The competitive exclusion principle states that phage diversity M should not exceed bacterial diversity N. By analyzing the steady-state solutions of multistrain equations, we find a new constraint: the diversity N of bacteria living on the same resources is constrained to be M or M+1 in terms of the diversity of their phage predators. We quantify how the parameter space of coexistence exponentially decreases with diversity. For diversity to grow, an open or evolving ecosystem needs to climb a narrowing 'diversity staircase' by alternatingly adding new bacteria and phages. The unfolding coevolutionary arms race will typically favor high growth rate, but a phage that infects two bacterial strains differently can occasionally eliminate the fastest growing bacteria. This context-dependent fitness allows abrupt resetting of the 'Red-Queen's race' and constrains the local diversity.
The lysogenic state of the ? switch is exceptionally stable, still, it is capable of responding to DNA-damage and rapidly enter the lytic state. We invented an assay where PNA mediated tethering of a plasmid allowed for single molecule investigations of the effect of supercoiling on the efficiency of the epigenetic ? switch. Compared with non-supercoiled DNA, the presence of supercoils enhances the CI-mediated DNA looping probability and renders the transition between the looped and unlooped states steeper, thus increasing the Hill coefficient. Interestingly, the transition occurs exactly at the CI concentration corresponding to the minimum number of CI molecules capable of maintaining the pRM-repressed state. Based on these results we propose that supercoiling maintains the pRM-repressible state as CI concentration decline during induction and thus prevent autoregulation of cI from interfering with induction.
Speciation, diversification, and competition between species challenge the stability of complex ecosystems. Laboratory experiments often focus on one or two species competing under conditions where they may grow exponentially. Field studies, in contrast, emphasize multi-species communities characterized by many types of ecological interactions. A general problem is to understand conditions that support a dynamically maintained coexistence of many species in an ecosystem over a long time span. In the present paper we propose a lattice model of multiple competing and evolving sessile species. When allowing the interspecies interactions to mutate, we obtain coexistence of many species in a complex ecosystem, provided that there is a cost for each interaction. The diversity reached by the model incorporating speciation is found to be substantially higher than in the case when entirely new species appear due to immigration from outside of the considered ecosystem. The species self-organize their spatial distribution through competitive interactions to create many patches, implicitly protecting each other from competitively superior species, and speciation in each patch leads the system to high diversity. We also show that species that exist a long time tend to have a relatively small population, as this allows them to avoid encounter with competitive invaders.
Inheritance of 5-methyl cytosine modification of CpG (CG/CG) DNA sequences is needed to maintain early developmental decisions in vertebrates. The standard inheritance model treats CpGs as independent, with methylated CpGs maintained by efficient methylation of hemimethylated CpGs produced after DNA replication, and unmethylated CpGs maintained by an absence of de novo methylation. By stochastic simulations of CpG islands over multiple cell cycles and systematic sampling of reaction parameters, we show that the standard model is inconsistent with many experimental observations. In contrast, dynamic collaboration between CpGs can provide strong error-tolerant somatic inheritance of both hypermethylated and hypomethylated states of a cluster of CpGs, reproducing observed stable bimodal methylation patterns. Known recruitment of methylating enzymes by methylated CpGs could provide the necessary collaboration, but we predict that recruitment of demethylating enzymes by unmethylated CpGs strengthens inheritance and allows CpG islands to remain hypomethylated within a sea of hypermethylation.
Bacteriophage ? stably maintains its dormant prophage state but efficiently enters lytic development in response to DNA damage. The mediator of these processes is the ? repressor protein, CI, and its interactions with ? operator DNA. This ? switch is a model on the basis of which epigenetic switch regulation is understood. Using single molecule analysis, we directly examined the stability of the CI-operator structure in its natural, supercoiled state. We marked positions adjacent to the ? operators with peptide nucleic acids and monitored their movement by tethered particle tracking. Compared with relaxed DNA, the presence of supercoils greatly enhances juxtaposition probability. Also, the efficiency and cooperativity of the ? switch is significantly increased in the supercoiled system compared with a linear assay, increasing the Hill coefficient.
