Posters presentations

Presenter : Seok Joo Chae

Title : Spatially coordinated collective phosphorylation filters spatiotemporal noises for precise circadian timekeeping

Abstract :

The circadian (∼24h) clock is based on a negative-feedback loop centered around the PERIOD protein (PER), translated in the cytoplasm and then enters the nucleus to repress its own transcription at the right time of day. Such precise nucleus entry is mysterious because thousands of PER molecules transit through crowded cytoplasm and arrive at the perinucleus across several hours. To understand this, we developed a mathematical model describing the complex spatiotemporal dynamics of PER as a single random time delay. We find that the spatially coordinated bistable phosphoswitch of PER, which triggers the phosphorylation of accumulated PER at the perinucleus, leads to the synchronous and precise nuclear entry of PER. This leads to robust circadian rhythms even when PER arrival times are heterogeneous and perturbed due to changes in cell crowdedness, cell size, and transcriptional activator levels. This shows how the circadian clock compensates for spatiotemporal noise.

Presenter : Sungkweon Cho

Title : Prevalence and Associations Between Metabolic Syndrome Components and Hyperuricemia by Race: Findings from 2011 – 2020 NHANES

Abstract :

Objective We explored the trend in prevalence of hyperuricemia and metabolic syndrome in the US populations and investigated associations between components of metabolic syndrome and hyperuricemia by race. Methods We analyzed data from the four most recent NHANES cycles (2011 to March 2020), comprising 10,175 participants. Hyperuricemia is defined as serum urate > 7.0 mg/dL (men) or > 5.7 mg/dL (women), following the NHANES III guideline. Definition of metabolic syndrome follows National Cholesterol Education Program’s Adult Treatment Panel III (NCEP ATP III) guideline. We estimated the prevalence of metabolic syndrome and hyperuricemia in each cycle and performed subgroup analyses with logistic regression to investigate the patterns of associated components of metabolic syndrome with hyperuricemia. Results In the most recent cycle (2017-March 2020), the prevalence of metabolic syndrome was 45.9% and that of hyperuricemia was 20.7%. Over the 2011-2020 period, a significant rise in metabolic syndrome prevalence was observed among Hispanic and Asian populations, and the prevalence of hyperuricemia has increased significantly only in Hispanic. After adjustment for confounding factors, subjects with metabolic syndrome exhibited a higher hyperuricemia in women than in men. Elevated BP was the strongest factor with hyperuricemia. The association was the weakest in Asian population. Waist circumference was the only significant factor associated with hyperuricemia in Asian. Conclusion The prevalence of metabolic syndrome has increasing pattern, but there was no specific decadal trend in prevalence of hyperuricemia. There is an ethnic-specific association of metabolic syndrome and hyperuricemia, especially in Asian.

Presenter : Hyeong Jun Jang

Title : Accurate and precise parameter estimation and type identification in enzyme inhibition

Abstract :

Enzyme inhibitors slow down substrate metabolism by binding free enzymes (competitive type), enzyme-substrate complexes (uncompetitive type), or both (mixed type). The potency and dynamics of enzyme inhibitors, specific to each type, are determined by enzyme inhibition parameters. The inhibition parameters and type have been estimated and identified from in vitro experimental data by applying the Michaelis-Menten (MM) rate law. However, we revealed that the limited experimental data can lead to inaccuracy in estimating the enzyme inhibition parameters and even cause incorrect identification of the inhibition type. To address these challenges, we suggest an experimental guideline that enables the accurate and precise estimation of enzyme inhibition parameters and the identification of the inhibition type based on the MM rate law.

Presenter : Seokhwan Moon

Title : Topological Criterion for Robust Perfect Adaptation of Reaction Fluxes in Biological Networks

Abstract :

Robust Perfect Adaptation (RPA) is a mechanism adopted by living systems such as metabolic networks to maintain homeostasis amidst fluctuating environmental conditions. Previous studies on the RPA of fluxes (e.g., the passage of a metabolite through a reaction) have suffered from a lack of generality due to the complexity of theory and are applicable only under specific conditions. Here, we present a simple and general topological criterion for networks to determine whether all reaction fluxes exhibit RPA. This offers a simple and scalable approach for predicting whether the perturbation of a reaction parameter or a conserved quantity affects network fluxes based solely on the network structure. By applying this approach to the metabolic pathways of Escherichia coli, we classify all reactions according to their perturbation effect on the metabolic fluxes, validated by single-gene knockout experiments. Our approach also solves the mystery of why plant growth is affected by the perturbation in only aspartate transcarbamoylase among various enzymes for de novo synthesis of the pyrimidine metabolism. Moreover, our criterion can be used to obtain a simpler network from which the reaction fluxes of the original system can be completely recovered.

