Hierarchical Modular Structure of the Drosophila Connectome.

The structure of neural circuitry plays a crucial role in brain function. Previous studies of brain organization generally had to trade off between coarse descriptions at a large scale and fine descriptions on a small scale. Researchers have now reconstructed tens to hundreds of thousands of neurons at synaptic resolution, enabling investigations into the interplay between global, modular organization, and cell type-specific wiring. Analyzing data of this scale, however, presents unique challenges. To address this problem, we applied novel community detection methods to analyze the synapse-level reconstruction of an adult female Drosophila melanogaster brain containing >20,000 neurons and 10 million synapses. Using a machine-learning algorithm, we find the most densely connected communities of neurons by maximizing a generalized modularity density measure. We resolve the community structure at a range of scales, from large (on the order of thousands of neurons) to small (on the order of tens of neurons). We find that the network is organized hierarchically, and larger-scale communities are composed of smaller-scale structures. Our methods identify well-known features of the fly brain, including its sensory pathways. Moreover, focusing on specific brain regions, we are able to identify subnetworks with distinct connectivity types. For example, manual efforts have identified layered structures in the fan-shaped body. Our methods not only automatically recover this layered structure, but also resolve finer connectivity patterns to downstream and upstream areas. We also find a novel modular organization of the superior neuropil, with distinct clusters of upstream and downstream brain regions dividing the neuropil into several pathways. These methods show that the fine-scale, local network reconstruction made possible by modern experimental methods are sufficiently detailed to identify the organization of the brain across scales, and enable novel predictions about the structure and function of its parts.Significance Statement The Hemibrain is a partial connectome of an adult female Drosophila melanogaster brain containing >20,000 neurons and 10 million synapses. Analyzing the structure of a network of this size requires novel and efficient computational tools. We applied a new community detection method to automatically uncover the modular structure in the Hemibrain dataset by maximizing a generalized modularity measure. This allowed us to resolve the community structure of the fly hemibrain at a range of spatial scales revealing a hierarchical organization of the network, where larger-scale modules are composed of smaller-scale structures. The method also allowed us to identify subnetworks with distinct cell and connectivity structures, such as the layered structures in the fan-shaped body, and the modular organization of the superior neuropil. Thus, network analysis methods can be adopted to the connectomes being reconstructed using modern experimental methods to reveal the organization of the brain across scales. This supports the view that such connectomes will allow us to uncover the organizational structure of the brain, which can ultimately lead to a better understanding of its function.

Inferring delays in partially observed gene regulation processes.

MOTIVATION: Cell function is regulated by gene regulatory networks (GRNs) defined by protein-mediated interaction between constituent genes. Despite advances in experimental techniques, we can still measure only a fraction of the processes that govern GRN dynamics. To infer the properties of GRNs using partial observation, unobserved sequential processes can be replaced with distributed time delays, yielding non-Markovian models. Inference methods based on the resulting model suffer from the curse of dimensionality. RESULTS: We develop a simulation-based Bayesian MCMC method employing an approximate likelihood for the efficient and accurate inference of GRN parameters when only some of their products are observed. We illustrate our approach using a two-step activation model: an activation signal leads to the accumulation of an unobserved regulatory protein, which triggers the expression of observed fluorescent proteins. With prior information about observed fluorescent protein synthesis, our method successfully infers the dynamics of the unobserved regulatory protein. We can estimate the delay and kinetic parameters characterizing target regulation including transcription, translation, and target searching of an unobserved protein from experimental measurements of the products of its target gene. Our method is scalable and can be used to analyze non-Markovian models with hidden components. AVAILABILITY AND IMPLEMENTATION: Our code is implemented in R and is freely available with a simple example data at https://github.com/Mathbiomed/SimMCMC.

Signaling in microbial communities with open boundaries.

Microbial communities such as swarms or biofilms often form at the interfaces of solid substrates and open fluid flows. At the same time, in laboratory environments these communities are commonly studied using microfluidic devices with media flows and open boundaries. Extracellular signaling within these communities is therefore subject to different constraints than signaling within classic, closed-boundary systems such as developing embryos or tissues, yet is understudied by comparison. Here, we use mathematical modeling to show how advective-diffusive boundary flows and population geometry impact cell-cell signaling in monolayer microbial communities. We reveal conditions where the intercellular signaling lengthscale depends solely on the population geometry and not on diffusion or degradation, as commonly expected. We further demonstrate that diffusive coupling with the boundary flow can produce signal gradients within an isogenic population, even when there is no flow within the population. We use our theory to provide new insights into the signaling mechanisms of published experimental results, and we make several experimentally verifiable predictions. Our research highlights the importance of carefully evaluating boundary dynamics and environmental geometry when modeling microbial cell-cell signaling and informs the study of cell behaviors in both natural and synthetic systems.