Many toxin-antitoxin operons are regulated by the toxin/antitoxin ratio by mechanisms collectively coined "conditional cooperativity". Toxin and antitoxin form heteromers with different stoichiometric ratios, and the complex with the intermediate ratio works best as a transcription repressor. This allows transcription at low toxin level, strong repression at intermediate toxin level, and then again transcription at high toxin level. Such regulation has two interesting features; firstly, it provides a non-monotonous response to the concentration of one of the proteins, and secondly, it opens for ultra-sensitivity mediated by the sequestration of the functioning heteromers. We explore possible functions of conditional regulation in simple feedback motifs, and show that it can provide bistability for a wide range of parameters. We then demonstrate that the conditional cooperativity in toxin-antitoxin systems combined with the growth-inhibition activity of free toxin can mediate bistability between a growing state and a dormant state.
The spatial rock-paper-scissors ecosystem, where three species interact cyclically, is a model example of how spatial structure can maintain biodiversity. We here consider such a system for a broad range of interaction rates. When one species grows very slowly, this species and its prey dominate the system by self-organizing into a labyrinthine configuration in which the third species propagates. The cluster size distributions of the two dominating species have heavy tails and the configuration is stabilized through a complex spatial feedback loop. We introduce a statistical measure that quantifies the amount of clustering in the spatial system by comparison with its mean-field approximation. Hereby, we are able to quantitatively explain how the labyrinthine configuration slows down the dynamics and stabilizes the system.
The olfactory system integrates signals from receptors expressed in olfactory sensory neurons. Each sensory neuron expresses only one of many similar olfactory receptors (ORs). The choice of receptor is made stochastically early in the differentiation process and is maintained throughout the life of the neuron. The underlying mechanism of this stochastic commitment to one of multiple similar OR genes remains elusive. We present a theoretical analysis of a mechanism that invokes important epigenetic properties of the system. The proposed model combines nucleosomes and associated read-write enzymes as mediators of a cis-acting positive feedback with a trans-acting negative feedback, thereby coupling the local epigenetic landscape of the individual OR genes in a way that allow one and only one gene to be active at any time. The model pinpoint that singular gene selection does not require transient mechanisms, enhancer elements or transcription factors to separate choice from maintenance. In addition, our hypothesis allow us to combine all reported characteristics of singular OR gene selection, in particular that OR genes are silenced from OR transgenes. Intriguingly, it predicts that OR transgenes placed in close proximity should always be expressed simultaneously, though rarely.
We introduce a stochastic model describing aggregation of misfolded proteins and degradation by the protein quality control system in a single cell. Aggregate growth is contrasted by the cell quality control system, that attacks them at different stages of the growth process, with an efficiency that decreases with their size. Model parameters are estimated from experimental data. Two qualitatively different behaviors emerge: a homeostatic state, where the quality control system is stable and aggregates of large sizes are not formed, and an oscillatory state, where the quality control system periodically breaks down, allowing for formation of large aggregates. We discuss how these periodic breakdowns may constitute a mechanism for the development of neurodegenerative diseases.
Sensing a graded input and differentiating between its different levels is at the core of many developmental decisions. Here, we want to examine how this can be realized for a simple system. We model gene regulatory circuits that reach distinct states when setting the underlying gene copy number to 1, 2 and 3. This distinction can be considered as counting the copy number. We explore different circuits that allow for counting and keeping memory of the count after resetting the copy number to 1. For this purpose, we sample different architectures and parameters, only considering circuits that contain repressive links, which we model by Michaelis-Menten terms. Interestingly, we find that counting to 3 does not require a hierarchy in Hill coefficients, in contrast to counting to 2, which is known from lambda phage. Furthermore, we find two main circuit architectures: one design also found in the vertebrate neural tube in a development governed by the sonic hedgehog morphogen and the more robust design of a repressilator supplemented with a weak repressilator acting in the opposite direction.
Bacteria have evolved diverse defense mechanisms that allow them to fight viral attacks. One such mechanism, the clustered, regularly interspaced, short palindromic repeat (CRISPR) system, is an adaptive immune system consisting of genetic loci that can take up genetic material from invasive elements (viruses and plasmids) and later use them to reject the returning invaders. It remains an open question how, despite the ongoing evolution of attack and defense mechanisms, bacteria and viral phages manage to coexist. Using a simple mathematical model and a two-dimensional numerical simulation, we found that CRISPR adaptive immunity allows for robust phage-bacterium coexistence even when the number of virus species far exceeds the capacity of CRISPR-encoded genetic memory. Coexistence is predicted to be a consequence of the presence of many interdependent species that stress but do not overrun the bacterial defense system.
