Fundamental limits on the suppression of molecular fluctuations
2022-01-07 13:00 - 14:00 (Asia/Seoul) | B378 Seminar room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, 34126, Korea, Republic of
We will discuss about “Fundamental limits on the suppression of molecular fluctuations”, Lestas et al, Nature, 2010
Abstract: Negative feedback is common in biological processes and can increase a system’s stability to internal and external perturbations. But at the molecular level, control loops always involve signalling steps with finite rates for random births and deaths of individual molecules. Here we show, by developing mathematical tools that merge control and information theory with physical chemistry, that seemingly mild constraints on these rates place severe limits on the ability to suppress molecular fluctuations. Specifically, the minimum standard deviation in abundances decreases with the quartic root of the number of signalling events, making it extremely expensive to increase accuracy. Our results are formulated in terms of experimental observables, and existing data show that cells use brute force when noise suppression is essential; for example, regulatory genes are transcribed tens of thousands of times per cell cycle. The theory challenges conventional beliefs about biochemical accuracy and presents an approach to the rigorous analysis of poorly characterized biological systems.

Quasi-Entropy Closure: A Fast and Reliable Approach to Close the Moment Equations of the Chemical Master Equation
2022-01-13 13:00 - 14:00 | B378 Seminar room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, 34126, Korea, Republic of
We will discuss about “Quasi-Entropy Closure: A Fast and Reliable Approach to Close the Moment Equations of the Chemical Master Equation”, Wagner et al, bioRxiv, 2021
Motivation: The Chemical Master Equation is the most comprehensive stochastic approach to describe the evolution of a (bio-)chemical reaction system. Its solution is a time-dependent probability distribution on all possible configurations of the system. As the number of possible configurations is typically very large, the Master Equation is often practically unsolvable. The Method of Moments reduces the system to the evolution of a few moments of this distribution, which are described by a system of ordinary differential equations. Those equations are not closed, since lower order moments generally depend on higher order moments. Various closure schemes have been suggested to solve this problem, with different advantages and limitations. Two major problems with these approaches are first that they are open loop systems, which can diverge from the true solution, and second, some of them are computationally expensive.
Results: Here we introduce Quasi-Entropy Closure, a moment closure scheme for the Method of Moments which estimates higher order moments by reconstructing the distribution that minimizes the distance to a uniform distribution subject to lower order moment constraints. Quasi-Entropy closure is similar to Zero-Information closure, which maximizes the information entropy. Results show that both approaches outperform truncation schemes. Moreover, Quasi-Entropy Closure is computationally much faster than Zero-Information Closure. Finally, our scheme includes a plausibility check for the existence of a distribution satisfying a given set of moments on the feasible set of configurations. Results are evaluated on different benchmark problems.

다중 오믹스 분야의 현황 및 유전자-환경 상호 모델링의 필요성 (Current status of multi-omics research field and necessity of gene-by-environment (GxE) interaction modeling)
2022-01-18 16:00 - 17:00 | B378 Seminar room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, 34126, Korea, Republic of
본 발표에서는 다양한 기초 생명-의학 분야에서 생성되고 있는 오믹스 자료의 연구 개발 현황에 대해서 다룰 예정이다. 보다 큰 규모로, 보다 빠르게, 보다 정확하게, 보다 정밀하게 라는 궁극적인 목표하에 이뤄지고 있는 오믹스 자료의 진화에 발맞춰, 이를 분석하는 수리통계적 모형 역시 진화하고 있다. 그 중, 이번 발표에서는 미국의 초 대형 정밀의료 프로젝트인 TopMed에서 진행하고 있는 COPD에 관한 다중 오믹스 자료의 통합 분석 방법 및 결과에 대해서 자세히 다룰 예정이다. 아울러 정밀의료라는 목표를 달성하기 위해 반드시 모형에서 고려해야 하는 “환경 특이적 효과”에 대해 강연할 예정이다.

