Biological significance of autoregulation through steady state analysis of genetic networks

Biomaterialomics: Data science-driven pathways to develop fourth-generation biomaterials

Conventional approaches to developing biomaterials and implants require intuitive tailoring of manufacturing protocols and biocompatibility assessment. This leads to longer development cycles, and high costs. To meet existing and unmet clinical needs, it is critical to accelerate the production of implantable biomaterials, implants and biomedical devices. Building on the Materials Genome Initiative, we define the concept 'biomaterialomics' as the integration of multi-omics data and high-dimensional analysis with artificial intelligence (AI) tools throughout the entire pipeline of biomaterials development. The Data Science-driven approach is envisioned to bring together on a single platform, the computational tools, databases, experimental methods, machine learning, and advanced manufacturing (e.g., 3D printing) to develop the fourth-generation biomaterials and implants, whose clinical performance will be predicted using 'digital twins'. While analysing the key elements of the concept of 'biomaterialomics', significant emphasis has been put forward to effectively utilize high-throughput biocompatibility data together with multiscale physics-based models, E-platform/online databases of clinical studies, data science approaches, including metadata management, AI/ Machine Learning (ML) algorithms and uncertainty predictions. Such integrated formulation will allow one to adopt cross-disciplinary approaches to establish processing-structure-property (PSP) linkages. A few published studies from the lead author's research group serve as representative examples to illustrate the formulation and relevance of the 'Biomaterialomics' approaches for three emerging research themes, i.e. patient-specific implants, additive manufacturing, and bioelectronic medicine. The increased adaptability of AI/ML tools in biomaterials science along with the training of the next generation researchers in data science are strongly recommended. STATEMENT OF SIGNIFICANCE: This leading opinion review paper emphasizes the need to integrate the concepts and algorithms of the data science with biomaterials science. Also, this paper emphasizes the need to establish a mathematically rigorous cross-disciplinary framework that will allow a systematic quantitative exploration and curation of critical biomaterials knowledge needed to drive objectively the innovation efforts within a suitable uncertainty quantification framework, as embodied in 'biomaterialomics' concept, which integrates multi-omics data and high-dimensional analysis with artificial intelligence (AI) tools, like machine learning. The formulation of this approach has been demonstrated for patient-specific implants, additive manufacturing, and bioelectronic medicine.

Modeling stochastic gene expression in growing cells

Gene expression is an inherently noisy process. Fluctuations arise at many points in the expression of a gene, as all the salient reactions such as transcription, translation, and mRNA degradation are stochastic processes. The fluctuations become important when the cellular copy numbers of the relevant molecules (mRNA or proteins) are low. For regulated genes, a computational complication arises from the fact that protein synthesis rates depend on the concentrations of the transcription factors that regulate the corresponding genes. Because of the growing cell volume, such rates are effectively time-dependent. We deal with the effects of volume growth computationally using a rather simple method: the growth of the cell volume is incorporated in our simulations by stochastically adding small volume elements to the cell volume. As an application of this method we study a gene circuit with positive autoregulation that exhibits bistability. We show how the region of bistability becomes diminished by increasing the effect of noise via a reduced copy number of the regulatory protein. Cell volume determines the region of bistability for different noise strengths. The method is general and can also be applied to other cases where synthesis rates of proteins are regulated and an appropriate analytical description is difficult to achieve.

Growth-related model of the GAL system in Saccharomyces cerevisiae predicts behaviour of several mutant strains

The genetic regulatory network responds dynamically to perturbations in the intracellular and extracellular environments of an organism. The GAL system in the yeast Saccharomyces cerevisiae has evolved to utilise galactose as an alternative carbon and energy source, in the absence of glucose in the environment. This work contains a modified dynamic model for GAL system in S. cerevisiae, which includes a novel mechanism for Gal3p activation upon induction with galactose. The modification enables the model to simulate the experimental observation that in absence of galactose, oversynthesis of Gal3p can also induce the GAL system. Subsequently, the model is related to growth on galactose and glucose in a structured manner. The growth-related models are validated with experimental data for growth on individual substrates as well as mixed substrates. Finally, the model is tested for its prediction of a variety of known mutant behaviours. The exercise shows that the authors' model with a single set of parameters is able to capture the rich behaviour of the GAL system in S. cerevisiae. [Includes supplementary material].

Order-preserving principles underlying genotype-phenotype maps ensure high additive proportions of genetic variance

In quantitative genetics, the degree of resemblance between parents and offspring is described in terms of the additive variance (V(A)) relative to genetic (V(G)) and phenotypic (V(P)) variance. For populations with extreme allele frequencies, high V(A)/V(G) can be explained without considering properties of the genotype-phenotype (GP) map. We show that randomly generated GP maps in populations with intermediate allele frequencies generate far lower V(A)/V(G) values than empirically observed. The main reason is that order-breaking behaviour is ubiquitous in random GP maps. Rearrangement of genotypic values to introduce order-preservation for one or more loci causes a dramatic increase in V(A)/V(G). This suggests the existence of order-preserving design principles in the regulatory machinery underlying GP maps. We illustrate this feature by showing how the ubiquitously observed monotonicity of dose-response relationships gives much higher V(A)/V(G) values than a unimodal dose-response relationship in simple gene network models.

