Hidden hysteresis – population dynamics can obscure gene network dynamics

Background

Positive feedback is a common motif in gene regulatory networks. It can be used in synthetic networks as an amplifier to increase the level of gene expression, as well as a nonlinear module to create bistable gene networks that display hysteresis in response to a given stimulus. Using a synthetic positive feedback-based tetracycline sensor in E. coli, we show that the population dynamics of a cell culture has a profound effect on the observed hysteretic response of a population of cells with this synthetic gene circuit.

Results

The amount of observable hysteresis in a cell culture harboring the gene circuit depended on the initial concentration of cells within the culture. The magnitude of the hysteresis observed was inversely related to the dilution procedure used to inoculate the subcultures; the higher the dilution of the cell culture, lower was the observed hysteresis of that culture at steady state. Although the behavior of the gene circuit in individual cells did not change significantly in the different subcultures, the proportion of cells exhibiting high levels of steady-state gene expression did change.Although the interrelated kinetics of gene expression and cell growth are unpredictable at first sight, we were able to resolve the surprising dilution-dependent hysteresis as a result of two interrelated phenomena - the stochastic switching between the ON and OFF phenotypes that led to the cumulative failure of the gene circuit over time, and the nonlinear, logistic growth of the cell in the batch culture.

Conclusions

These findings reinforce the fact that population dynamics cannot be ignored in analyzing the dynamics of gene networks. Indeed population dynamics may play a significant role in the manifestation of bistability and hysteresis, and is an important consideration when designing synthetic gene circuits intended for long-term application.

     

Microbial secretor–cheater dynamics

Microbial secretions manipulate the environment and communicate information to neighbours. The secretions of an individual microbe typically act externally and benefit all members of the local group. Secreting imposes a cost in terms of growth, so that cheaters that do not secrete gain by sharing the benefits without paying the costs. Cheaters have been observed in several experimental and natural settings. Given that cheaters grow faster than secretors when in direct competition, what maintains the widely observed patterns of secretion? Recent theory has emphasized the genetic structure of populations, in which secretors tend to associate spatially with other secretors, reducing direct competition and allowing highly secreting groups to share mutual benefits. Such kin selection can be a powerful force favouring cooperative traits. Here, I argue that, although kin selection is a factor, the combination of mutation and demographic processes dominate in determining the relative fitness of secretors versus cheaters when measured over the full cycle of microbial life history. Key demographic factors include the local density of microbes at which secretion significantly alters the environment, the extent to which secretion enhances microbial growth and maximum local density, and the ways in which secretion alters colony survival and dispersal.     

What drives community dynamics?

The search for general mechanisms of community assembly is a major focus of community ecology. The common practice so far has been to examine alternative assembly theories using dichotomist approaches of the form neutrality versus niche, or compensatory dynamics versus environmental forcing. In reality, all these mechanisms will be operating, albeit with different strengths. While there have been different approaches to community structure and dynamics, including neutrality and niche differentiation, less work has gone into separating out the temporal variation in species abundances into relative contributions from different components. Here we use a refined statistical machinery to decompose temporal fluctuations in species abundances into contributions from environmental stochasticity and inter-/intraspecific interactions, to see which ones dominate. We apply the methodology to community data from a range of taxa. Our results show that communities are largely driven by environmental fluctuations, and that member populations are, to different extents, regulated through intraspecific interactions, the effects of interspecific interactions remaining broadly minor. By decomposing the temporal variation in this way, we have been able to show directly what has been previously inferred indirectly: compensatory dynamics are in fact largely outweighed by environmental forcing, and the latter tends to synchronize the population dynamics.     