Positive feedback in nucleosome modification has been proposed to allow large chromatin regions to exist stably and heritably in distinct expression states. However, modeling has shown that such epigenetic bistability requires that modifying enzymes recruited by nucleosomes are active on distant nucleosomes, potentially allowing uncontrollable spreading of modification. By modeling the silencing of mating-type loci in Saccharomyces cerevisiae, we show that a modification reaction that combines a long-range component and a locally acting component can provide bistability and can be blocked by simple barriers that interrupt the nucleosome chain. We find that robust containment of the silenced region could be achieved by the presence of a number of weak simple barriers in the surrounding chromatin and a limited capacity of the positive feedback reaction. In addition, we show that the state of the silenced region can be regulated by silencer elements acting only on neighboring nucleosomes. Thus, a relatively simple set of nucleosome-modifying enzymes and recognition domains is all that is needed to make chromatin-based epigenetics useful and safe.
Optimal response to environmental stimuli often requires activation of certain genes and repression of others. Dual function regulatory proteins play a key role in the differential regulation of gene expression. While repression can be achieved by any DNA binding protein through steric occlusion of RNA polymerase in the promoter region, activation often requires a surface on the regulatory protein to contact RNAP and thus facilitate transcription initiation. RNAP itself is also a DNA binding protein, therefore it can function as a transcriptional repressor. Searching the Escherichia coli promoter database we found that ?14% of the identified forward promoters overlap with a promoter oriented in the opposite direction. In this article we combine a mathematical model with experimental analysis of synthetic regulatory regions to investigate interference of overlapping promoters. We find that promoter interference depends on the characteristics of overlapping promoters. The model predicts that promoter strength and interference can be regulated separately, which provides unique opportunities for regulation. Our experimental data suggest that in principle any DNA binding protein can be used for both activation and repression of promoter transcription, depending on the context. These findings can be exploited in the construction of synthetic networks.
Diseases emerge, persist, and vanish in an ongoing battle for available hosts. Hosts, on the other hand, defend themselves by developing immunity that limits the ability of pathogens to reinfect them. We here explore a multidisease system with emphasis on mutual exclusion. We demonstrate that such a system develops toward a steady state, where the spread of individual diseases self-organizes to a state close to that of critical percolation, without any global control mechanism or separation of time scale. For a broad range of introduction rates of new diseases, the likelihood of transmitting diseases remains approximately constant.
Ecological systems comprise an astonishing diversity of species that cooperate or compete with each other forming complex mutual dependencies. The minimum requirements to maintain a large species diversity on long time scales are in general unknown. Using lichen communities as an example, we propose a model for the evolution of mutually excluding organisms that compete for space. We suggest that chainlike or cyclic invasions open for creation of spatially separated subpopulations that subsequently can lead to increased diversity. In contrast to its nonspatial counterpart, our model predicts robust coexistence of a large number of species. It is demonstrated that large species diversity can be obtained on evolutionary time scales, provided that interactions between species have spatial constraints. In particular, a phase transition to a sustainable state of high diversity is identified.
Cultural competition has throughout our history shaped and reshaped the geography of boundaries between humans. Language and culture are intimately connected and linguists often use distinctive keywords to quantify the dynamics of information spreading in societies harboring strong culture centers. One prominent example, which is addressed here, is Kyotos historical impact on Japanese culture. We construct a minimal model, based on shared properties of linguistic maps, to address the interplay between information flow and geography. We show that spreading of information over Japan in the premodern time can be described by an Eden growth process with noise levels corresponding to coherent spatial patches of sizes given by a single days walk (~15 km), and that new words appear in Kyoto at times comparable to the time between human generations (~30 yr).
After infection of a sensitive host temperate phages may enter either a lytic or a lysogenic pathway leading to new phage assembly or silencing as a prophage, respectively. The decision about which pathway to enter is centered in the genetic switch of the phage. In this work, we explore the bistable genetic switch of bacteriophage TP901-1 through experiments and statistical mechanical modeling. We examine the activity of the lysogenic promoter P(R) at different concentrations of the phage repressor, CI, and compare the effect of CI on P(R) in the presence or absence of the phage-encoded MOR protein expressed from the lytic promoter P(L). We find that the presence of large amounts of MOR prevents repression of the P(R) promoter, verifying that MOR works as an antirepressor. We compare our experimental data with simulations based on previous mathematical formulations of this switch. Good agreement between data and simulations verify the model of CI repression of P(R). By including MOR in the simulations, we are able to discard a model that assumes that CI and MOR do not interact before binding together at the DNA to repress P(R). The second model of Pr repression assumes the formation of a CI:MOR complex in the cytoplasm. We suggest that a CI:MOR complex may exist in different forms that either prevent or invoke P(R) repression, introducing a new twist on mixed feedback systems.
