Modeling and simulation of a synthetic genetic circuit that implements a multicelled behavior in a growing microcolony of E. coli

Synthetic Biology is a relatively new discipline, born at the beginning of the New Millennium, that brings the typical engineering approach (abstraction, modularity and standardization) to biotechnology. These principles aim to tame the extreme complexity of the various components and aid the construction of artificial biological systems with specific functions, usually by means of synthetic genetic circuits implemented in bacteria or simple eukaryotes like yeast. The cell becomes a programmable machine and its low-level programming language is made of strings of DNA. This work was performed in collaboration with researchers of the Department of Electrical Engineering of the University of Washington in Seattle and also with a student of the Corso di Laurea Magistrale in Ingegneria Biomedica at the University of Bologna: Marilisa Cortesi. During the collaboration I contributed to a Synthetic Biology project already started in the Klavins Laboratory. In particular, I modeled and subsequently simulated a synthetic genetic circuit that was ideated for the implementation of a multicelled behavior in a growing bacterial microcolony. In the first chapter the foundations of molecular biology are introduced: structure of the nucleic acids, transcription, translation and methods to regulate gene expression. An introduction to Synthetic Biology completes the section. In the second chapter is described the synthetic genetic circuit that was conceived to make spontaneously emerge, from an isogenic microcolony of bacteria, two different groups of cells, termed leaders and followers. The circuit exploits the intrinsic stochasticity of gene expression and intercellular communication via small molecules to break the symmetry in the phenotype of the microcolony. The four modules of the circuit (coin flipper, sender, receiver and follower) and their interactions are then illustrated. In the third chapter is derived the mathematical representation of the various components of the circuit and the several simplifying assumptions are made explicit. Transcription and translation are modeled as a single step and gene expression is function of the intracellular concentration of the various transcription factors that act on the different promoters of the circuit. A list of the various parameters and a justification for their value closes the chapter. In the fourth chapter are described the main characteristics of the gro simulation environment, developed by the Self Organizing Systems Laboratory of the University of Washington. Then, a sensitivity analysis performed to pinpoint the desirable characteristics of the various genetic components is detailed. The sensitivity analysis makes use of a cost function that is based on the fraction of cells in each one of the different possible states at the end of the simulation and the wanted outcome. Thanks to a particular kind of scatter plot, the parameters are ranked. Starting from an initial condition in which all the parameters assume their nominal value, the ranking suggest which parameter to tune in order to reach the goal. Obtaining a microcolony in which almost all the cells are in the follower state and only a few in the leader state seems to be the most difficult task. A small number of leader cells struggle to produce enough signal to turn the rest of the microcolony in the follower state. It is possible to obtain a microcolony in which the majority of cells are followers by increasing as much as possible the production of signal. Reaching the goal of a microcolony that is split in half between leaders and followers is comparatively easy. The best strategy seems to be increasing slightly the production of the enzyme. To end up with a majority of leaders, instead, it is advisable to increase the basal expression of the coin flipper module. At the end of the chapter, a possible future application of the leader election circuit, the spontaneous formation of spatial patterns in a microcolony, is modeled with the finite state machine formalism. The gro simulations provide insights into the genetic components that are needed to implement the behavior. In particular, since both the examples of pattern formation rely on a local version of Leader Election, a short-range communication system is essential. Moreover, new synthetic components that allow to reliably downregulate the growth rate in specific cells without side effects need to be developed. In the appendix are listed the gro code utilized to simulate the model of the circuit, a script in the Python programming language that was used to split the simulations on a Linux cluster and the Matlab code developed to analyze the data.