Structure and dynamics of two β-peptides in solution from molecular dynamics simulations validated against experiment

We have studied two different beta-peptides in methanol using explicit solvent molecular dynamics simulations and the GROMOS 53A6 force field: a heptapeptide (peptide 1) expected to form a left-handed 3(14)-helix, and a hexapeptide (peptide 2) expected to form a beta-hairpin in solution. Our analysis has focused on identifying and analyzing the stability of the dominant secondary structure conformations adopted by the peptides, as well as on comparing the experimental NOE distance upper bounds and 3J-coupling values with their counterparts calculated on the basis of the simulated ensembles. Moreover, we have critically compared the present results with the analogous results obtained with the GROMOS 45A3 (peptide 1) and 43A1 (peptide 2) force fields. We conclude that within the limits of conformational sampling employed here, the GROMOS 53A6 force field satisfactorily reproduces experimental findings regarding the behavior of short beta-peptides, with accuracy that is comparable to but not exceeding that of the previous versions of the force field. GCE legend Conformational clustering analysis of the simulated ensemble of a ss-hexapeptide with two different simulation setups (a and b). The central members of all of the clusters populating more than 5% of all of the structures are shown, together with the most dominant hydrogen bonds and the corresponding percentages of cluster members containing them.     

Is there chaos in plankton dynamics?

A controversial issue in ecosystem modeling is whether the irregularfluctuations that one observes in nature are due solely to randomenvironmental factors or whether, at least partially, a deterministicmechanism is responsible for the unpredictable behavior. Thissecond alternative is called deterministic chaos and the issuein this paper is to decide if actual plankton time series canvindicate the hypothesis of chaotic dynamics. The near-neighborforecasting method is a recent technique for detecting determinismin a time series and we apply it to measurements of phytoplanktonand zooplankton biomass obtained at a single station in theMiddle Atlantic Bight. Although the results do not concludethe presence of chaos, they do give some support to the ideathat deterministic non-linear trophic dynamics may account forat least some of the variability that is seen in the data, particularlyin terms of inferring zooplankton oscillations from those ofphytoplankton.     

Diet choice and predator—prey dynamics

Summary We compare the dynamics of predator-prey systems with specialist predators or adaptive generalist predators that base diet choice on energy-maximizing criteria. Adaptive predator behaviour leads to functional responses that are influenced by the relative abundance of alternate prey. This results in the per capita predation risk being positively density-dependent near points of diet expansion. For a small set of parameter values, systems with adaptive predators can be locally stable whereas systems with specialist predators would be unstable. This occurs mainly when alternate prey have low enough profitability that predators cannot sustain themselves indefinitely when feeding on alternate prey. Local stability of systems with adaptive predator behaviour is inversely related to the goodness of fit to optimal diet choice criteria. Hence, typical patterns of partial prey preference are more stabilizing than perfect optimal diet selection. Locally stable systems with adaptive predators are often globally unstable, converging on limit cycles for many initial population densities. The small range of parameter combinations and initial population densities leading to stable equilibria suggest that adaptive diet selection is unlikely to be a ubiquitous stabilizing factor in trophic interactions.     

How do toxicants affect epidemiological dynamics?

Populations are formed of their constituent interacting individuals, each with their own respective within‐host biological processes. Infection not only spreads within the host organism but also spreads between individuals. Here we propose and study a multilevel model which links the within‐host statuses of immunity and parasite density to population epidemiology under sublethal and lethal toxicant exposure. We analyse this nested model in order to better understand how toxicants impact the spread of disease within populations. We demonstrate that outbreak of infection within a population is completely determined by the level of toxicant exposure, and that it is maximised by intermediate toxicant dosage. We classify the population epidemiology into five phases of increasing toxicant exposure and calculate the conditions under which disease will spread, showing that there exists a threshold toxicant level under which epidemics will not occur. In general, higher toxicant load results in either extinction of the population or outbreak of infection. The within‐host statuses of the individual host also determine the outcome of the epidemic at the population level. We discuss applications of our model in the context of environmental epidemiology, predicting that increased exposure to toxicants could result in greater risk of epidemics within ecological systems. We predict that reducing sublethal toxicant exposure below our predicted safe threshold could contribute to controlling population level disease and infection.     