Bacterial mRNAs are translated by closely spaced ribosomes and degraded from the 5-end, with half-lives of around 2 min at 37 °C in most cases. Ribosome-free or "naked" mRNA is known to be readily degraded, but the initial event that inactivates the mRNA functionally has not been fully described. Here, we characterize a determinant of the functional stability of an mRNA, which is located in the early coding region. Using literature values for the mRNA half-lives of variant lacZ mRNAs in Escherichia coli, we modeled how the ribosome spacing is affected by the translation rate of the individual codons. When comparing the ribosome spacing at various segments of the mRNA to its functional half-life, we found a clear correlation between the functional mRNA half-life and the ribosome spacing in the mRNA region approximately between codon 20 and codon 45. From this finding, we predicted that inserts of slowly translated codons before codon 20 or after codon 45 should shorten or prolong, respectively, the functional mRNA half-life by altering the ribosome density in the important region. These predictions were tested on eight new lacZ variants, and their experimentally determined mRNA half-lives all supported the model. We thus suggest that translation-rate-mediated differences in the spacing between ribosomes in this early coding region is a parameter that determines the mRNAs functional half-life. We present a model that is in accordance with many earlier observations and that allows a prediction of the functional half-life of a given mRNA sequence.
Genes of prokaryotes and Archaea are often organized in cotranscribed groups, or operons. In contrast, eukaryotic genes are generally transcribed independently. Here we show that there is a substantial economic gain for the cell to cotranscribe genes encoding protein complexes because it synchronizes the fluctuations, or noise, in the levels of the different components. This correlation substantially reduces the shortfall in production of the complex. This benefit is relatively large in small cells such as bacterial cells, in which there are few mRNAs and proteins per cell, and is diminished in larger cells such as eukaryotic cells.
Gene regulatory networks (GRNs) that make reliable decisions should have design features to cope with random fluctuations in the levels or activities of biological molecules. The phage ? GRN makes a lysis-lysogeny decision informed by the number of phages infecting the cell. To analyse the design of decision making GRNs, we generated random in silico GRNs comprised of two or three transcriptional regulators and selected those able to perform a ?-like decision in the presence of noise. Various two-protein networks analogous to the ? CI-Cro GRN worked in noise-less conditions but failed when noise was introduced. Adding a ? CII-like protein significantly improved robustness to noise. CII relieves the CI-like protein of its decider function, allowing CI to be optimized as a decision maintainer. CIIs lysogenic decider function was improved by its instability and rapid removal once the decision was taken, preventing its interference with maintenance. A more reliable decision also resulted from simulated co-transcription of the genes for CII and the Cro-like protein, which correlates fluctuations in these opposing decider functions and makes their ratio less noisy. Thus, the ? decision network contains design features for reducing and resisting noise.
Cells can often choose among several stably heritable phenotypes. Examples are the expressions of genes in eukaryotic cells where long chromosomal regions can adopt persistent and heritable silenced or active states that may be associated with positive feedback in dynamic modification of nucleosomes. We generalize this mechanism in terms of bistability associated with valleys in an epigenetic landscape. A transfer matrix method was used to rigorously follow the system through the disruptive process of cell division. This combined treatment of noisy dynamics both between and during cell division provides an efficient way to calculate the stability of alternative states in a broad range of epigenetic systems.
Pathogens and parasites are ubiquitous in the living world, being limited only by availability of suitable hosts. The ability to transmit a particular disease depends on competing infections as well as on the status of host immunity. Multiple diseases compete for the same resource and their fate is coupled to each other. Such couplings have many facets, for example cross-immunization between related influenza strains, mutual inhibition by killing the host, or possible even a mutual catalytic effect if host immunity is impaired. We here introduce a minimal model for an unlimited number of unrelated pathogens whose interaction is simplified to simple mutual exclusion. The model incorporates an ongoing development of host immunity to past diseases, while leaving the system open for emergence of new diseases. The model exhibits a rich dynamical behavior with interacting infection waves, leaving broad trails of immunization in the host population. This obtained immunization pattern depends only on the system size and on the mutation rate that initiates new diseases.
