretically the mRNA-related transient features of gene expression occurring in stable, bistable, and oscillatory regimes in a single cell. Qualitatively, the results obtained are found to be fairly similar to those reported earlier for the situation when the release is slow. Thus, the features of the transient kinetics under consideration appear to be less sensitive to the duration of mRNA release compared to what one might expect.

Kinetics of lipid-nanoparticle-mediated intracellular mRNA delivery and function

mRNA delivery into cells forms the basis for one of the new and promising ways to treat various diseases. Among suitable carriers, lipid nanoparticles (LNPs) with a size of about 100 nm are now often employed. Despite high current interest in this area, the understanding of the basic details of LNP-mediated mRNA delivery and function is limited. To clarify the kinetics of mRNA release from LNPs, the author uses three generic models implying (i) exponential, (ii) diffusion-controlled, and (iii) detachment-controlled kinetic regimes, respectively. Despite the distinct differences in these kinetics, the associated transient kinetics of mRNA translation to the corresponding protein and its degradation are shown to be not too sensitive to the details of the mRNA delivery by LNPs (or other nanocarriers). In addition, the author illustrates how this protein may temporarily influence the expression of one gene or a few equivalent genes. The analysis includes positive or negative regulation of the gene transcription via the attachment of the protein without or with positive or negative feedback in the gene expression. Stable, bistable, and oscillatory schemes have been scrutinized in this context.

EFFECT OF NON-CODING RNA ON BISTABILITY AND OSCILLATIONS IN THE mRNA-PROTEIN INTERPLAY

The feedbacks between the mRNA and protein synthesis may result in kinetic bistability and oscillations. Two generic models predicting bistability include, respectively, a gene with positive regulation of the mRNA production by protein and two genes with mutual suppression of the mRNA production due to negative regulation of the gene transcription by protein. The simplest model predicting oscillations describes a gene with negative regulation of the mRNA production by protein formed via mRNA translation and a few steps of conversion. We complement these models by the steps of non-coding RNA (ncRNA) formation and ncRNA-mRNA association and degradation. With this extension, the bistability can often be observed as well. Without and with ncRNA, the biochemistry behind the steady states may be different. In the latter case, for example, ncRNA may control the mRNA population in the situations when this population is relatively small, and one can observe a switch in the mRNA, protein and ncRNA populations. Our analysis of oscillatory kinetics of the mRNA-protein interplay shows that with ncRNA the oscillations may be observed in a wider range of parameters and the amplitude of oscillations may be larger.

Hierarchical genetic networks and noncoding RNAs

In eukaryotic cells, many genes are transcribed into noncoding RNAs. Such RNAs may associate with mRNAs and inhibit their translation and facilitate degradation. To clarify what may happen in this case, we propose a kinetic model describing the effect of noncoding RNAs on a mRNA-protein network with the hierarchical three-layer architecture. For positive regulation of the layers, our model predicts either bistability with a fairly narrow hysteresis loop or a unique steady state. For negative or mixed regulation, the steady state is found to be unique.

Attractor and basin entropies of random Boolean networks under asynchronous stochastic update

We introduce a method to study random Boolean networks with asynchronous stochastic update. Each node in the state space network starts with equal occupation probability, which then evolves to a steady state. Attractors and the sizes of their basins are determined by the nodes left occupied at late times. As for synchronous update, the basin entropy grows with system size only for critical networks. We determine analytically the distribution for the number of attractors and basin sizes for networks with connectivity K=1 . These differ from the case of synchronous update for all K .

Spanning traceroutes over modular networks and general scaling degree distributions

We analyze the class of networks characterized by modular structure where a sequence of l Erdös-Renyi random networks of size Nl with random average degrees is joined by links whose structure must remain immaterial. We find that traceroutes spanning the entire macronetwork exhibit scaling degree distributions P(k) approximately k-gamma, where gamma depends on how the degrees of the joined clusters are distributed. We thus suggest that yet another mechanism for the dynamic origin of arbitrary power-law degree distributions observed in natural and artificial networks, many of which belong to the range 2<or=gamma<or=3 , may be found in random processes on modular networks.

Model of gene transcription including the return of a RNA polymerase to the beginning of a transcriptional cycle

The gene transcription occurs via the RNA polymerase (RNAP) recruitment on the DNA promoter sequence, formation of a locally open DNA chain, promoter escape, steps of the RNA synthesis, and RNA and RNAP release after reading the final DNA base. Just after the end of the RNA synthesis, RNAP surrounds the closed DNA chain and may diffuse along DNA, desorb, or reach the promoter and start the RNA-synthesis cycle again. We present a generic kinetic model taking the latter steps into account and show analytically and by Monte Carlo simulations that it predicts transcriptional bursts even in the absence of explicit regulation of the transcription by master proteins.