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

Evaluating statistical methods used to estimate the number of postsynaptic receptors.

Calcium levels in spines play a significant role in determining the sign and magnitude of synaptic plasticity. The magnitude of calcium influx into spines is highly dependent on influx through N-methyl D-aspartate (NMDA) receptors, and therefore depends on the number of postsynaptic NMDA receptors in each spine. We have calculated previously how the number of postsynaptic NMDA receptors determines the mean and variance of calcium transients in the postsynaptic density, and how this alters the shape of plasticity curves. However, the number of postsynaptic NMDA receptors in the postsynaptic density is not well known. Anatomical methods for estimating the number of NMDA receptors produce estimates that are very different than those produced by physiological techniques. The physiological techniques are based on the statistics of synaptic transmission and it is difficult to experimentally estimate their precision. In this paper we use stochastic simulations in order to test the validity of a physiological estimation technique based on failure analysis. We find that the method is likely to underestimate the number of postsynaptic NMDA receptors, explain the source of the error, and re-derive a more precise estimation technique. We also show that the original failure analysis as well as our improved formulas are not robust to small estimation errors in key parameters

Methods for large-scale genome-wide association studies

Genome-wide association studies (GWAS) have led to the identification of thousands of associations between genetic polymorphisms and complex traits or diseases, facilitating several downstream applications such as genetic risk prediction and drug target prioritisation. Biobanks containing extensive genetic and phenotypic data continue to grow, creating new opportunities for the study of complex traits, such as the analysis of rare genomic variation across multiple populations. These opportunities are coupled with computational challenges, creating the need for the development of novel methodology. This thesis develops computational tools to facilitate large-scale association studies of rare and common variation. First, we develop methods to improve the analysis of ultra-rare variants, leveraging the sharing of identical-by-descent (IBD) genomic regions within large biobanks. We compare ∼ 400k genotyped UK Biobank (UKBB) samples with 50k exome-sequenced samples and devise a score that quantifies the extent to which a genotyped individual shares IBD segments with carriers of rare loss-of-function mutations. Our approach detects several associations and replicates 11/14 loci of a pilot exome sequencing study. Second, we develop a linear mixed model framework, FMA, that builds on previous techniques and is suitable for scalable and robust association testing. We benchmark FMA and several state-of-the-art approaches using synthetic and UKBB data, evaluating computational performance, statistical power, and robustness to known confounders, such as cryptic relatedness and population stratification. Finally, we integrate FMA with recently developed methods for genealogical analysis of complex traits, enabling it to perform scalable genealogy-based estimation of narrow-sense heritability and association

Randomized learning-augmented auctions with revenue guarantees

We consider the fundamental problem of designing a truthful single-item auction with the challenging objective of extracting a large fraction of the highest agent valuation as revenue. Following a recent trend in algorithm design, we assume that the agent valuations belong to a known interval, and a (possibly erroneous) prediction for the highest valuation is available. Then, auction design aims for high consistency and robustness, meaning that, for appropriate pairs of values $\gamma$ and $\rho$, the extracted revenue should be at least a $\gamma$- or $\rho$-fraction of the highest valuation when the prediction is correct for the input instance or not. We characterize all pairs of parameters $\gamma$ and $\rho$ so that a randomized $\gamma$-consistent and $\rho$-robust auction exists. Furthermore, for the setting in which robustness can be a function of the prediction error, we give sufficient and necessary conditions for the existence of robust auctions and present randomized auctions that extract a revenue that is only a polylogarithmic (in terms of the prediction error) factor away from the highest agent valuation

Structural Plasticity Can Produce Metaplasticity

BACKGROUND:Synaptic plasticity underlies many aspect of learning memory and development. The properties of synaptic plasticity can change as a function of previous plasticity and previous activation of synapses, a phenomenon called metaplasticity. Synaptic plasticity not only changes the functional connectivity between neurons but in some cases produces a structural change in synaptic spines; a change thought to form a basis for this observed plasticity. Here we examine to what extent structural plasticity of spines can be a cause for metaplasticity. This study is motivated by the observation that structural changes in spines are likely to affect the calcium dynamics in spines. Since calcium dynamics determine the sign and magnitude of synaptic plasticity, it is likely that structural plasticity will alter the properties of synaptic plasticity. METHODOLOGY/PRINCIPAL FINDINGS:In this study we address the question how spine geometry and alterations of N-methyl-D-aspartic acid (NMDA) receptors conductance may affect plasticity. Based on a simplified model of the spine in combination with a calcium-dependent plasticity rule, we demonstrated that after the induction phase of plasticity a shift of the long term potentiation (LTP) or long term depression (LTD) threshold takes place. This induces a refractory period for further LTP induction and promotes depotentiation as observed experimentally. That resembles the BCM metaplasticity rule but specific for the individual synapse. In the second phase, alteration of the NMDA response may bring the synapse to a state such that further synaptic weight alterations are feasible. We show that if the enhancement of the NMDA response is proportional to the area of the post synaptic density (PSD) the plasticity curves most likely return to the initial state. CONCLUSIONS/SIGNIFICANCE:Using simulations of calcium dynamics in synaptic spines, coupled with a biophysically motivated calcium-dependent plasticity rule, we find under what conditions structural plasticity can form the basis of synapse specific metaplasticity

Utilitarian distortion with predictions

We study the utilitarian distortion of social choice mechanisms under the recently proposed learning-augmented framework where some (possibly unreliable) predicted information about the preferences of the agents is given as input. In particular, we consider two fundamental social choice problems: single-winner voting and one-sided matching. In these settings, the ordinal preferences of the agents over the alternatives (either candidates or items) is known, and some prediction about their underlying cardinal values is also provided. The goal is to leverage the prediction to achieve improved distortion guarantees when it is accurate, while simultaneously still achieving reasonable worst-case bounds when it is not. This leads to the notions of consistency and robustness, and the quest to achieve the best possible tradeoffs between the two. We show tight tradeoffs between the consistency and robustness of ordinal mechanisms for single-winner voting and one-sided matching, for different levels of information provided as prediction

A scalable variational inference approach for increased mixed-model association power

The rapid growth of modern biobanks is creating new opportunities for large-scale genome-wide association studies (GWASs) and the analysis of complex traits. However, performing GWASs on millions of samples often leads to trade-offs between computational efficiency and statistical power, reducing the benefits of large-scale data collection efforts. We developed Quickdraws, a method that increases association power in quantitative and binary traits without sacrificing computational efficiency, leveraging a spike-and-slab prior on variant effects, stochastic variational inference and graphics processing unit acceleration. We applied Quickdraws to 79 quantitative and 50 binary traits in 405,088 UK Biobank samples, identifying 4.97% and 3.25% more associations than REGENIE and 22.71% and 7.07% more than FastGWA. Quickdraws had costs comparable to REGENIE, FastGWA and SAIGE on the UK Biobank Research Analysis Platform service, while being substantially faster than BOLT-LMM. These results highlight the promise of leveraging machine learning techniques for scalable GWASs without sacrificing power or robustness