What contributions to protein side-chain dynamics are probed by NMR experiments? A molecular dynamics simulation analysis

Molecular dynamics simulations of the structurally homologous proteins TNfn3 and FNfn10 have been used to investigate the contributions to side-chain dynamics measured by NMR relaxation experiments. The results reproduce the variation in core side-chain dynamics observed by NMR and highlight the relevance of anharmonic motion and transitions between local minima for explaining NMR side-chain order parameters. A method is described for calculating converged order parameters by use of replica exchange molecular dynamics in conjunction with an implicit solvent model. These simulations allow the influence of various factors, such as the flexibility of side-chains and their free volume, on the mobility to be tested by perturbing the system. Deletion mutations are found to have the largest effect on the more densely packed FNfn10. Some counterintuitive effects are seen, such as an increase in order parameters close to deletion mutation sites, but these can be rationalized in terms of direct interactions with the modified side-chains. A statistical analysis of published order parameters supports the conclusions drawn from the simulations.     

Interaction of fast and slow dynamics in endocrine control systems with an application to β-cell dynamics

Endocrine dynamics spans a wide range of time scales, from rapid responses to physiological challenges to with slow responses that adapt the system to the demands placed on it. We outline a non-linear averaging procedure to extract the slower dynamics in a way that accounts properly for the non-linear dynamics of the faster time scale and is applicable to a hierarchy of more than two time scales, although we restrict our discussion to two scales for the sake of clarity. The procedure is exact if the slow time scale is infinitely slow (the dimensionless ε-quantity is the period of the fast time scale fluctuation times an upper bound to the slow time scale rate of change). However, even for an imperfect separation of time scales we find that this construction provides an excellent approximation for the slow-time dynamics at considerably reduced computational cost. Besides the computation advantage, the averaged equation provided a qualitative insight into the interaction of the time scales. We demonstrate the procedure and its advantages by applying the theory to the model described by Toli? et al. [I.M. Toli?, E. Mosekilde, J. Sturis, Modeling the insulin–glucose feedback system: the significance of pulsatile insulin secretion, J. Theor. Biol. 207 (2000) 361–375.] for ultradian dynamics of the glucose–insulin homeostasis feedback system, extended to include β-cell dynamics. We find that the dynamics of the β-cell mass are dependent not only on the glycemic load (amount of glucose administered to the system), but also on the way this load is applied (i.e. three meals daily versus constant infusion), effects that are lost in the inappropriate methods used by the earlier authors. Furthermore, we find that the loss of the protection against apoptosis conferred by insulin that occurs at elevated levels of insulin has a functional role in keeping the β-cell mass in check without compromising regulatory function. We also find that replenishment of β-cells from a rapidly proliferating pool of cells, as opposed to the slow turn-over which characterises fully differentiated β-cells, is essential to the prevention of type 1 diabetes.     

NF-κB pathway controls mitochondrial dynamics

The Optic atrophy 1 protein (OPA1) is a key element in the dynamics and morphology of mitochondria. We demonstrated that the absence of IκB kinase-α, which is a key element of the nonclassical NF-κB pathway, has an impact on the mitochondrial network morphology and OPA1 expression. In contrast, the absence of NF-κB essential modulator (NEMO) or IκB kinase-β, both of which are essential for the canonical NF-κB pathway, has no impact on mitochondrial dynamics. Whereas Parkin has been reported to positively regulate the expression of OPA1 through NEMO, herein we found that PARK2 overexpression did not modify the expression of OPA1. PARK2 expression reduced the levels of Bax, and it prevented stress-induced cell death only in Bak-deficient mouse embryonic fibroblast cells. Collectively, our results point out a role of the nonclassical NF-κB pathway in the regulation of mitochondrial dynamics and OPA1 expression.Mitochondria perform multiple functions that are critical to the maintenance of cellular homeostasis. Mitochondrial dysfunctions have been linked to the development of degenerative diseases and aging. Damaged mitochondria are removed by mitophagy, a process partially regulated by the PARK2-encoded E3 ubiquitin ligase (Parkin) in a PTEN-induced putative protein kinase 1 (PINK1)-dependent manner.^{1, 2, 3, 4} During mitophagy, the phosphorylation of mitofusin (Mfn) 2 by PINK1 has been suggested to induce the recruitment of Parkin to the mitochondria in cardiomyocytes.⁵ However, previous groups have shown that that Mfn 1 and 2 are dispensable for Parkin-dependent mitophagy in fibroblasts, whereas the Parkin-dependent degradation of these proteins may impair fusion of damaged mitochondria with the healthy network.^{6, 7, 8} PINK1 and Parkin thus act as a quality control machinery on the outer mitochondrial membrane (OMM) to preserve mitochondrial integrity through the ubiquitination of OMM proteins.^{9, 10} Moreover, through its E3 ubiquitin ligase activity,^{11, 12} Parkin was reported to bind to the linear ubiquitin chain assembly complex (LUBAC) and to increase the ubiquitination of NF-κB essential modulator (NEMO),¹³ a component of the classical NF-κB signaling pathway.¹⁴ Müller–Rischart et al. also proposed that Parkin positively regulates the expression of the mitochondrial guanosine triphosphatase Optic atrophy 1 protein (OPA1) through linear ubiquitination of NEMO.¹³ OPA1 is a regulator of mitochondrial inner membrane fusion and cristae remodeling.^{15, 16, 17} A defect in OPA1 expression is associated with mitochondrial network fragmentation and enhanced sensitivity of the cells to undergo apoptosis by promoting cytochrome c release from the mitochondria.^{18, 19, 20} Because NEMO-deficient mouse embryonic fibroblast (MEF) cells display a normal mitochondrial network morphology, we decided to re-examine the role of Parkin in regulating OPA1 expression through the NF-κB signaling pathway.     