Suboptimal human inference can invert the bias-variance trade-off for decisions with asymmetric evidence.

Solutions to challenging inference problems are often subject to a fundamental trade-off between: 1) bias (being systematically wrong) that is minimized with complex inference strategies, and 2) variance (being oversensitive to uncertain observations) that is minimized with simple inference strategies. However, this trade-off is based on the assumption that the strategies being considered are optimal for their given complexity and thus has unclear relevance to forms of inference based on suboptimal strategies. We examined inference problems applied to rare, asymmetrically available evidence, which a large population of human subjects solved using a diverse set of strategies that varied in form and complexity. In general, subjects using more complex strategies tended to have lower bias and variance, but with a dependence on the form of strategy that reflected an inversion of the classic bias-variance trade-off: subjects who used more complex, but imperfect, Bayesian-like strategies tended to have lower variance but higher bias because of incorrect tuning to latent task features, whereas subjects who used simpler heuristic strategies tended to have higher variance because they operated more directly on the observed samples but lower, near-normative bias. Our results help define new principles that govern individual differences in behavior that depends on rare-event inference and, more generally, about the information-processing trade-offs that can be sensitive to not just the complexity, but also the optimality, of the inference process.

Hierarchical Bayesian models of transcriptional and translational regulation processes with delays.

MOTIVATION: Simultaneous recordings of gene network dynamics across large populations have revealed that cell characteristics vary considerably even in clonal lines. Inferring the variability of parameters that determine gene dynamics is key to understanding cellular behavior. However, this is complicated by the fact that the outcomes and effects of many reactions are not observable directly. Unobserved reactions can be replaced with time delays to reduce model dimensionality and simplify inference. However, the resulting models are non-Markovian, and require the development of new inference techniques. RESULTS: We propose a non-Markovian, hierarchical Bayesian inference framework for quantifying the variability of cellular processes within and across cells in a population. We illustrate our approach using a delayed birth-death process. In general, a distributed delay model, rather than a popular fixed delay model, is needed for inference, even if only mean reaction delays are of interest. Using in silico and experimental data we show that the proposed hierarchical framework is robust and leads to improved estimates compared to its non-hierarchical counterpart. We apply our method to data obtained using time-lapse microscopy and infer the parameters that describe the dynamics of protein production at the single cell and population level. The mean delays in protein production are larger than previously reported, have a coefficient of variation of around 0.2 across the population, and are not strongly correlated with protein production or growth rates. AVAILABILITY AND IMPLEMENTATION: Accompanying code in Python is available at https://github.com/mvcortez/Bayesian-Inference. CONTACT: kresimir.josic@gmail.com or jaekkim@kaist.ac.kr or cbskust@korea.ac.kr. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Balanced networks under spike-time dependent plasticity.

The dynamics of local cortical networks are irregular, but correlated. Dynamic excitatory-inhibitory balance is a plausible mechanism that generates such irregular activity, but it remains unclear how balance is achieved and maintained in plastic neural networks. In particular, it is not fully understood how plasticity induced changes in the network affect balance, and in turn, how correlated, balanced activity impacts learning. How do the dynamics of balanced networks change under different plasticity rules? How does correlated spiking activity in recurrent networks change the evolution of weights, their eventual magnitude, and structure across the network? To address these questions, we develop a theory of spike-timing dependent plasticity in balanced networks. We show that balance can be attained and maintained under plasticity-induced weight changes. We find that correlations in the input mildly affect the evolution of synaptic weights. Under certain plasticity rules, we find an emergence of correlations between firing rates and synaptic weights. Under these rules, synaptic weights converge to a stable manifold in weight space with their final configuration dependent on the initial state of the network. Lastly, we show that our framework can also describe the dynamics of plastic balanced networks when subsets of neurons receive targeted optogenetic input.

Emergent spatiotemporal population dynamics with cell-length control of synthetic microbial consortia.