The "six degrees of separation" between any two individuals on Earth has become emblematic of the "small world" theme, even though the information conveyed via a chain of human encounters decays very rapidly with increasing chain length, and diffusion of information via this process may be very inefficient in large human organizations. The information flow on a communication network in a large organization, the University of Oslo, has been studied by analyzing email records. The records allow for quantification of communication intensity across organizational levels and between organizational units (referred to as "modules"). We find that the number of email messages within modules scales with module size to the power of 1.29±.06 , and the frequency of communication between individuals decays exponentially with the number of links required upward in the organizational hierarchy before they are connected. Our data also indicates that the number of messages sent by administrative units is proportional to the number of individuals at lower levels in the administrative hierarchy, and the "divergence of information" within modules is associated with this linear relationship. The observed scaling is consistent with a hierarchical system in which individuals far apart in the organization interact little with each other and receive a disproportionate number of messages from higher levels in the administrative hierarchy.
The function of living cells is controlled by complex regulatory networks that are built of a wide diversity of interacting molecular components. The sheer size and intricacy of molecular networks of even the simplest organisms are obstacles toward understanding network functionality. This review discusses the achievements and promise of a bottom-up approach that uses well-characterized subnetworks as model systems for understanding larger networks. It highlights the interplay between the structure, logic, and function of various types of small regulatory circuits. The bottom-up approach advocates understanding regulatory networks as a collection of entangled motifs. We therefore emphasize the potential of negative and positive feedback, as well as their combinations, to generate robust homeostasis, epigenetics, and oscillations.
Virulent phages and their bacterial hosts represent an unusual sort of predator-prey system where each time a prey is eaten, hundreds of new predators are born. It is puzzling how, despite the apparent effectiveness of the phage predators, they manage to avoid driving their bacterial prey to extinction. Here we consider a phage-bacterial ecosystem on a two-dimensional (2-d) surface and show that homogeneous space in itself enhances coexistence. We analyze different behavioral mechanisms that can facilitate coexistence in a spatial environment. For example, we find that when the latent times of the phage are allowed to evolve, selection favors "mediocre killers," since voracious phage rapidly deplete local resources and go extinct. Our model system thus emphasizes the differences between short-term proliferation and long-term ecosystem sustainability.
We present detailed results on the C4-HSL-mediated quorum sensing (QS) regulatory system of the opportunistic Gram-negative bacterium Aeromonas hydrophila. This bacterium contains a particularly simple QS system that allows for a detailed modeling of kinetics. In a model system (i.e., the Escherichia coli monitor strain MH205), the C4-HSL production of A. hydrophila is interrupted by fusion of gfp(ASV). In the present in vitro study, we measure the response of the QS regulatory ahyRI locus in the monitor strain to predetermined concentrations of C4-HSL signal molecules. A minimal kinetic model describes the data well. It can be solved analytically, providing substantial insight into the QS mechanism: at high concentrations of signal molecules, a slow decay of the activated regulator sets the timescale for the QS regulation loop. Slow saturation ensures that, in an A. hydrophila cell, the QS system is activated only by signal molecules produced by other A. hydrophila cells. Separate information on the ahyR and ahyI loci can be extracted, thus allowing the probe to be used in identifying the target when testing QS inhibitors.
Phage lambda is among the simplest organisms that make a developmental decision. An infected bacterium goes either into the lytic state, where the phage particles rapidly replicate and eventually lyse the cell, or into a lysogenic state, where the phage goes dormant and replicates along with the cell. Experimental observations by P. Kourilsky are consistent with a single phage infection deterministically choosing lysis and double infection resulting in a stochastic choice. We argue that the phage are playing a "game" of minimizing the chance of extinction and that the shift from determinism to stochasticity is due to a shift from a single-player to a multiplayer game. Crucial to the argument is the clonal identity of the phage.
Small regulatory RNAs (sRNAs) in eukaryotes and bacteria play an important role in the regulation of gene expression either by binding to regulatory proteins or directly to target mRNAs. Two of the best-characterized bacterial sRNAs, Spot42 and RyhB, form a complementary pair with the ribosome binding region of their target mRNAs, thereby inhibiting translation or promoting mRNA degradation. To investigate the steady-state and dynamic potential of such sRNAs, we examine the 2 key parameters characterizing sRNA regulation: the capacity to overexpress the sRNA relative to its target mRNA and the speed at which the target mRNA is irreversibly inactivated. We demonstrate different methods to determine these 2 key parameters, for Spot42 and RyhB, which combine biochemical and genetic experiments with computational analysis. We have developed a mathematical model that describes the functional properties of sRNAs with various characteristic parameters. We observed that Spot42 and RyhB function in distinctive parameter regimes, which result in divergent mechanisms.