Protein dynamics of a β-sheet protein

Rhodnius prolixus Nitrophorin 4 (abbreviated NP4) is an almost pure β-sheet heme protein. Its dynamics is investigated by X-ray structure determination at eight different temperatures from 122 to 304 K and by means of Mössbauer spectroscopy. A comparison of this β-sheet protein with the pure α-helical protein myoglobin (abbreviated Mbmet) is performed. The mean square displacement derived from the Mössbauer spectra increases linearly with temperature below a characteristic temperature T _c. It is about 10 K larger than that of myoglobin. Above T _c the mean square displacements increase dramatically. The Mössbauer spectra are analyzed by a two state model. The increased mean square displacements are caused by very slow motions occurring on a time scale faster than 140 ns. With respect to these motions NP4 shows the same protein specific modes as Mbmet. There is, however, a difference in the fast vibration regime. The B values found in the X-ray structures vary linearly over the entire temperature range. The mean square displacements in NP4 increase with slopes which are 60% larger than those observed for Mbmet. This indicates that nitrophorin has a larger structural distribution which makes it more flexible than myoglobin.     

Characterization of the internal dynamics and conformational space of zinc-bound amyloid β peptides by replica-exchange molecular dynamics simulations

Amyloid β (Aβ) peptides and metal ions have been associated with the pathogenesis of Alzheimer’s disease. The conformational space of Aβ fragments of different length with and without binding of metal ions has been extensively investigated by replica-exchange molecular dynamics (REMD) simulation. However, only trajectories extracted at relatively low temperatures have been used for this analysis. The capability of REMD simulations to characterize the internal dynamics of such intrinsically disordered proteins (IDPs) as Aβ has been overlooked. In this work, we use an approach recently developed by Xue and Skrynnikov (J Am Chem Soc 133:14614–14628, 2011) to calculate NMR observables, including ¹⁵N relaxation rates and ¹⁵N–¹H nuclear Overhauser enhancement (NOE), from the high-temperature trajectory of REMD simulations for zinc-bound Aβ peptides. The time axis of the trajectory was rescaled to correct for the effect of the high temperature (408 K) compared with the experimental temperature (278 K). Near-quantitative agreement between simulated values and experimental results was obtained. When the structural properties and free-energy surfaces of zinc-bound Aβ_(1–40) and Aβ_(1–42) were compared at the physiological temperature 310 K it was found that zinc-bound Aβ_(1–42) was more rigid than Aβ_(1–40) at the C terminus, and its conformational transitions were also more preferred. The self-consistent results derived from trajectories at high and low temperatures demonstrate the capability of REMD simulations to capture the internal dynamics of IDPs.     