The increased complexity of synthetic microbial biocircuits highlights the need for distributed cell functionality due to concomitant increases in metabolic and regulatory burdens imposed on single-strain topologies. Distributed systems, however, introduce additional challenges since consortium composition and spatiotemporal dynamics of constituent strains must be robustly controlled to achieve desired circuit behaviors. Here, we address these challenges with a modeling-based investigation of emergent spatiotemporal population dynamics using cell-length control in monolayer, two-strain bacterial consortia. We demonstrate that with dynamic control of a strain's division length, nematic cell alignment in close-packed monolayers can be destabilized. We find that this destabilization confers an emergent, competitive advantage to smaller-length strains-but by mechanisms that differ depending on the spatial patterns of the population. We used complementary modeling approaches to elucidate underlying mechanisms: an agent-based model to simulate detailed mechanical and signaling interactions between the competing strains, and a reductive, stochastic lattice model to represent cell-cell interactions with a single rotational parameter. Our modeling suggests that spatial strain-fraction oscillations can be generated when cell-length control is coupled to quorum-sensing signaling in negative feedback topologies. Our research employs novel methods of population control and points the way to programming strain fraction dynamics in consortial synthetic biology.

Bayesian inference of distributed time delay in transcriptional and translational regulation.

MOTIVATION: Advances in experimental and imaging techniques have allowed for unprecedented insights into the dynamical processes within individual cells. However, many facets of intracellular dynamics remain hidden, or can be measured only indirectly. This makes it challenging to reconstruct the regulatory networks that govern the biochemical processes underlying various cell functions. Current estimation techniques for inferring reaction rates frequently rely on marginalization over unobserved processes and states. Even in simple systems this approach can be computationally challenging, and can lead to large uncertainties and lack of robustness in parameter estimates. Therefore we will require alternative approaches to efficiently uncover the interactions in complex biochemical networks. RESULTS: We propose a Bayesian inference framework based on replacing uninteresting or unobserved reactions with time delays. Although the resulting models are non-Markovian, recent results on stochastic systems with random delays allow us to rigorously obtain expressions for the likelihoods of model parameters. In turn, this allows us to extend MCMC methods to efficiently estimate reaction rates, and delay distribution parameters, from single-cell assays. We illustrate the advantages, and potential pitfalls, of the approach using a birth-death model with both synthetic and experimental data, and show that we can robustly infer model parameters using a relatively small number of measurements. We demonstrate how to do so even when only the relative molecule count within the cell is measured, as in the case of fluorescence microscopy. AVAILABILITY AND IMPLEMENTATION: Accompanying code in R is available at https://github.com/cbskust/DDE_BD. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Long-range temporal coordination of gene expression in synthetic microbial consortia.

Synthetic microbial consortia have an advantage over isogenic synthetic microbes because they can apportion biochemical and regulatory tasks among the strains. However, it is difficult to coordinate gene expression in spatially extended consortia because the range of signaling molecules is limited by diffusion. Here, we show that spatio-temporal coordination of gene expression can be achieved even when the spatial extent of the consortium is much greater than the diffusion distance of the signaling molecules. To do this, we examined the dynamics of a two-strain synthetic microbial consortium that generates coherent oscillations in small colonies. In large colonies, we find that temporally coordinated oscillations across the population depend on the presence of an intrinsic positive feedback loop that amplifies and propagates intercellular signals. These results demonstrate that synthetic multicellular systems can be engineered to exhibit coordinated gene expression using only transient, short-range coupling among constituent cells.

Heterogeneity Improves Speed and Accuracy in Social Networks.

How does temporally structured private and social information shape collective decisions? To address this question we consider a network of rational agents who independently accumulate private evidence that triggers a decision upon reaching a threshold. When seen by the whole network, the first agent's choice initiates a wave of new decisions; later decisions have less impact. In heterogeneous networks, first decisions are made quickly by impulsive individuals who need little evidence to make a choice but, even when wrong, can reveal the correct options to nearly everyone else. We conclude that groups comprised of diverse individuals can make more efficient decisions than homogenous ones.

A hierarchical model of perceptual multistability involving interocular grouping.

