The validity of quasi steady-state approximations in discrete stochastic simulations

In biochemical networks, reactions often occur on disparate timescales and can be characterized as either "fast" or "slow." The quasi-steady state approximation (QSSA) utilizes timescale separation to project models of biochemical networks onto lower-dimensional slow manifolds. As a result, fast elementary reactions are not modeled explicitly, and their effect is captured by non-elementary reaction rate functions (e.g. Hill functions). The accuracy of the QSSA applied to deterministic systems depends on how well timescales are separated. Recently, it has been proposed to use the non-elementary rate functions obtained via the deterministic QSSA to define propensity functions in stochastic simulations of biochemical networks. In this approach, termed the stochastic QSSA, fast reactions that are part of non-elementary reactions are not simulated, greatly reducing computation time. However, it is unclear when the stochastic QSSA provides an accurate approximation of the original stochastic simulation. We show that, unlike the deterministic QSSA, the validity of the stochastic QSSA does not follow from timescale separation alone, but also depends on the sensitivity of the non-elementary reaction rate functions to changes in the slow species. The stochastic QSSA becomes more accurate when this sensitivity is small. Different types of QSSAs result in non-elementary functions with different sensitivities, and the total QSSA results in less sensitive functions than the standard or the pre-factor QSSA. We prove that, as a result, the stochastic QSSA becomes more accurate when non-elementary reaction functions are obtained using the total QSSA. Our work provides a novel condition for the validity of the QSSA in stochastic simulations of biochemical reaction networks with disparate timescales.Comment: 21 pages, 4 figure

Flexibility and development of mirroring mechanisms

The empirical support for the SCM is mixed. We review recent results from our own lab and others supporting a central claim of SCM that mirroring occurs at multiple levels of representation. By contrast, the model is silent as to why human infants are capable of showing imitative behaviours mediated by a mirror system. This limitation is a problem with formal models that address neither the neural correlates nor the behavioural evidence directly

Synthetic Biology and the Gut Microbiome

The gut microbiome plays a crucial role in maintaining human health. Functions performed by gastrointestinal microbes range from regulating metabolism to modulating immune and nervous system development. Scientists have attempted to exploit this importance through the development of engineered probiotics that are capable of producing and delivering small molecule therapeutics within the gut. However, existing synthetic probiotics are simplistic and fail to replicate the complexity and adaptability of native homeostatic mechanisms. In this review, the ways in which the tools and approaches of synthetic biology have been applied to improve the efficacy of therapeutic probiotics, and the ways in which they might be applied in the future is discussed. Simple devices, such as a bistable switches and integrase memory arrays, have been successfully implemented in the mammalian gut, and models for targeted delivery in this environment have also been developed. In the future, it will be necessary to introduce concepts such as logic-gating and biocontainment mechanisms into synthetic probiotics, as well as to expand the collection of relevant biosensors. Ideally, this will bring us closer to a reality in which engineered therapeutic microbes will be able to accurately diagnose and effectively respond to a variety of disease states

Transcriptional delay stabilizes bistable gene networks

Transcriptional delay can significantly impact the dynamics of gene networks. Here we examine how such delay affects bistable systems. We investigate several stochastic models of bistable gene networks and find that increasing delay dramatically increases the mean residence times near stable states. To explain this, we introduce a non-Markovian, analytically tractable reduced model. The model shows that stabilization is the consequence of an increased number of failed transitions between stable states. Each of the bistable systems that we simulate behaves in this manner

Effects of cell cycle noise on excitable gene circuits

We assess the impact of cell cycle noise on gene circuit dynamics. For bistable genetic switches and excitable circuits, we find that transitions between metastable states most likely occur just after cell division and that this concentration effect intensifies in the presence of transcriptional delay. We explain this concentration effect with a 3-states stochastic model. For genetic oscillators, we quantify the temporal correlations between daughter cells induced by cell division. Temporal correlations must be captured properly in order to accurately quantify noise sources within gene networks.Comment: 15 pages, 8 figure