Structural dynamics of protein backbone φ angles: extended molecular dynamics simulations versus experimental 3 J scalar couplings

³ J scalar couplings report on the conformational averaging of backbone φ angles in peptides and proteins, and therefore represent a potentially powerful tool for studying the details of both structure and dynamics in solution. We have compared an extensive experimental dataset with J-couplings predicted from unrestrained molecular dynamics simulation using enhanced sampling available from accelerated molecular dynamics or using long timescale trajectories (200 ns). The dynamic fluctuations predicted to be present along the backbone, in agreement with residual dipolar coupling analysis, are compatible with the experimental ³ J scalar couplings providing a slightly better reproduction of these experimental parameters than a high-resolution static structure.     

Solution NMR studies of Aβ monomer dynamics

Aβ is widely recognized as a key molecule in Alzheimer's disease, causing neurotoxicity through Aβ aggregates such as Aβ oligomers and fibrils. Aβ40 and Aβ42, composed of 40 and 42 residues, respectively, are the major Aβ species in human brain. Aβ42 aggregates much faster than Aβ40 but the mechanism of such difference in aggregation propensity is poorly understood. Using NMR spin relaxation, we have shown that Aβ40 and Aβ42 monomers have different dynamics in both backbone and sidechain on the ps-ns time scale. Aβ42 is more rigid in C-terminus in both backbone and sidechain while Aβ40 has more rigid methyl groups in the central hydrophobic cluster (CHC: Aβ17-21). These observations are consistent with differences in the major conformations of Aβ40 and Aβ42 monomers derived from replica exchange MD (REMD). To further demonstrate the relevance of dynamics in aggregation mechanism, a perturbation was introduced to Aβ42 in the form of M35 oxidation. After M35 side chain oxidation to sulfoxide, Aβ42 experiences Aβ40-like changes in dynamics. At the same time, M35 oxidation causes dramatic reduction in Aβ42 aggregation rate. These data have thus established an important role for protein dynamics in the mechanism of Aβ aggregation.     

Conformational dynamics of Peb4 exhibit “mother’s arms” chain model: a molecular dynamics study

Peb4 from Campylobacter jejuni is an intertwined dimeric, periplasmic holdase, which also exhibits peptidyl prolyl cis/trans isomerase (PPIase) activity. Peb4 gene deletion alters the outer membrane protein profile and impairs cellular adhesion and biofilm formation for C. jejuni. Earlier crystallographic study has proposed that the PPIase domains are flexible and might form a cradle for holding the substrate and these aspects of Peb4 were explored using sub-microsecond molecular dynamics simulations in solution environment. Our simulations have revealed that PPIase domains are highly flexible and undergo a large structural change where they move apart from each other by 8 nm starting at .5 nm. Further, this large conformational change renders Peb4 as a compact protein with crossed-over conformation, forms a central cavity, which can “cradle” the target substrate. As reported for other chaperone proteins, flexibility of linker region connecting the chaperone and PPIase domains is key to forming the “crossed-over” conformation. The conformational transition of the Peb4 protein from the X-ray structure to the crossed-over conformation follows the “mother’s arms” chain model proposed for the FkpA chaperone protein. Our results offer insights into how Peb4 and similar chaperones can use the conformational heterogeneity at their disposal to perform its much-revered biological function.     

Disease dynamics: all caused by males?

Some host individuals tend to acquire parasites at a much faster rate than do others--a consequence of heterogeneities in susceptibility and/or exposure. This is termed 'overdispersion' and, as for many other statistical phenomena, the degree of overdispersion often conforms to a 20/80 rule, where 20% of the host population is responsible for approximately 80% of the parasite transmission. But which are the hosts driving so much of the dynamics of an infectious disease? If host individuals at the tail of the frequency distribution can be identified by some common label, controlling parasitic diseases would be much easier. In two recent papers, Perkins et al. and Ferrari et al. have shown that male hosts are much more important than female hosts in the transmission of parasites.     

Do telomere dynamics link lifestyle and lifespan?

Identifying and understanding the processes that underlie the observed variation in lifespan within and among species remains one of the central areas of biological research. Questions directed at how, at what rate and why organisms grow old and die link disciplines such as evolutionary ecology to those of cell biology and gerontology. One process now thought to have a key role in ageing is the pattern of erosion of the protective ends of chromosomes, the telomeres. Here, we discuss what is currently known about the factors influencing telomere regulation, and how this relates to fundamental questions about the relationship between lifestyle and lifespan.