Network design principle for robust oscillatory behaviors with respect to biological noise
2022-01-19 11:00 - 12:00 | B378 Seminar room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, 34126, Korea, Republic of
We will discuss about “Network design principle for robust oscillatory behaviors with respect to biological noise”, Qiao et al, bioRxiv, 2021
Oscillatory behaviors, which are ubiquitous in transcriptional regulatory networks, are often subject to inevitable biological noise. Thus a natural question is how transcriptional regulatory networks can robustly achieve accurate oscillation in the presence of biological noise. Here, we search all two- and three-node transcriptional regulatory network topologies for those robustly capable of accurate oscillation against the parameter variability (extrinsic noise) or stochasticity of chemical reactions (intrinsic noise). We find that, no matter what source of the noise is applied, the topologies containing the repressilator with positive auto-regulation show higher robustness of accurate oscillation than those containing the activator-inhibitor oscillator, and additional positive auto-regulation enhances the robustness against noise. Nevertheless, the attenuation of different sources of noise is governed by distinct mechanisms: the parameter variability is buffered by the long period, while the stochasticity of chemical reactions is filtered by the high amplitude. Furthermore, we analyze the noise of a synthetic human nuclear factor κB (NF-κB) signaling network by varying three different topologies, and verify that the addition of a repressilator to the activator-inhibitor oscillator, which leads to the emergence of high-robustness motif—the repressilator with positive auto-regulation, improves the oscillation accuracy in comparison to the topology with only an activator-inhibitor oscillator. These design principles may be applicable to other oscillatory circuits.

Introduction to Bayesian Variable Selection.
2022-01-27 11:00 - 13:00 | B378 Seminar room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, 34126, Korea, Republic of
Abstract:
Variable selection is an approach to identifying a set of covariates that are truly important to explain the feature of a response variable. It is closely connected or belongs to model selection approaches. This talk provides a gentle introduction to Bayesian variable selection methods. The basic notion of variable selection is introduced, followed by several Bayesian approaches with a simple application example.

Mechanisms for the generation of robust circadian oscillations through ultrasensitivity and differential binding affinity
2022-02-04 13:00 - 14:00 | B378 Seminar room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, 34126, Korea, Republic of
We will discuss about “Mechanisms for the generation of robust circadian oscillations through ultrasensitivity and differential binding affinity”, Behera, Junco, and Vaikuntanathan, The Journal of Physical Chemistry B, 2021
Biochemical circadian rhythm oscillations play an important role in many signaling mechanisms. In this work, we explore some of the biophysical mechanisms responsible for sustaining robust oscillations by constructing a minimal but analytically tractable model of the circadian oscillations in the KaiABC protein system found in the cyanobacteria S. elongatus. In particular, our minimal model explicitly accounts for two experimentally characterized biophysical features of the KaiABC protein system, namely, a differential binding affinity and an ultrasensitive response. Our analytical work shows how these mechanisms might be crucial for promoting robust oscillations even in suboptimal nutrient conditions. Our analytical and numerical work also identifies mechanisms by which biological clocks can stably maintain a constant time period under a variety of nutrient conditions. Finally, our work also explores the thermodynamic costs associated with the generation of robust sustained oscillations and shows that the net rate of entropy production alone might not be a good figure of merit to asses the quality of oscillations.

Stochastic Modeling of Foot and Mouth Diseases with Vehicle Network & Assessment of Social Distancing for Controlling COVID-19 in Korea
2022-02-08 11:00 - 11:30 | B378 Seminar room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, 34126, Korea, Republic of
Abstract: TBA

수리모델을 통한 전염병 통제 분석
2022-02-08 11:30 - 12:00 | B378 Seminar room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, 34126, Korea, Republic of

Phiclust: a clusterability measure for single-cell transcriptomics reveals phenotypic subpopulations
2022-02-11 13:00 - 14:00 | B378 Seminar room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, 34126, Korea, Republic of
We will discuss about “Phiclust: a clusterability measure for single-cell transcriptomics reveals phenotypic subpopulations”, Mircea et al., 2022, Genome Biology
The ability to discover new cell phenotypes by unsupervised clustering of single-cell transcriptomes has revolutionized biology. Currently, there is no principled way to decide whether a cluster of cells contains meaningful subpopulations that should be further resolved. Here, we present phiclust (ϕ_clust), a clusterability measure derived from random matrix theory that can be used to identify cell clusters with non-random substructure, testably leading to the discovery of previously overlooked phenotypes.