Master Equation: Biological Applications and Thermodynamic Description

It is well known that many realistic mathematical models of biological systems, such as cell growth, cellular development and differentiation, gene expression, gene regulatory networks, enzyme cascades, synaptic plasticity, aging and population growth need to include stochasticity. These systems are not isolated, but rather subject to intrinsic and extrinsic fluctuations, which leads to a quasi equilibrium state (homeostasis). The natural framework is provided by Markov processes and the Master equation (ME) describes the temporal evolution of the probability of each state, specified by the number of units of each species. The ME is a relevant tool for modeling realistic biological systems and allow also to explore the behavior of open systems. These systems may exhibit not only the classical thermodynamic equilibrium states but also the nonequilibrium steady states (NESS). This thesis deals with biological problems that can be treat with the Master equation and also with its thermodynamic consequences. It is organized into six chapters with four new scientific works, which are grouped in two parts: (1) Biological applications of the Master equation: deals with the stochastic properties of a toggle switch, involving a protein compound and a miRNA cluster, known to control the eukaryotic cell cycle and possibly involved in oncogenesis and with the propose of a one parameter family of master equations for the evolution of a population having the logistic equation as mean field limit. (2) Nonequilibrium thermodynamics in terms of the Master equation: where we study the dynamical role of chemical fluxes that characterize the NESS of a chemical network and we propose a one parameter parametrization of BCM learning, that was originally proposed to describe plasticity processes, to study the differences between systems in DB and NESS.

Metacommunity Dynamics Of Benthic Macroinvertebrates In A Large River

Metacommunity ecology focuses on the interaction between local communities and is inherently linked to dispersal as a result. Within this framework, communities are structured by a combination of in-site responses to the immediate environment (species sorting), stochasticity (patch dynamics), and connections to other communities via distance between communities and dispersal (neutrality), and source-sink dynamics (mass effects; see Chapter 1 for a detailed description of metacommunity theory, the study site, and macroinvertebrate communities found). In Chapter 2 I describe spatial scale of study and dispersal ability as both have the ability to influence the degree to which communities interact. However, little is known about how these factors influence the importance of all metacommunity dynamics. I compared dispersal mode of immature aquatic insects and dispersal ability of winged adults across multiple spatial scales in a large river. The strongest drivers of river communities were patch dynamics, followed by species sorting, then neutrality. Active dispersers during aquatic lifestages on average exhibited lower patch dynamics, higher species sorting, and significant mass effects compared to passive dispersers. Active and strong dispersers also had a scale-independent influence of neutrality, while neutrality was stronger at broader spatial scale for passive and weak dispersers. These results indicate as dispersal ability increases patch dynamics decreases, species sorting increases, and neutrality should decrease. The perceived influence of neutrality may also be dependent on spatial scale and dispersal ability. In Chapter 3 I describe how river benthic macroinvertebrate communities may influence tributary invertebrate communities via adult flight and tributaries may influence mainstem communities via immature drift. This relationship may also depend on relative mainstem and tributary size, as well as abiotic tributary influence on mainstem habitat. To investigate the interaction between a larger river and tributary I sampled mainstem benthic invertebrate communities and quantified habitat of a 7th order river (West Branch Susquehanna River) above and below a 5th order tributary confluence, as well as 0.95-3.2 km upstream in the tributary. Non-metric multidimensional scaling showed similar patterns of clustering between sampling locations for both habitat characteristics and invertebrate communities. In addition, mainstem river communities and habitat directly downstream of the tributary confluence cluster tightly together, intermediate between tributary and mid-channel river samples. In Bray-Curtis dissimilarity comparisons between tributary and mainstem river communities the furthest upstream tributary communities were least similar to river communities. Middle tributary samples were also closest by Euclidean distance to the upstream mainstem riffle and exhibited higher similarity to mid-channel samples than the furthest downstream tributary communities. My results indicate river and tributary benthic invertebrate communities may interact and likely result in direct and indirect mass effects of a tributary on the downstream mainstem community by invertebrate drift and habitat restructuring via material delivery from the tributary. I also showed likely direct effects of adult dispersal from the river and oviposition in proximal tributary locations where Euclidian, rather than river, distance may be more important in determining river-tributary interactions.

Sampling-Design Effects on Properties of Species-Area Relationships - A Case Study from Estonian Dry Grassland Communities