Ambiguous visual images can generate dynamic and stochastic switches in perceptual interpretation known as perceptual rivalry. Such dynamics have primarily been studied in the context of rivalry between two percepts, but there is growing interest in the neural mechanisms that drive rivalry between more than two percepts. In recent experiments, we showed that split images presented to each eye lead to subjects perceiving four stochastically alternating percepts (Jacot-Guillarmod et al. Vision research, 133, 37-46, 2017): two single eye images and two interocularly grouped images. Here we propose a hierarchical neural network model that exhibits dynamics consistent with our experimental observations. The model consists of two levels, with the first representing monocular activity, and the second representing activity in higher visual areas. The model produces stochastically switching solutions, whose dependence on task parameters is consistent with four generalized Levelt Propositions, and with experiments. Moreover, dynamics restricted to invariant subspaces of the model demonstrate simpler forms of bistable rivalry. Thus, our hierarchical model generalizes past, validated models of binocular rivalry. This neuromechanistic model also allows us to probe the roles of interactions between populations at the network level. Generalized Levelt's Propositions hold as long as feedback from the higher to lower visual areas is weak, and the adaptation and mutual inhibition at the higher level is not too strong. Our results suggest constraints on the architecture of the visual system and show that complex visual stimuli can be used in perceptual rivalry experiments to develop more detailed mechanistic models of perceptual processing.

Bayesian Evidence Accumulation on Social Networks.

To make decisions we are guided by the evidence we collect and the opinions of friends and neighbors. How do we combine our private beliefs with information we obtain from our social network? To understand the strategies humans use to do so, it is useful to compare them to observers that optimally integrate all evidence. Here we derive network models of rational (Bayes optimal) agents who accumulate private measurements and observe the decisions of their neighbors to make an irreversible choice between two options. The resulting information exchange dynamics has interesting properties: When decision thresholds are asymmetric, the absence of a decision can be increasingly informative over time. In a recurrent network of two agents, the absence of a decision can lead to a sequence of belief updates akin to those in the literature on common knowledge. On the other hand, in larger networks a single decision can trigger a cascade of agreements and disagreements that depend on the private information agents have gathered. Our approach provides a bridge between social decision making models in the economics literature, which largely ignore the temporal dynamics of decisions, and the single-observer evidence accumulator models used widely in neuroscience and psychology.

Analyzing dynamic decision-making models using Chapman-Kolmogorov equations.

Decision-making in dynamic environments typically requires adaptive evidence accumulation that weights new evidence more heavily than old observations. Recent experimental studies of dynamic decision tasks require subjects to make decisions for which the correct choice switches stochastically throughout a single trial. In such cases, an ideal observer's belief is described by an evolution equation that is doubly stochastic, reflecting stochasticity in the both observations and environmental changes. In these contexts, we show that the probability density of the belief can be represented using differential Chapman-Kolmogorov equations, allowing efficient computation of ensemble statistics. This allows us to reliably compare normative models to near-normative approximations using, as model performance metrics, decision response accuracy and Kullback-Leibler divergence of the belief distributions. Such belief distributions could be obtained empirically from subjects by asking them to report their decision confidence. We also study how response accuracy is affected by additional internal noise, showing optimality requires longer integration timescales as more noise is added. Lastly, we demonstrate that our method can be applied to tasks in which evidence arrives in a discrete, pulsatile fashion, rather than continuously.

Linking structure and activity in nonlinear spiking networks.

Recent experimental advances are producing an avalanche of data on both neural connectivity and neural activity. To take full advantage of these two emerging datasets we need a framework that links them, revealing how collective neural activity arises from the structure of neural connectivity and intrinsic neural dynamics. This problem of structure-driven activity has drawn major interest in computational neuroscience. Existing methods for relating activity and architecture in spiking networks rely on linearizing activity around a central operating point and thus fail to capture the nonlinear responses of individual neurons that are the hallmark of neural information processing. Here, we overcome this limitation and present a new relationship between connectivity and activity in networks of nonlinear spiking neurons by developing a diagrammatic fluctuation expansion based on statistical field theory. We explicitly show how recurrent network structure produces pairwise and higher-order correlated activity, and how nonlinearities impact the networks' spiking activity. Our findings open new avenues to investigating how single-neuron nonlinearities-including those of different cell types-combine with connectivity to shape population activity and function.

Modeling mechanical interactions in growing populations of rod-shaped bacteria.

Advances in synthetic biology allow us to engineer bacterial collectives with pre-specified characteristics. However, the behavior of these collectives is difficult to understand, as cellular growth and division as well as extra-cellular fluid flow lead to complex, changing arrangements of cells within the population. To rationally engineer and control the behavior of cell collectives we need theoretical and computational tools to understand their emergent spatiotemporal dynamics. Here, we present an agent-based model that allows growing cells to detect and respond to mechanical interactions. Crucially, our model couples the dynamics of cell growth to the cell's environment: Mechanical constraints can affect cellular growth rate and a cell may alter its behavior in response to these constraints. This coupling links the mechanical forces that influence cell growth and emergent behaviors in cell assemblies. We illustrate our approach by showing how mechanical interactions can impact the dynamics of bacterial collectives growing in microfluidic traps.