A Deficiency-Based Approach to Parametrizing Positive Equilibria of Biochemical Reaction Systems
2022-02-18 13:00 - 14:00 | B378 Seminar room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, 34126, Korea, Republic of
We will discuss about “A Deficiency-Based Approach to Parametrizing Positive Equilibria of Biochemical Reaction Systems”, Johnston, Müller, and Pantea, Bulletin of Mathematical Biology, 2019
We present conditions which guarantee a parametrization of the set of positive equilibria of a generalized mass-action system. Our main results state that (1) if the underlying generalized chemical reaction network has an effective deficiency of zero, then the set of positive equilibria coincides with the parametrized set of complex-balanced equilibria and (2) if the network is weakly reversible and has a kinetic deficiency of zero, then the equilibrium set is nonempty and has a positive, typically rational, parametrization. Via the method of network translation, we apply our results to classical mass-action systems studied in the biochemical literature, including the EnvZ–OmpR and shuttled WNT signaling pathways. A parametrization of the set of positive equilibria of a (generalized) mass-action system is often a prerequisite for the study of multistationarity and allows an easy check for the occurrence of absolute concentration robustness, as we demonstrate for the EnvZ–OmpR pathway.

Spatiotemporal reconstruction of static single-cell genomics data
2022-03-03 11:00 - 12:00 | ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: [REDACTED]
This talk will be presented online. Zoom link: 997 8258 4700 (pw: [REDACTED]
Abstract: Cells make fate decisions in response to dynamic environments and multicellular structure emerges from interplays among cells in space and time. The recent single-cell genomics technology provides an unprecedented opportunity to profile cells. However, those measurements are taken as snapshots for groups of individual cells with only static information. Can one infer interactions among cells from such datasets? Is it possible to recover spatial information from non-spatial datasets? How to obtain temporal relationships of cells from the static measurements? In this talk I will present our newly developed computational tools that reconstruct interactions and spatiotemporal relationships for cells using single-cell RNA-seq, ATAC-seq, and spatial transcriptomics datasets. Through applications of those methods to systems in development and regeneration, we show the discovery power of such methods and identify areas for further development in spatiotemporal reconstruction.

Modeling polypharmacy side effects with graph convolutional networks
2022-03-04 13:00 - 14:00 | B378 Seminar room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, 34126, Korea, Republic of
We will discuss about “Modeling polypharmacy side effects with graph convolutional networks”, Zitnik, Agrawal, and Leskovec, Bioinformatics, 2018
Motivation
The use of drug combinations, termed polypharmacy, is common to treat patients with complex diseases or co-existing conditions. However, a major consequence of polypharmacy is a much higher risk of adverse side effects for the patient. Polypharmacy side effects emerge because of drug-drug interactions, in which activity of one drug may change, favorably or unfavorably, if taken with another drug. The knowledge of drug interactions is often limited because these complex relationships are rare, and are usually not observed in relatively small clinical testing. Discovering polypharmacy side effects thus remains an important challenge with significant implications for patient mortality and morbidity.
Results
Here, we present Decagon, an approach for modeling polypharmacy side effects. The approach constructs a multimodal graph of protein-protein interactions, drug-protein target interactions and the polypharmacy side effects, which are represented as drug-drug interactions, where each side effect is an edge of a different type. Decagon is developed specifically to handle such multimodal graphs with a large number of edge types. Our approach develops a new graph convolutional neural network for multirelational link prediction in multimodal networks. Unlike approaches limited to predicting simple drug-drug interaction values, Decagon can predict the exact side effect, if any, through which a given drug combination manifests clinically. Decagon accurately predicts polypharmacy side effects, outperforming baselines by up to 69%. We find that it automatically learns representations of side effects indicative of co-occurrence of polypharmacy in patients. Furthermore, Decagon models particularly well polypharmacy side effects that have a strong molecular basis, while on predominantly non-molecular side effects, it achieves good performance because of effective sharing of model parameters across edge types. Decagon opens up opportunities to use large pharmacogenomic and patient population data to flag and prioritize polypharmacy side effects for follow-up analysis via formal pharmacological studies.