It has been reported that the number of transcription factors encoded in prokaryotic genomes scales approximately quadratically with their total number of genes. We propose a conceptual explanation of this finding and illustrate it using a simple model in which metabolic and regulatory networks of prokaryotes are shaped by horizontal gene transfer of coregulated metabolic pathways. Adapting to a new environmental condition monitored by a new transcription factor (e.g., learning to use another nutrient) involves both acquiring new enzymes and reusing some of the enzymes already encoded in the genome. As the repertoire of enzymes of an organism (its toolbox) grows larger, it can reuse its enzyme tools more often and thus needs to get fewer new ones to master each new task. From this observation, it logically follows that the number of functional tasks and their regulators increases faster than linearly with the total number of genes encoding enzymes. Genomes can also shrink, e.g., because of a loss of a nutrient from the environment, followed by deletion of its regulator and all enzymes that become redundant. We propose several simple models of network evolution elaborating on this toolbox argument and reproducing the empirically observed quadratic scaling. The distribution of lengths of pathway branches in our model agrees with that of the real-life metabolic network of Escherichia coli. Thus, our model provides a qualitative explanation for broad distributions of regulon sizes in prokaryotes.
Longevity of a taxonomic group is an important issue in understanding the dynamics of evolution. In this respect a key observation is that genera, families or orders can each be assigned a characteristic average lifetime (Van Valen in Evol Theory 1:1-30, 1973). Using the fossil marine animal genera database (Sepkoski in Bull Am Paleontol 363, pp 563, 2002) we here examine the relationship between longevity of a higher taxonomic group (orders) and the longevity of its lower taxonomic groups (genera). We find insignificant correlation between the size of an order and its longevity, whereas we observe large correlation between the lifetime of an order and the lifetime of its constituent genera. These observations suggest that longevity of taxonomic groups is heritable intrinsically or on the grounds of environmental preferences.
Many transcription factors repress transcription of their own genes. Negative autoregulation has been shown to reduce cell-cell variation in regulatory protein levels and speed up the response time in gene networks. In this work we examined transcription regulation of the galS gene and the function of its product, the GalS protein. We observed a unique operator preference of the GalS protein characterized by dominant negative autoregulation. We show that this pattern of regulation limits the repression level of the target genes in steady states. We suggest that transcription factors with dominant negative autoregulation are designed for regulating gene expression during environmental transitions.
In Parkinsons disease (PD), there is evidence that alpha-synuclein (alphaSN) aggregation is coupled to dysfunctional or overburdened protein quality control systems, in particular the ubiquitin-proteasome system. Here, we develop a simple dynamical model for the on-going conflict between alphaSN aggregation and the maintenance of a functional proteasome in the healthy cell, based on the premise that proteasomal activity can be titrated out by mature alphaSN fibrils and their protofilament precursors. In the presence of excess proteasomes the cell easily maintains homeostasis. However, when the ratio between the available proteasome and the alphaSN protofilaments is reduced below a threshold level, we predict a collapse of homeostasis and onset of oscillations in the proteasome concentration. Depleted proteasome opens for accumulation of oligomers. Our analysis suggests that the onset of PD is associated with a proteasome population that becomes occupied in periodic degradation of aggregates. This behavior is found to be the general state of a proteasome/chaperone system under pressure, and suggests new interpretations of other diseases where protein aggregation could stress elements of the protein quality control system.
The lytic-lysogenic switch of the temperate lactococcal phage TP901-1 is fundamentally different from that of phage lambda. In phage TP901-1, the lytic promoter P(L) is repressed by CI, whereas repression of the lysogenic promoter P(R) requires the presence of both of the antagonistic regulator proteins, MOR and CI. We model the central part of the switch and compare the two cases for P(R) repression: the one where the two regulators interact only on the DNA and the other where the two regulators form a heteromer complex in the cytoplasm prior to DNA binding. The models are analyzed for bistability, and the predicted promoter repression folds are compared to experimental data. We conclude that the experimental data are best reproduced the latter case, where a heteromer complex forms in solution. We further find that CI sequestration by the formation of MOR:CI complexes in cytoplasm makes the genetic switch robust.