Despite widespread use of species-area relationships (SARs), dispute remains over the most representative SAR model. Using data of small-scale SARs of Estonian dry grassland communities, we address three questions: (1) Which model describes these SARs best when known artifacts are excluded? (2) How do deviating sampling procedures (marginal instead of central position of the smaller plots in relation to the largest plot; single values instead of average values; randomly located subplots instead of nested subplots) influence the properties of the SARs? (3) Are those effects likely to bias the selection of the best model? Our general dataset consisted of 16 series of nested-plots (1 cm(2)-100 m(2), any-part system), each of which comprised five series of subplots located in the four corners and the centre of the 100-m(2) plot. Data for the three pairs of compared sampling designs were generated from this dataset by subsampling. Five function types (power, quadratic power, logarithmic, Michaelis-Menten, Lomolino) were fitted with non-linear regression. In some of the communities, we found extremely high species densities (including bryophytes and lichens), namely up to eight species in 1 cm(2) and up to 140 species in 100 m(2), which appear to be the highest documented values on these scales. For SARs constructed from nested-plot average-value data, the regular power function generally was the best model, closely followed by the quadratic power function, while the logarithmic and Michaelis-Menten functions performed poorly throughout. However, the relative fit of the latter two models increased significantly relative to the respective best model when the single-value or random-sampling method was applied, however, the power function normally remained far superior. These results confirm the hypothesis that both single-value and random-sampling approaches cause artifacts by increasing stochasticity in the data, which can lead to the selection of inappropriate models.

Learning flexible sensori-motor mappings in a complex network

Given the complex structure of the brain, how can synaptic plasticity explain the learning and forgetting of associations when these are continuously changing? We address this question by studying different reinforcement learning rules in a multilayer network in order to reproduce monkey behavior in a visuomotor association task. Our model can only reproduce the learning performance of the monkey if the synaptic modifications depend on the pre- and postsynaptic activity, and if the intrinsic level of stochasticity is low. This favored learning rule is based on reward modulated Hebbian synaptic plasticity and shows the interesting feature that the learning performance does not substantially degrade when adding layers to the network, even for a complex problem.

Plurality of tree species responses to drought perturbation in Bornean tropical rain forest

Drought perturbation driven by the El Niño Southern Oscillation (ENSO) is a principal stochastic variable determining the dynamics of lowland rain forest in S.E. Asia. Mortality, recruitment and stem growth rates at Danum in Sabah (Malaysian Borneo) were recorded in two 4-ha plots (trees ≥ 10 cm gbh) for two periods, 1986–1996 and 1996–2001. Mortality and growth were also recorded in a sample of subplots for small trees (10 to <50 cm gbh) in two sub-periods, 1996–1999 and 1999–2001. Dynamics variables were employed to build indices of drought response for each of the 34 most abundant plot-level species (22 at the subplot level), these being interval-weighted percentage changes between periods and sub-periods. A significant yet complex effect of the strong 1997/1998 drought at the forest community level was shown by randomization procedures followed by multiple hypothesis testing. Despite a general resistance of the forest to drought, large and significant differences in short-term responses were apparent for several species. Using a diagrammatic form of stability analysis, different species showed immediate or lagged effects, high or low degrees of resilience or even oscillatory dynamics. In the context of the local topographic gradient, species’ responses define the newly termed perturbation response niche. The largest responses, particularly for recruitment and growth, were among the small trees, many of which are members of understorey taxa. The results bring with them a novel approach to understanding community dynamics: the kaleidoscopic complexity of idiosyncratic responses to stochastic perturbations suggests that plurality, rather than neutrality, of responses may be essential to understanding these tropical forests. The basis to the various responses lies with the mechanisms of tree-soil water relations which are physiologically predictable: the timing and intensity of the next drought, however, is not. To date, environmental stochasticity has been insufficiently incorporated into models of tropical forest dynamics, a step that might considerably improve the reality of theories about these globally important ecosystems.

Relaxation of species-specific neighborhood effects in Bornean rain forest under climatic perturbation

Evidence of negative conspecific density dependence (NDD) operating on seedling survival and sapling recruitment has accumulated recently. In contrast, evidence of NDD operating on growth of trees has been circumstantial at best. Whether or not local NDD at the level of individual trees leads to NDD at the level of the community is still an open question. Moreover, whether and how perturbations interfere with these processes have rarely been investigated. We applied neighborhood models to permanent plot data from a Bornean dipterocarp forest censused over two 10-11 year periods. Although the first period was only lightly perturbed, a moderately strong El Nino event causing severe drought occurred in the first half of the second period. Such events are an important component of the environmental stochasticity affecting the region. We show that local NDD on growth of small-to-medium-sized trees may indeed translate to NDD at the level of the community. This interpretation is based on increasingly negative effects of bigger conspecific neighbors on absolute growth rates of individual trees with increasing basal area across the 18 most abundant overstory species in the first period. However, this relationship was much weaker in the second period. We interpreted this relaxation of local and community-level NDD as a consequence of increased light levels at the forest floor due to temporary leaf and twig loss of large trees in response to the drought event. Mitigation of NDD under climatic perturbation acts to decrease species richness, especially in forest overstory and therefore has an important role in determining species relative abundances at the site.