Transcription factor competition facilitates self-sustained oscillations in single gene genetic circuits
2022-03-11 13:00 - 14:00 | B378 Seminar room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, 34126, Korea, Republic of
Abstract: Genetic feedback loops can be used by cells as a means to regulate internal processes or keep track of time. It is often thought that, for a genetic circuit to display self-sustained oscillations, a degree of cooperativity is needed in the binding and unbinding of actor species. This cooperativity is usually modeled using a Hill function, regardless of the actual promoter architecture. Moreover, genetic circuits do not operate in isolation and often transcription factors are shared between different promoters. In this work we show how mathematical modelling of genetic feedback loops can be facilitated with a mechanistic fold-change function that takes into account the titration effect caused by competing binding sites for transcription factors. The model shows how the titration effect aids self-sustained oscillations in a minimal genetic feedback loop: a gene that produces its own repressor directly — without cooperative transcription factor binding. The use of delay differential equations leads to a stability contour that predicts whether a genetic feedback loop will show self-sustained oscillations, even when taking the bursty nature of transcription into account.

Data-driven discovery of coordinates and governing equations
2022-03-18 13:00 - 14:00 | B378 Seminar room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, 34126, Korea, Republic of
Abstract: The discovery of governing equations from scientific data has the potential to transform data-rich fields that lack well-characterized quantitative descriptions. Advances in sparse regression are currently enabling the tractable identification of both the structure and parameters of a nonlinear dynamical system from data. The resulting models have the fewest terms necessary to describe the dynamics, balancing model complexity with descriptive ability, and thus promoting interpretability and generalizability. This provides an algorithmic approach to Occam’s razor for model discovery. However, this approach fundamentally relies on an effective coordinate system in which the dynamics have a simple representation. In this work, we design a custom deep autoencoder network to discover a coordinate transformation into a reduced space where the dynamics may be sparsely represented. Thus, we simultaneously learn the governing equations and the associated coordinate system. We demonstrate this approach on several example high-dimensional systems with low-dimensional behavior. The resulting modeling framework combines the strengths of deep neural networks for flexible representation and sparse identification of nonlinear dynamics (SINDy) for parsimonious models. This method places the discovery of coordinates and models on an equal footing.

Introduction to topological data analysis
2022-03-24 10:30 - 11:00 | ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: [REDACTED]
This talk will be presented online. Zoom link: 997 8258 4700 (pw: [REDACTED]
Abstract: I will give an introduction to topological data analysis (TDA), in which one uses ideas from algebraic topology to study the “shape” of data. I will focus on persistent homology (PH), which is the most common approach in TDA.

Topological data analysis of spatial systems
2022-03-24 11:00 - 12:00 | ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: [REDACTED]
This talk will be presented online. Zoom link: 997 8258 4700 (pw: [REDACTED]
Abstract: From the venation patterns of leaves to spider webs, roads in cities, social networks, and the spread of COVID-19 infections and vaccinations, the structure of many systems is influenced significantly by space. In this talk, I will discuss the application of topological data analysis (specifically, persistent homology) to spatial systems. I will present a few examples, such as voting in presidential elections, city street networks, spatiotemporal dynamics of COVID-19 infections and vaccinations, and webs that were spun by spiders under the influence of various drugs.

Universal structural requirements for maximal robust perfect adaptation in biomolecular networks
2022-03-25 13:00 - 14:00 | B378 Seminar room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, 34126, Korea, Republic of
Abstract: Consider a biomolecular reaction network that exhibits robust perfect adaptation to disturbances from several parallel sources. The well-known Internal Model Principle of control theory suggests that such systems must include a subsystem (called the “internal model”) that is able to recreate the dynamic structure of the disturbances. This requirement poses certain structural constraints on the network which we elaborate in this paper for the scenario where constant-in-time disturbances maximally affect network interactions and there is model uncertainty and possible stochasticity in the dynamics. We prove that these structural constraints are primarily characterized by a simple linear-algebraic stoichiometric condition which remains the same for both deterministic and stochastic descriptions of the dynamics. Our results reveal the essential requirements for maximal robust perfect adaptation in biology, with important implications for both systems and synthetic biology. We exemplify our results through many known examples of robustly adapting networks and we construct new examples of such networks with the aid of our linear-algebraic characterization.

Design principles of physiological circuits
2022-03-31 11:00 - 12:00 | ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: [REDACTED]
This talk will be presented online. Zoom link: 997 8258 4700 (pw: [REDACTED]
Abstract: We will discuss hormone circuits and their dynamics using new models that take into account timescales of weeks due to growth of the hormone glands. This explains some mysteries in diabetes and autoimmune disease.