Negative auto-regulation increases the input dynamic-range of the arabinose system of Escherichia coli

Background

Gene regulation networks are made of recurring regulatory patterns, called network motifs. One of the most common network motifs is negative auto-regulation, in which a transcription factor represses its own production. Negative auto-regulation has several potential functions: it can shorten the response time (time to reach halfway to steady-state), stabilize expression against noise, and linearize the gene's input-output response curve. This latter function of negative auto-regulation, which increases the range of input signals over which downstream genes respond, has been studied by theory and synthetic gene circuits. Here we ask whether negative auto-regulation preserves this function also in the context of a natural system, where it is embedded within many additional interactions. To address this, we studied the negative auto-regulation motif in the arabinose utilization system of Escherichia coli, in which negative auto-regulation is part of a complex regulatory network.

Results

We find that when negative auto-regulation is disrupted by placing the regulator araC under constitutive expression, the input dynamic range of the arabinose system is reduced by 10-fold. The apparent Hill coefficient of the induction curve changes from about n = 1 with negative auto-regulation, to about n = 2 when it is disrupted. We present a mathematical model that describes how negative auto-regulation can increase input dynamic-range, by coupling the transcription factor protein level to the input signal.

Conclusions

Here we demonstrate that the negative auto-regulation motif in the native arabinose system of Escherichia coli increases the range of arabinose signals over which the system can respond. In this way, negative auto-regulation may help to increase the input dynamic-range while maintaining the specificity of cooperative regulatory systems. This function may contribute to explaining the common occurrence of negative auto-regulation in biological systems.

A kinetic model of TBP auto-regulation exhibits bistability

Background

TATA Binding Protein (TBP) is required for transcription initiation by all three eukaryotic RNA polymerases. It participates in transcriptional initiation at the majority of eukaryotic gene promoters, either by direct association to the TATA box upstream of the transcription start site or by indirectly localizing to the promoter through other proteins. TBP exists in solution in a dimeric form but binds to DNA as a monomer. Here, we present the first mathematical model for auto-catalytic TBP expression and use it to study the role of dimerization in maintaining the steady state TBP level.

Results

We show that the autogenous regulation of TBP results in a system that is capable of exhibiting three steady states: an unstable low TBP state, one stable state corresponding to a physiological TBP concentration, and another stable steady state corresponding to unviable cells where no TBP is expressed. Our model predicts that a basal level of TBP is required to establish the transcription of the TBP gene, and hence for cell viability. It also predicts that, for the condition corresponding to a typical mammalian cell, the high-TBP state and cell viability is sensitive to variation in DNA binding strength. We use the model to explore the effect of the dimer in buffering the response to changes in TBP levels, and show that for some physiological conditions the dimer is not important in buffering against perturbations.

Conclusions

Results on the necessity of a minimum basal TBP level support the in vivo observations that TBP is maternally inherited, providing the small amount of TBP required to establish its ubiquitous expression. The model shows that the system is sensitive to variations in parameters indicating that it is vulnerable to mutations in TBP. A reduction in TBP-DNA binding constant can lead the system to a regime where the unviable state is the only steady state. Contrary to the current hypotheses, we show that under some physiological conditions the dimer is not very important in restoring the system to steady state. This model demonstrates the use of mathematical modelling to investigate system behaviour and generate hypotheses governing the dynamics of such nonlinear biological systems.

Reviewers

This article was reviewed by Tomasz Lipniacki, James Faeder and Anna Marciniak-Czochra.

Experimental and steady-state analysis of the GAL regulatory system in Kluyveromyces lactis

The galactose uptake mechanism in yeast is a well-studied regulatory network. The regulatory players in the galactose regulatory mechanism (GAL system) are conserved in Saccharomyces cerevisiae and Kluyveromyces lactis, but the molecular mechanisms that occur as a result of the molecular interactions between them are different. The key differences in the GAL system of K. lactis relative to that of S. cerevisiae are: (a) the autoregulation of KlGAL4; (b) the dual role of KlGal1p as a metabolizing enzyme as well as a galactose-sensing protein; (c) the shuttling of KlGal1p between nucleus and cytoplasm; and (d) the nuclear confinement of KlGal80p. A steady-state model was used to elucidate the roles of these molecular mechanisms in the transcriptional response of the GAL system. The steady-state results were validated experimentally using measurements of beta-galactosidase to represent the expression for genes having two binding sites. The results showed that the autoregulation of the synthesis of activator KlGal4p is responsible for the leaky expression of GAL genes, even at high glucose concentrations. Furthermore, GAL gene expression in K. lactis shows low expression levels because of the limiting function of the bifunctional protein KlGal1p towards the induction process in order to cope with the need for the metabolism of lactose/galactose. The steady-state model of the GAL system of K. lactis provides an opportunity to compare with the design prevailing in S. cerevisiae. The comparison indicates that the existence of a protein, Gal3p, dedicated to the sensing of galactose in S. cerevisiae as a result of genome duplication has resulted in a system which metabolizes galactose efficiently.