Transcription of many genes is regulated by combinations of multiple signals. In Escherichia coli, combinatorial control is typical in the case of operons related to utilization of different sugars in the absence of glucose. To understand regulation of the transport and metabolic pathways in the galactose system, we measured activities of the six gal regulon promoters simultaneously, using an in vitro transcription system containing purified components. Input functions were computed on the basis of the experimental measurements. We observed four different shapes of input functions. From the results, we can conclude that the structure of the regulatory network is insufficient for the determination of signal integration. It is the actual structure of the promoter and regulatory region, the mechanism of transcription regulation, and the interplay between transcription factors that shape the input function to be suitable for adaptation.
Proper cellular function requires uptake of small molecules from the environment. In response to changes in extracellular conditions cells alter the import and utilization of small molecules. For a wide variety of small molecules the cellular response is regulated by a network motif that combines two feedback loops, one which regulates the transport and the other which regulates the subsequent metabolism.
Pathogen-host relationships are the result of an ongoing coevolutionary race where the immune system of the host attempts to eliminate the pathogen, while the successful pathogen mutates to become invisible for the hosts immune system. We here propose a minimal pathogen-host evolution model that takes into account cross immunization and allows for evolution of a spatially heterogeneous immune status of a population of hosts. With only the mutation rate as a determining parameter, the model allows us to produce an evolutionary tree of diseases which is highly branched, but hardly ever splits into separate long-lived trunks. Side branches remain short lived and seldom diverge to the extent of losing all cross immunizations.
The biological requirements for an ecosystem to develop and maintain species diversity are in general unknown. Here we consider a model ecosystem of sessile and mutually excluding organisms competing for space [Mathiesen et al. Phys. Rev. Lett. 107, 188101 (2011)]. Competition is controlled by an interaction network with fixed links chosen by a Bernoulli process. New species are introduced in the system at a predefined rate. In the limit of small introduction rates, the system becomes bistable and can undergo a phase transition from a state of low diversity to high diversity. We suggest that isolated patches of metapopulations formed by the collapse of cyclic relations are essential for the transition to the state of high diversity.
Complex dynamical systems often show multiple metastable states. In macroevolution, such behavior is suggested by punctuated equilibrium and discrete geological epochs. In molecular biology, bistability is found in epigenetics and in the many mutually exclusive states that a human cell can take. Sociopolitical systems can be single-party regimes or a pluralism of balancing political fractions. To introduce multistability, we suggest a model system of D mutually exclusive microstates that battle for dominance in a large system. Assuming one common intermediate state, we obtain D+1 metastable macrostates for the system, one of which is a self-reinforced mixture of all D+1 microstates. Robustness of this metastable mixed state increases with diversity D.
The rock-paper-scissors game is a model example of the ongoing cyclic turnover typical of many ecosystems, ranging from the terrestrial and aquatic to the microbial. Here we explore the evolution of a rock-paper-scissors system where three species compete for space. The species are allowed to mutate and change the speed by which they invade one another. In the case when all species have similar mutation rates, we observe a perpetual arms race where no single species prevails. When only two species mutate, their aggressions increase indefinitely until the ecosystem collapses and only the nonmutating species survives. Finally we show that when only one species mutates, group selection removes individual predators with the fastest growth rates, causing the growth rate of the species to stabilize. We explain this group selection quantitatively.
The historical interplay between societies is governed by many factors, including in particular the spreading of languages, religion, and other symbolic traits. Cultural development, in turn, is coupled to the emergence and maintenance of information spreading. Strong centralized cultures exist due to attention from their members, whose faithfulness in turn relies on the supply of information. Here we discuss a culture evolution model on a planar geometry that takes into account aspects of the feedback between information spreading and its maintenance. Features of the model are highlighted by comparing it to cultural spreading in ancient and medieval Europe, where it suggests in particular that long-lived centers should be located in geographically remote regions.
The P1 promoter of the galactose operon in Escherichia coli is one of the best studied examples of extended -10 promoters. Recognition of the P1 promoter does not require specific contacts between RNA polymerase and its poor -35 element. To investigate whether specific recognition of the -35 element would affect the regulation of P1 by GalR, we mutagenized the -35 element of P1, isolated variants of the -35 element and studied the regulation of the mutant promoters by in vitro transcription assays and by mathematical modeling. The results show that the GalR-mediated DNA loop is less efficient in repressing P1 transcription when RNA polymerase binds to the -10 and -35 elements concomitantly. Our results suggest that promoters that lack specific -35 element recognition allow decoupling of local chromosome structure from transcription initiation.