Physics-informed learning of governing equations from scarce data
2022-04-01 13:00 - 14:00 | B378 Seminar room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, 34126, Korea, Republic of
We will discuss about “Physics-informed learning of governing equations from scarce data”, Chen et al., Nature Communications, 2021
Abstract: Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology, to name only a few examples. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing equations from noisy measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. This results in parsimonious models that balance accuracy with model complexity to avoid overfitting. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including linear and nonlinear oscillators and the chaotic Lorenz system, to the fluid vortex shedding behind an obstacle. The fluid example illustrates the ability of this method to discover the underlying dynamics of a system that took experts in the community nearly 30 years to resolve. We also show that this method generalizes to parameterized systems and systems that are time-varying or have external forcing.

대학원생 길라잡이 (Tips for graduate students)
2022-04-05 17:00 - 18:00 | B378 Seminar room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, 34126, Korea, Republic of
4월 5일 오후 5시, <대학원생 때 알았더라면 좋았을 것들>의 저자이신 권창현 교수님께서 대학원생 길라잡이라는 주제로 워크샵을 진행해주실 예정입니다.

줄리아 언어 프로그래밍 튜토리얼 (Julia programming tutorial)
2022-04-05 20:00 - 21:00 | B378 Seminar room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, 34126, Korea, Republic of
<경영과학을 위한 줄리아 언어 프로그래밍>의 저자이신 권창현 교수님께서 4월 5일 오후 8시 줄리아 프로그래밍 튜토리얼을 진행합니다. 본 튜토리얼은 한국어로 진행됩니다.

Universal biology in adaptation and evolution: dimensional reduction, and fluctuation-response relationship
2022-04-07 11:00 - 12:00 | ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: [REDACTED]
This talk will be presented online. Zoom link: 997 8258 4700 (pw: [REDACTED]
Abstract: A macroscopic theory for cellular states with steady-growth is presented, based on consistency between cellular growth and molecular replication, together with robustness of phenotypes against perturbations. Adaptive changes in high-dimensional phenotypes are shown to be restricted within a low-dimensional slow manifold, from which a macroscopic law for cellular states is derived, as is confirmed by adaptation experiments of bacteria under stress. The theory is extended to phenotypic evolution, leading to proportionality between phenotypic responses against genetic evolution and by environmental adaptation, which explains the evolutionary fluctuation-response relationship previously uncovered.
References

Kaneko K., Life: An Introduction to Complex Systems Biology, Springer (2006)
K. Kaneko, C.Furusawa, T. Yomo, “Macroscopic phenomenology for cells in steady-growth state”, Phys.Rev.X(2015) 011014
C. Furusawa, K. Kaneko “Global Relationships in Fluctuation and Response in Adaptive Evolution”, J of Royal Society Interface 12(2015), 20150482.
C. Furusawa, K. Kaneko ” Formation of Dominant Mode by Evolution in Biological Systems” Phys. Rev. E 97(2018)042410
K. Kaneko, C. Furusawa “Macroscopic Theory for Evolving Biological Systems Akin to Thermodynamics”, Annual Rev. Biophys. (2018) 47, 273-290
A. Sakata and K. Kaneko, “Dimensional Reduction in Evolving Spin-Glass Model: Correlation of Phenotypic Responses to Environmental and Mutational Changes”, Phys. Rev. Lett. (2020) 124, 218101
Q-Y. Tang and K. Kaneko, “ Dynamics-evolution correspondence in protein structures”, Phys. Rev. Lett. (2021) 127, 098103

RTransferEntropy — Quantifying information flow between different time series using effective transfer entropy
2022-04-08 13:00 - 14:00 | B378 Seminar room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, 34126, Korea, Republic of
We will discuss about “RTransferEntropy — Quantifying information flow between different time series using effective transfer entropy”, Behrendt et al., SoftwareX, 2019
Abstract: This paper shows how to quantify and test for the information flow between two time series with Shannon transfer entropy and Rényi transfer entropy using the R package RTransferEntropy. We discuss the methodology, the bias correction applied to calculate effective transfer entropy and outline how to conduct statistical inference. Furthermore, we describe the package in detail and demonstrate its functionality by means of several simulated processes and present an application to financial time series.