Activating and inhibiting connections in biological network dynamics

Background

Many studies of biochemical networks have analyzed network topology. Such work has suggested that specific types of network wiring may increase network robustness and therefore confer a selective advantage. However, knowledge of network topology does not allow one to predict network dynamical behavior – for example, whether deleting a protein from a signaling network would maintain the network's dynamical behavior, or induce oscillations or chaos.

Results

Here we report that the balance between activating and inhibiting connections is important in determining whether network dynamics reach steady state or oscillate. We use a simple dynamical model of a network of interacting genes or proteins. Using the model, we study random networks, networks selected for robust dynamics, and examples of biological network topologies. The fraction of activating connections influences whether the network dynamics reach steady state or oscillate.

Conclusion

The activating fraction may predispose a network to oscillate or reach steady state, and neutral evolution or selection of this parameter may affect the behavior of biological networks. This principle may unify the dynamics of a wide range of cellular networks.

Reviewers

Reviewed by Sergei Maslov, Eugene Koonin, and Yu (Brandon) Xia (nominated by Mark Gerstein). For the full reviews, please go to the Reviewers' comments section.

Steady state approach to model gene regulatory networks—Simulation of microarray experiments

Genetic regulatory networks (GRN) represent complex interactions between genes brought about through proteins that they code for. Quantification of expression levels in GRN either through experiments or theoretical modeling is a challenging task. Recently, microarray experiments have gained importance in evaluating GRN at the genome level. Microarray experiments yield log fold change in mRNA abundance which is helpful in deciphering connectivity in GRN. Current approaches such as data mining, Boolean or Bayesian modeling and combined use of expression and location data are useful in analyzing microarray data. However, these methodologies lack underlying mechanistic details present in GRN. We present here a steady state gene expression simulator (SSGES) which sets up steady state equations and simulates the response for a given network structure of a GRN. SSGES includes mechanistic details such as stoichiometry, protein-DNA and protein-protein interactions, translocation of regulatory proteins and autoregulation. SSGES can be used to simulate the response of a GRN in terms of fractional transcription and protein expression. SSGES can also be used to generate log fold change in mRNA abundance and protein expression implying that it is useful to simulate microarray type experiments. We have demonstrated these capabilities of SSGES by modeling the steady state response of GAL regulatory system in Saccharomyces cerevisiae. We have demonstrated that the predicted data qualitatively matched the microarray data obtained experimentally by Ideker et al. [Ideker, T., Thorsson, V., Ranish, J.A., Christmas, R., Buhler, J., Eng, J.K., Bumgarner, R., Goodlett, D.R., Aebersold, R., Hood, L., 2001. Integrated genomic and proteomic analyses of a systematically perturbed metabolic network. Science 292, 929-934]. SSGES is available from authors upon request.

Nonlinear regulation enhances the phenotypic expression of trans-acting genetic polymorphisms

BACKGROUND

Genetic variation explains a considerable part of observed phenotypic variation in gene expression networks. This variation has been shown to be located both locally (cis) and distally (trans) to the genes being measured. Here we explore to which degree the phenotypic manifestation of local and distant polymorphisms is a dynamic feature of regulatory design.

RESULTS

By combining mathematical models of gene expression networks with genetic maps and linkage analysis we find that very different network structures and regulatory motifs give similar cis/trans linkage patterns. However, when the shape of the cis-regulatory input functions is more nonlinear or threshold-like, we observe for all networks a dramatic increase in the phenotypic expression of distant compared to local polymorphisms under otherwise equal conditions.

CONCLUSION

Our findings indicate that genetic variation affecting the form of cis-regulatory input functions may reshape the genotype-phenotype map by changing the relative importance of cis and trans variation. Our approach combining nonlinear dynamic models with statistical genetics opens up for a systematic investigation of how functional genetic variation is translated into phenotypic variation under various systemic conditions.

Canalization breakdown and evolution in a source-sink system

Understanding the process of adaptation to novel environments may help to elucidate several ecological phenomena, from the stability of species range margins to host-pathogen specificity and persistence in degraded habitats. We study evolution in one type of novel environment: a sink habitat where populations cannot persist without recurrent immigration from a source population. Previous studies on source-sink evolution have focused on how extrinsic environmental factors influence adaptation to a sink, but few studies have examined how intrinsic genetic factors influence adaptation. We use an individual-based model to explore how genetic canalization that evolves in gene regulation networks influences the adaptation of a population to a sink. We find that as canalization in the regulation network increases, the probability of adaptation to the novel habitat decreases. When adaptation to the habitat does occur, it is usually preceded by a breakdown of canalization. As evolution continues in the novel habitat, canalization reemerges, but a legacy of the breakdown may remain, even after several generations. We also find that environmental noise tends to increase the probability of adaptation to the novel habitat. Our results suggest that the details of genetic architecture can significantly influence the likelihood of niche evolution in novel environments.