Evidence Accumulation and Change Rate Inference in Dynamic Environments.

In a constantly changing world, animals must account for environmental volatility when making decisions. To appropriately discount older, irrelevant information, they need to learn the rate at which the environment changes. We develop an ideal observer model capable of inferring the present state of the environment along with its rate of change. Key to this computation is an update of the posterior probability of all possible change point counts. This computation can be challenging, as the number of possibilities grows rapidly with time. However, we show how the computations can be simplified in the continuum limit by a moment closure approximation. The resulting low-dimensional system can be used to infer the environmental state and change rate with accuracy comparable to the ideal observer. The approximate computations can be performed by a neural network model via a rate-correlation-based plasticity rule. We thus show how optimal observers accumulate evidence in changing environments and map this computation to reduced models that perform inference using plausible neural mechanisms.

Engineered temperature compensation in a synthetic genetic clock.

Synthetic biology promises to revolutionize biotechnology by providing the means to reengineer and reprogram cellular regulatory mechanisms. However, synthetic gene circuits are often unreliable, as changes to environmental conditions can fundamentally alter a circuit's behavior. One way to improve robustness is to use intrinsic properties of transcription factors within the circuit to buffer against intra- and extracellular variability. Here, we describe the design and construction of a synthetic gene oscillator in Escherichia coli that maintains a constant period over a range of temperatures. We started with a previously described synthetic dual-feedback oscillator with a temperature-dependent period. Computational modeling predicted and subsequent experiments confirmed that a single amino acid mutation to the core transcriptional repressor of the circuit results in temperature compensation. Specifically, we used a temperature-sensitive lactose repressor mutant that loses the ability to repress its target promoter at high temperatures. In the oscillator, this thermoinduction of the repressor leads to an increase in period at high temperatures that compensates for the decrease in period due to Arrhenius scaling of the reaction rates. The result is a transcriptional oscillator with a nearly constant period of 48 min for temperatures ranging from 30 °C to 41 °C. In contrast, in the absence of the mutation the period of the oscillator drops from 60 to 30 min over the same temperature range. This work demonstrates that synthetic gene circuits can be engineered to be robust to extracellular conditions through protein-level modifications.

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 three-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.

Sources of Variability in a Synthetic Gene Oscillator.

Synthetic gene oscillators are small, engineered genetic circuits that produce periodic variations in target protein expression. Like other gene circuits, synthetic gene oscillators are noisy and exhibit fluctuations in amplitude and period. Understanding the origins of such variability is key to building predictive models that can guide the rational design of synthetic circuits. Here, we developed a method for determining the impact of different sources of noise in genetic oscillators by measuring the variability in oscillation amplitude and correlations between sister cells. We first used a combination of microfluidic devices and time-lapse fluorescence microscopy to track oscillations in cell lineages across many generations. We found that oscillation amplitude exhibited high cell-to-cell variability, while sister cells remained strongly correlated for many minutes after cell division. To understand how such variability arises, we constructed a computational model that identified the impact of various noise sources across the lineage of an initial cell. When each source of noise was appropriately tuned the model reproduced the experimentally observed amplitude variability and correlations, and accurately predicted outcomes under novel experimental conditions. Our combination of computational modeling and time-lapse data analysis provides a general way to examine the sources of variability in dynamic gene circuits.

Timing and Variability of Galactose Metabolic Gene Activation Depend on the Rate of Environmental Change.

Modulation of gene network activity allows cells to respond to changes in environmental conditions. For example, the galactose utilization network in Saccharomyces cerevisiae is activated by the presence of galactose but repressed by glucose. If both sugars are present, the yeast will first metabolize glucose, depleting it from the extracellular environment. Upon depletion of glucose, the genes encoding galactose metabolic proteins will activate. Here, we show that the rate at which glucose levels are depleted determines the timing and variability of galactose gene activation. Paradoxically, we find that Gal1p, an enzyme needed for galactose metabolism, accumulates more quickly if glucose is depleted slowly rather than taken away quickly. Furthermore, the variability of induction times in individual cells depends non-monotonically on the rate of glucose depletion and exhibits a minimum at intermediate depletion rates. Our mathematical modeling suggests that the dynamics of the metabolic transition from glucose to galactose are responsible for the variability in galactose gene activation. These findings demonstrate that environmental dynamics can determine the phenotypic outcome at both the single-cell and population levels.