An overview of methods used for multi-scale modeling and analysis
2022-04-14 10:30 - 11:00 | ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: [REDACTED]
This talk will be presented online. Zoom link: 997 8258 4700 (pw: [REDACTED]
Abstract: TBA

A systems biology approach using multi-scale modeling to understand the immune response to tuberculosis infection and treatment
2022-04-14 11:00 - 12:00 | ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: [REDACTED]
This talk will be presented online. Zoom link: 997 8258 4700 (pw: [REDACTED]
Abstract: Tuberculosis (TB) is one of the world’s deadliest infectious diseases. Caused by the pathogen Mycobacterium tuberculosis (Mtb), the standard regimen for treating TB consists of treatment with multiple antibiotics for at least six months. There are a number of complicating factors that contribute to the need for this long treatment duration and increase the risk of treatment failure. The structure of granulomas, lesions forming in lungs in response to Mtb infection, create heterogeneous antibiotic distributions that limit antibiotic exposure to Mtb. We can use a systems biology approach pairing experimental data from non-human primates with computational modeling to represent and predict how factors impact antibiotic regimen efficacy and granuloma bacterial sterilization. We utilize an agent-based, computational model that simulates granuloma formation, function and treatment, called GranSim. A goal in improving antibiotic treatment for TB is to find regimens that can shorten the time it takes to sterilize granulomas while minimizing the amount of antibiotic required. We also created a whole host model, called HOSTSIM, to study Mtb dynamics within a human host. Overall, we use these models to help better understand TB treatment and strengthen our ability to predict regimens that can improve clinical treatment of TB.

A topological data analysis based classifier
2022-04-15 11:00 - 13:00 | B378 Seminar room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, 34126, Korea, Republic of
We will discuss about “A topological data analysis based classifier”, Kindelan et al., arXiv, 2022
Abstract: Topological Data Analysis is an emergent field that aims to discover the underlying dataset’s topological information. Topological Data Analysis tools have been commonly used to create filters and topological descriptors to improve Machine Learning (ML) methods. This paper proposes a different Topological Data Analysis pipeline to classify balanced and imbalanced multi-class datasets without additional ML methods. Our proposed method was designed to solve multi-class problems. It resolves multi-class imbalanced classification problems with no data resampling preprocessing stage. The proposed Topological Data Analysis-based classifier builds a filtered simplicial complex on the dataset representing high-order data relationships. Following the assumption that a meaningful sub-complex exists in the filtration that approximates the data topology, we apply Persistent Homology to guide the selection of that sub-complex by considering detected topological features. We use each unlabeled point’s link and star operators to provide different sized and multi-dimensional neighborhoods to propagate labels from labeled to unlabeled points. The labeling function depends on the filtration entire history of the filtered simplicial complex and is encoded within the persistent diagrams at various dimensions. We select eight datasets with different dimensions, degrees of class overlap, and imbalanced samples per class. The TDABC outperforms all baseline methods classifying multi-class imbalanced data with high imbalanced ratios and data with overlapped classes. Also, on average, the proposed method was better than KNN and weighted-KNN and behaved competitively with SVM and Random Forest baseline classifiers in balanced datasets.

Dynamical and topological hallmarks of regulatory networks driving phenotypic plasticity and heterogeneity in cancers
2022-04-21 16:00 - 17:00 | B378 Seminar room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, 34126, Korea, Republic of
This talk will be presented online. Zoom link: 997 8258 4700 (pw: [REDACTED]
Abstract:
Metastasis and therapy resistance cause over 90% of cancer-related deaths. Despite extensive ongoing efforts, no unique genetic or mutational signature has emerged for metastasis. Instead, the ability of genetically identical cells to adapt reversibly by exhibiting multiple phenotypes (phenotypic/non-genetic heterogeneity) and switch among them (phenotypic plasticity) is proposed as a hallmark of metastasis. Also, drug resistance can emerge from such non-genetic adaptive cellular changes. However, the origins of such non-genetic heterogeneity in most cancers are poorly understood. I will present our findings on a) how non-genetic heterogeneity emerges in a population of cancer, and b) what design principles underlie regulatory networks enabling non-genetic heterogeneity across multiple cancers. Our results unravel how systems-levels approaches integrating mechanistic mathematical modeling with in vitro and in vivo data can identify causes and consequences of such non-genetic heterogeneity.