Stochastic Gene Expression in Single Gene Oscillator Variants

It is infeasible to understand all dynamics in cell, but we can aim to understand the impact of design choices under our control. Here we consider a single gene oscillator as a case study to understand the influence of DNA copy number and repressor choice on the resulting dynamics. We first switch the repressor in the oscillator from the originally published lacI to treRL, a chimeric repressor with a lacI DNA binding domain that is inducible by trehalose. This slightly modified system produces faster and more regular oscillations than the original lacI oscillator. We then compare the treRL oscillator at three different DNA copy numbers. The period and amplitude of oscillations increases as the copy number is decreased. We cannot explain the change in period with differential equation models without changing delays or degradation rates. The correlation and phase coherence between daughter cells after cell division also tend to fall off faster for the lower copy oscillator variants. These results suggest that lower copy number variants of our single gene oscillator produce more synchronized oscillations

Using cellular fitness to map the structure and function of a major facilitator superfamily effluxer.

The major facilitator superfamily (MFS) effluxers are prominent mediators of antimicrobial resistance. The biochemical characterization of MFS proteins is hindered by their complex membrane environment that makes in vitro biochemical analysis challenging. Since the physicochemical properties of proteins drive the fitness of an organism, we posed the question of whether we could reverse that relationship and derive meaningful biochemical parameters for a single protein simply from fitness changes it confers under varying strengths of selection. Here, we present a physiological model that uses cellular fitness as a proxy to predict the biochemical properties of the MFS tetracycline efflux pump, TetB, and a family of single amino acid variants. We determined two lumped biochemical parameters roughly describing Km and Vmax for TetB and variants. Including in vivo protein levels into our model allowed for more specified prediction of pump parameters relating to substrate binding affinity and pumping efficiency for TetB and variants. We further demonstrated the general utility of our model by solely using fitness to assay a library of tet(B) variants and estimate their biochemical properties

Footprints and human evolution: Homeostasis in foot function?

Human, and hominin tracks, occur infrequently within the geological record as rare acts of sedimentary preservation. They have the potential, however, to reveal important information about the locomotion of our ancestors, especially when the tracks pertain to different hominin species. The number of known track sites is small and in making inter-species comparisons, one has to work with small track populations that are often from different depositional settings, thereby complicating our interpretations of them. Here we review several key track sites of palaeoanthropological significance across one of the most important evolutionary transitions (Australopithecus to Homo) which involved the development of anatomy and physiology better-suited to endurance running and walking. The sites include the oldest known hominin track site at Laetoli (3.66 Ma; Tanzania) and those at Ileret (1.5 Ma; Kenya). Tracks from both sites are compared with modern tracks made by habitually unshod individuals using a whole-foot analysis. We conclude that, contrary to some authors, foot function has remained relatively unchanged, perhaps experiencing evolutionary homeostasis, for the last 3.66 Ma. These data suggest that the evolutionary development of modern biomechanical locomotion pre-dates the earliest human tracks and also the transition from the genus Australopithecus to Homo

Modeling delay in genetic networks: From delay birth-death processes to delay stochastic differential equations

Delay is an important and ubiquitous aspect of many biochemical processes. For example, delay plays a central role in the dynamics of genetic regulatory networks as it stems from the sequential assembly of first mRNA and then protein. Genetic regulatory networks are therefore frequently modeled as stochastic birth-death processes with delay. Here we examine the relationship between delay birth-death processes and their appropriate approximating delay chemical Langevin equations. We prove that the distance between these two descriptions, as measured by expectations of functionals of the processes, converges to zero with increasing system size. Further, we prove that the delay birth-death process converges to the thermodynamic limit as system size tends to infinity. Our results hold for both fixed delay and distributed delay. Simulations demonstrate that the delay chemical Langevin approximation is accurate even at moderate system sizes. It captures dynamical features such as the spatial and temporal distributions of transition pathways in metastable systems, oscillatory behavior in negative feedback circuits, and cross-correlations between nodes in a network. Overall, these results provide a foundation for using delay stochastic differential equations to approximate the dynamics of birth-death processes with delay