Hybrid stochastic simulations of intracellular reaction-diffusion systems.

With the observation that stochasticity is important in biological systems, chemical kinetics have begun to receive wider interest. While the use of Monte Carlo discrete event simulations most accurately capture the variability of molecular species, they become computationally costly for complex reaction-diffusion systems with large populations of molecules. On the other hand, continuous time models are computationally efficient but they fail to capture any variability in the molecular species. In this study a hybrid stochastic approach is introduced for simulating reaction-diffusion systems. We developed an adaptive partitioning strategy in which processes with high frequency are simulated with deterministic rate-based equations, and those with low frequency using the exact stochastic algorithm of Gillespie. Therefore the stochastic behavior of cellular pathways is preserved while being able to apply it to large populations of molecules. We describe our method and demonstrate its accuracy and efficiency compared with the Gillespie algorithm for two different systems. First, a model of intracellular viral kinetics with two steady states and second, a compartmental model of the postsynaptic spine head for studying the dynamics of Ca+2 and NMDA receptors.

Short communication: Immunoglobulin variation in quarter-milked colostrum

Whereas whole first-milked colostrum IgG1 variation is documented, the IgG1 difference between the quarter mammary glands of dairy animals is unknown. First colostrum was quarter-collected from healthy udders of 8 multiparous dairy cows, all within 3h of parturition. Weight of colostrum produced by individual quarters was determined and a sample of each was frozen for subsequent analysis. Immunoglobulin G1 concentration (mg/mL) was measured by ELISA and total mass (g) was calculated. Standard addition method was used to overcome colostrum matrix effects and validate the standard ELISA measures. Analysis of the data showed that cow and quarter (cow) were significantly different in both concentration and total mass per quarter. Analysis of the mean IgG1 concentration of the front and rear quarters showed that this was not different, but the large variation in individual quarters confounds the analysis. This quarter difference finding indicates that each mammary gland develops a different capacity to accumulate precolostrum IgG1, whereas the circulating hormone concentrations that induce colostrogenesis reach the 4 glands similarly. This finding also shows that the variation in quarter colostrum production is a contributor to the vast variation in first milking colostrum IgG1 content. Finally, the data suggests other factors, such as locally acting autocrine or paracrine, epigenetic, or stochasticity, in gene regulation mechanisms may impinge on colostrogenesis capacity.

Revealing Assembly of a Pore-Forming Complex Using Single-Cell Kinetic Analysis and Modeling

Many biological processes depend on the sequential assembly of protein complexes. However, studying the kinetics of such processes by direct methods is often not feasible. As an important class of such protein complexes, pore-forming toxins start their journey as soluble monomeric proteins, and oligomerize into transmembrane complexes to eventually form pores in the target cell membrane. Here, we monitored pore formation kinetics for the well-characterized bacterial pore-forming toxin aerolysin in single cells in real time to determine the lag times leading to the formation of the first functional pores per cell. Probabilistic modeling of these lag times revealed that one slow and seven equally fast rate-limiting reactions best explain the overall pore formation kinetics. The model predicted that monomer activation is the rate-limiting step for the entire pore formation process. We hypothesized that this could be through release of a propeptide and indeed found that peptide removal abolished these steps. This study illustrates how stochasticity in the kinetics of a complex process can be exploited to identify rate-limiting mechanisms underlying multistep biomolecular assembly pathways.