An Efficient Characterization of Complex-Balanced, Detailed-Balanced, and Weakly Reversible Systems
2022-04-22 13:00 - 14:00 | B378 Seminar room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, 34126, Korea, Republic of
We will discuss about “An Efficient Characterization of Complex-Balanced, Detailed-Balanced, and Weakly Reversible Systems”, Craciun et al., SIAM Journal on Applied Mathematics, 2020
Abstract: Very often, models in biology, chemistry, physics, and engineering are systems of polynomial or power-law ordinary differential equations, arising from a reaction network. Such dynamical systems can be generated by many different reaction networks. On the other hand, networks with special properties (such as reversibility or weak reversibility) are known or conjectured to give rise to dynamical systems that have special properties: existence of positive steady states, persistence, permanence, and (for well-chosen parameters) complex balancing or detailed balancing. These last two are related to thermodynamic equilibrium, and therefore the positive steady states are unique and stable. We describe a computationally efficient characterization of polynomial or power-law dynamical systems that can be obtained as complex-balanced, detailed-balanced, weakly reversible, and reversible mass-action systems.

Scaling behaviors in physiological fluctuations: relevance to circadian regulation and insights into the development of Alzheimer’s disease
2022-04-28 11:00 - 12:00 | ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: [REDACTED]
This talk will be presented online. Zoom link: 997 8258 4700 (pw: [REDACTED]
Abstract: Outputs from health biological systems display complex fluctuations that are not random but display robust and often self-similar (fractal) temporal correlations at different time scales— scaling behaviors. The scaling behaviors in the fluctuations of biological outputs such as neural activities, cardiac dynamics, motor activity are believed to be originated from feedbacks within the complex biological networks, reflecting the system adaptability to internal and external inputs. Supporting this concept, our studies have demonstrated a mechanistic link between the scaling regulation of physiological fluctuations and the circadian control system— a result of evolutionary adaptation to daily environmental light-dark cycles on the earth. In this talk, I will discuss certain evidence for this ‘scaling-circadian’ link and its related implications. Moreover, I will review some recent studies, in which we examined how the scaling patterns of human motor activity fluctuations change with aging and in Alzheimer’s disease. Our results showed that (1) alterations in scaling activity patterns occur before the clinical manifestation of Alzheimer’s disease (i.e., cognitive impairment) and predict cognitive decline and the risk for Alzheimer’s dementia; and (2) the progression of Alzheimer’s disease accelerates the aging effect on the scaling activity patterns. Our work provides strong evidence that altered scaling activity patterns may also be a risk factor for neurodegeneration, playing a role in the development and progression of Alzheimer’s disease.

Toroidal topology of population activity in grid cells
2022-04-29 13:00 - 14:00 | B378 Seminar room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, 34126, Korea, Republic of
We will discuss about “Toroidal topology of population activity in grid cells”, Gardner et al., Nature, 2021.
Abstract: The medial entorhinal cortex is part of a neural system for mapping the position of an individual within a physical environment. Grid cells, a key component of this system, fire in a characteristic hexagonal pattern of locations, and are organized in modules that collectively form a population code for the animal’s allocentric position. The invariance of the correlation structure of this population code across environments and behavioral states, independent of specific sensory inputs, has pointed to intrinsic, recurrently connected continuous attractor networks (CANs) as a possible substrate of the grid pattern. However, whether grid cell networks show continuous attractor dynamics, and how they interface with inputs from the environment, has remained unclear owing to the small samples of cells obtained so far. Here, using simultaneous recordings from many hundreds of grid cells and subsequent topological data analysis, we show that the joint activity of grid cells from an individual module resides on a toroidal manifold, as expected in a two-dimensional CAN. Positions on the torus correspond to the positions of the moving animal in the environment. Individual cells are preferentially active at singular positions on the torus. Their positions are maintained between environments and from wakefulness to sleep, as predicted by CAN models for grid cells but not by alternative feedforward models. This demonstration of network dynamics on a toroidal manifold provides a population-level visualization of CAN dynamics in grid cells.