Presenter : Hyunsuk Choo

Title : Inferring the network structure of a plankton community using time series data

Abstract :

Identifying causal relationships from observational time series data has been a core challenge in the field of ecological sciences. Although model-free methods such as Granger causality are widely used, they encounter difficulties in distinguishing synchrony and indirect effects from direct effects, often resulting in false-positive outcomes. To deal with this, we employ a recently developed causal inference method which uses minimal assumptions common in ecological models. With this method, we infer the plankton community network with complicated food chains consisting of 10 species and effectively address false-positive issues.

Presenter : Dongju Lim

Title : Accurate Prediction of Mood Episodes Using Sleep and Circadian Rhythm Features from Wearables

Abstract :

Advances in wearable devices enable the collection of extensive data including sleep, heart rate, step count, and light exposure. These datasets have been utilized to develop mood episode prediction models for mood disorder patients. However, existing models require the collection of various types of data, limiting their applicability in the real world. Here, we present a model that can accurately predict mood episodes using only sleep-wake data, which can be collected passively and easily through smartphones or wearable devices. Specifically, by applying mathematical modeling to longitudinal sleep-wake data of mood disorder patients, we obtained 36 comprehensive and accurate features of sleep and estimated circadian rhythm. When these features were used for machine learning algorithms, we accurately predicted the following day’s depressive, manic, and hypomanic episodes (AUC 0.925, 0.984, and 0.985 respectively). Additionally, we used SHAP value analysis to show the difference in dependency of depressive and manic episodes on circadian rhythm.

Presenter : Lucas MacQuarrie

Title : TBD

Abstract :

TBD

Presenter : Yun Min Song

Title : Noisy delay denoises biochemical oscillators

Abstract :

Genetic oscillators arise from delayed transcriptional negative feedback loops, wherein repressor proteins inhibit their own synthesis after a temporal production delay. This delay, generated by sequential processes involved in gene expressions such as transcription, translation, folding, and translocation, is distributed due to the inherent noise of the processes. Because the delay determines repression timing and therefore the oscillation period, it has been commonly believed that delay noise weakens oscillatory dynamics. However, in this talk, we demonstrate that noisy delay can actually denoise genetic oscillators by improving the temporal peak reliability.

Presenter : 신설아

Title : Beyond Homogeneity: Assessing the Validity of the Michaelis-Menten Rate Law in Spatially Heterogeneous Environments

Abstract :

The Michaelis-Menten (MM) rate law has been a fundamental tool in describing enzyme-catalyzed reactions for over a century. While the applicability of the MM rate law can be easily assessed in homogeneous environments, its application becomes challenging in heterogeneous environments, which are common in biological systems. In this study, we demonstrate that the MM rate law can lead to misleading results under spatial heterogeneity. To address these limitations, we propose an alternative method suitable for spatially heterogeneous environments.

Presenter : Pan Li

Title : Modeling the circadian regulation of cardiac pacemaking function

Abstract :

The mammalian heart relies on the sinoatrial node, known as the cardiac pacemaker, to orchestrate heartbeats. These heartbeats slow down during sleep and accelerate upon waking, in anticipation of daily environmental changes. The heart's ability to rhythmically adapt to these 24-hour changes, known as circadian rhythms, is crucial for flexible cardiac performance throughout the day, accommodating various physiological states. However, with aging, the heart's circadian flexibility gradually weakens, accompanied by a decline in maximal heart rate. Previous studies have implicated the involvement of a master circadian clock and a local circadian clock within the heart, but their time-of-day interactions and altered dynamics during aging remain unclear. In this study, we developed a mathematical model to simulate the regulation of sinoatrial nodal cell pacemaking function by the master and local circadian clocks in adult and aged mice. Our results unveiled distinct roles played by these clocks in determining circadian patterns of sinoatrial nodal cells, shedding light on their critical alliance in regulating time-of-day cardiac pacemaking function and dysfunction.

Presenter : Gyuyoung Hwang

Title : Existence of a perodic solution in models for coupled oscillators

Abstract :

The dynamics of coupled oscillators can be effectively described using systems of ordinary differential equations, with models including the Kuramoto and Winfree models. These models often incorporate a parameter called the coupling strength. It has been experimentally and mathematically shown that if the coupling strength exceeds a certain number, then the coupled oscillators exhibit synchronization, meaning that the frequencies of oscillators become identical. However, insufficient coupling strength prevents synchronization. Instead, the system becomes unstable in the low coupling regime. In this study, we prove that under sufficient conditions on the initial data and frequencies, there exists a periodic solution to a class of systems of coupled of oscillators even under the low coupling strength. The proof relies on the construction of an invariant set and the use of the Poincare map.