Spatial and temporal aspects of synaptic plasticity

The notion that changes in synaptic efficacy underlie learning and memory processes is now widely accepted even if definitive proof of the synaptic plasticity and memory hypothesis is still lacking. When learning occurs, patterns of neural activity representing the occurrence of events cause changes in the strength of synaptic connections within the brain. Reactivation of these altered connections constitutes the experience of memory for these events and for other events with which they may be associated. These statements summarize a long-standing theory of memory formation that we refer to as the synaptic plasticity and memory hypothesis. Since activity-dependent synaptic plasticity is induced at appropriate synapses during memory formation, and is both necessary and sufficient for the information storage, we can speculate that a methodological study of the synapse will help us understand the mechanism of learning. Random events underlie a wide range of biological processes as diverse as genetic drift and molecular diffusion, regulation of gene expression and neural network function. Additionally spatial variability may be important especially in systems with nonlinear behavior. Since synapse is a complex biological system we expect that stochasticity as well as spatial gradients of different enzymes may be significant for induction of plasticity. ^ In that study we address the question "how important spatial and temporal aspects of synaptic plasticity may be". We developed methods to justify our basic assumptions and examined the main sources of variability of calcium dynamics. Among them, a physiological method to estimate the number of postsynaptic receptors as well as a hybrid algorithm for simulating postsynaptic calcium dynamics. Additionally we studied how synaptic geometry may enhance any possible spatial gradient of calcium dynamics and how that spatial variability affect plasticity curves. Finally, we explored the potential of structural synaptic plasticity to provide a metaplasticity mechanism specific for the synapse. ^

Metapopulation extinction caused by mutation accumulation

Theory suggests that the risk of extinction by mutation accumulation can be comparable to that by environmental stochasticity for an isolated population smaller than a few thousand individuals. Here we show that metapopulation structure, habitat loss or fragmentation, and environmental stochasticity can be expected to greatly accelerate the accumulation of mildly deleterious mutations, lowering the genetic effective size to such a degree that even large metapopulations may be at risk of extinction. Because of mutation accumulation, viable metapopulations may need to be far larger and better connected than would be required under just stochastic demography.

Estimating risks in declining populations with poor data

Census data on endangered species are often sparse, error-ridden, and confined to only a segment of the population. Estimating trends and extinction risks using this type of data presents numerous difficulties. In particular, the estimate of the variation in year-to-year transitions in population size (the “process error” caused by stochasticity in survivorship and fecundities) is confounded by the addition of high sampling error variation. In addition, the year-to-year variability in the segment of the population that is sampled may be quite different from the population variability that one is trying to estimate. The combined effect of severe sampling error and age- or stage-specific counts leads to severe biases in estimates of population-level parameters. I present an estimation method that circumvents the problem of age- or stage-specific counts and is markedly robust to severe sampling error. This method allows the estimation of environmental variation and population trends for extinction-risk analyses using corrupted census counts—a common type of data for endangered species that has hitherto been relatively unusable for these analyses.

Evolution of genome–phenome diversity under environmental stress

The genomic era revolutionized evolutionary biology. The enigma of genotypic-phenotypic diversity and biodiversity evolution of genes, genomes, phenomes, and biomes, reviewed here, was central in the research program of the Institute of Evolution, University of Haifa, since 1975. We explored the following questions. (i) How much of the genomic and phenomic diversity in nature is adaptive and processed by natural selection? (ii) What is the origin and evolution of adaptation and speciation processes under spatiotemporal variables and stressful macrogeographic and microgeographic environments? We advanced ecological genetics into ecological genomics and analyzed globally ecological, demographic, and life history variables in 1,200 diverse species across life, thousands of populations, and tens of thousands of individuals tested mostly for allozyme and partly for DNA diversity. Likewise, we tested thermal, chemical, climatic, and biotic stresses in several model organisms. Recently, we introduced genetic maps and quantitative trait loci to elucidate the genetic basis of adaptation and speciation. The genome–phenome holistic model was deciphered by the global regressive, progressive, and convergent evolution of subterranean mammals. Our results indicate abundant genotypic and phenotypic diversity in nature. The organization and evolution of molecular and organismal diversity in nature at global, regional, and local scales are nonrandom and structured; display regularities across life; and are positively correlated with, and partly predictable by, abiotic and biotic environmental heterogeneity and stress. Biodiversity evolution, even in small isolated populations, is primarily driven by natural selection, including diversifying, balancing, cyclical, and purifying selective regimes, interacting with, but ultimately overriding, the effects of mutation, migration, and stochasticity.

Operations and Planning in Sustainable Power Systems

Thesis (Ph.D.)--University of Washington, 2016-06