Nucleosomes can be covalently modified by addition of various chemical groups on several of their exposed histone amino acids. These modifications are added and removed by enzymes (writers) and can be recognized by nucleosome-binding proteins (readers). Linking a reader domain and a writer domain that recognize and create the same modification state should allow nucleosomes in a particular modification state to recruit enzymes that create that modification state on nearby nucleosomes. This positive feedback has the potential to provide the alternative stable and heritable states required for epigenetic memory. However, analysis of simple histone codes involving interconversions between only two or three types of modified nucleosomes has revealed only a few circuit designs that allow heritable bistability. Here we show by computer simulations that a histone code involving alternative modifications at two histone positions, producing four modification states, combined with reader-writer proteins able to distinguish these states, allows for hundreds of different circuits capable of heritable bistability. These expanded possibilities result from multiple ways of generating two-step cooperativity in the positive feedback--through alternative pathways and an additional, novel cooperativity motif. Our analysis reveals other properties of such epigenetic circuits. They are most robust when the dominant nucleosome types are different at both modification positions and are not the type inserted after DNA replication. The dominant nucleosome types often recruit enzymes that create their own type or destroy the opposing type, but never catalyze their own destruction. The circuits appear to be evolutionary accessible; most circuits can be changed stepwise into almost any other circuit without losing heritable bistability. Thus, our analysis indicates that systems that utilize an expanded histone code have huge potential for generating stable and heritable nucleosome modification states and identifies the critical features of such systems.
Even within similar bacterial strains, it has been found that the clustered, regularly interspaced short palindromic repeat (CRISPR) shows a large variability of spacers. Modeling bacterial strains with different levels of immunity to infection by a single virulent phage, we find that coexistence in a well-mixed environment is possible only when these levels are distinctly different. When bacterial strains are similar, one subpopulation collapses. In the case of bacteria with various levels of CRISPR immunity to a range of phages, small differences in spacer composition will accordingly be suppressed under well-mixed conditions. Using a numerical model of populations spreading in space, we predict that it is the Lamarckian nature of CRISPR evolution that combines with spatial correlations to sustain the experimentally observed distribution of spacer diversity.
Bacteriophage are voracious predators of bacteria and a major determinant in shaping bacterial life strategies. Many phage species are virulent, meaning that infection leads to certain death of the host and immediate release of a large batch of phage progeny. Despite this apparent voraciousness, bacteria have stably coexisted with virulent phages for eons. Here, using individual-based stochastic spatial models, we study the conditions for achieving coexistence on the edge between two habitats, one of which is a bacterial refuge with conditions hostile to phage whereas the other is phage friendly. We show how bacterial density-dependent, or quorum-sensing, mechanisms such as the formation of biofilm can produce such refuges and edges in a self-organized manner. Coexistence on these edges exhibits the following properties, all of which are observed in real phage-bacteria ecosystems but difficult to achieve together in nonspatial ecosystem models: (i) highly efficient virulent phage with relatively long lifetimes, high infection rates and large burst sizes; (ii) large, stable, and high-density populations of phage and bacteria; (iii) a fast turnover of both phage and bacteria; and (iv) stability over evolutionary timescales despite imbalances in the rates of phage vs. bacterial evolution.
Many toxin-antitoxin (TA) loci are known to strongly repress their own transcription. This auto-inhibition is often called conditional cooperativity as it relies on cooperative binding of TA complexes to operator DNA that occurs only when toxins are in a proper stoichiometric relationship with antitoxins. There has recently been an explosion of interest in TA systems due to their role in bacterial persistence, however the role of conditional cooperativity is still unclear. We reveal the biological function of conditional cooperativity by constructing a mathematical model of the well studied TA system, relBE of Escherichia coli. We show that the model with the in vivo and in vitro established parameters reproduces experimentally observed response to nutritional stress. We further demonstrate that conditional cooperativity stabilizes the level of antitoxin in rapidly growing cells such that random induction of relBE is minimized. At the same time it enables quick removal of free toxin when the starvation is terminated.
Localization of activity is ubiquitous in life, and also within sub-cellular compartments. Localization provides potential advantages as different proteins involved in the same cellular process may supplement each other on a fast timescale. It might also prevent proteins from being active in other regions of the cell. However localization is at odds with the spreading of unbound molecules by diffusion. We model the cost and gain for specific enzyme activity using localization strategies based on binding to sites of intermediate specificity. While such bindings in themselves decrease the activity of the protein on its target site, they may increase protein activity if stochastic motion allows the acting protein to touch both the intermediate binding site and the specific site simultaneously. We discuss this strategy in view of recent suggestions on long non-coding RNA as a facilitator of localized activity of chromatin modifiers.
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