Presenter : Boya Yang

Title : Crafting Mathematical Models for Type 2 Diabetes Progression: Leveraging Longitudinal Data as the Guide

Abstract :

Mathematical modeling stands out as a powerful quantitative tool to investigate the intricate pathogenesis of type 2 diabetes (T2D). The majority of modeling work studying or involving the progression of T2D was formulated by modifying the pioneering model of Topp et all due to its simple structure. However, certain parameter values in Topp’s model deviate from the actual clinical scenario, and the oversimplified structure hinders its explanatory capacity for clinical data. Leveraging a four-dimensional longitudinal T2D data from Southwest Native American, we developed a series of models, starting with a minimal modified version of Topp’s model and iteratively incorporating additional model elements to account for new biological mechanisms until optimal data fit was achieved. The notable variability of individual data was overcome by the non-linear mixed-effect modeling approach. Despite the absence of a discernible common trend among the individual trajectories of each variable, our model effectively captures the diverse glucose-insulin dynamics of individuals progressing to T2D.The reliability of the model is reinforced by its successful cross-sectional validation against subset of individuals progressing only to prediabetes. The systematic model selection process aided in navigating the trade-off between model complexity and practicability, culminating in a robust framework to address controversial questions in the diabetes field in future research.

Presenter : Eui Min Jeong

Title : A robust ultrasensitive transcriptional switch in noisy cellular environments

Abstract :

Ultrasensitive transcriptional switches are essential for cells to respond to environmental cues with high fidelity. However, conventional switches that rely on direct repressor-DNA binding are sensitive to noise, leading to unintended changes in gene expression. We discovered that an alternative design combining three indirect transcriptional repression mechanisms can generate a noise-resilient ultrasensitive switch. In this design, sequestration, blocking, and displacement are used to inhibit a transcriptional activator instead of directly binding to DNA. The combination of these mechanisms is required because sequestration alone can generate an ultrasensitive transcriptional response, but the switch remains sensitive to noise because the unintended on or off state induced by noise can persist for long periods However, by jointly utilizing blocking and displacement, these noise-induced transitions can be rapidly restored to the original desired transcriptional state. Furthermore, by deriving Fano factors and equations describing the combination of these repression mechanisms, we theoretically proved that their combination can reduce noise in the transcription while generating an ultrasensitive transcriptional switch. Therefore, this transcriptional switch is effective in noisy cellular contexts, making it valuable for robust synthetic system design. Our findings also provide insights into the evolution of robust ultrasensitive switches in real cells.

Presenter : Jinyoung Kim

Title : A reaction network description for microscale liquid-liquid phase separation reveals influences of spatial dimension

Abstract :

In this poster, we aim to understand droplet formation for Liquid-Liquid Phase Separation (LLPS) in 2D and 3D environments. LLPS involves protein aggregation, forming droplets similar to water and oil mixing. Our model, based on stochastic chemical reaction networks defines all reaction rates using diffusion models. Importantly, our model captures the concept of the protein threshold number, crucial for droplet formation and varying with spatial dimensions. As a main result, we mathematically demonstrate how 2D and 3D LLPS can be qualitatively different using the stationary distribution. We analyzed the different in terms of the droplet viscosity and the minimum size of droplets experimental outcomes. Our model sheds light on LLPS processes.

Presenter : Irmak Özgüç

Title : Pfaffian methods for two dimensional Ising model, dimer statistics and phase transition:

Abstract :

There are many exact solutions of the two dimensional Ising model. For the 100th year of the first solution of the model, we investigate several of these solutions and write them more clearly so they can be more accessible. Here, we investigate Kasteleyn's method of computing partition functions of Onsager's lattice, who discovered that the partition function of the two dimensional Ising model with H=0 was related to a combinatorial problem about dimers. We investigate non-ideal thermodynamic properties of liquids composed of varying-sized components with zero energy of mixing in the context of a regular space lattice, which is called an "arrangement problem". We are intrested in the combinatorial problem of a two-dimensional quadratic lattice covered completely with dimers, i. e., in terms of graph theory, we look for the number of "perfect matchings" of the lattice. We also investigate the relation between this problem and another combinatorial problem connected with the Ising model of cooperative phenomena.

Presenter : Hyun Kim

Title : scLENS: Overcoming signal distortion and bias in scRNA-seq data analysis through data-driven dimensionality reduction

Abstract :

Single-cell RNA sequencing (scRNA-seq) data is characterized by high dimensionality and noise, making it challenging to extract biologically meaningful signals. While various dimensionality reduction tools have been developed to address this issue, most require manual determination of the signal dimension, potentially introducing user bias. Additionally, log normalization, a common preprocessing step, can unintentionally distort the signals in the data. To overcome these challenges, we developed scLENS, a tool that accurately captures biological signals from scRNA-seq data while minimizing user bias and signal distortion. By integrating L2 normalization into the preprocessing step, scLENS effectively addresses the primary cause of signal distortion resulting from log normalization. Furthermore, scLENS employs random matrix theory-based noise filtering and a signal robustness test to determine the data-driven threshold for the dimension of signals. We compared scLENS to 11 widely used dimensionality reduction tools and found that it outperformed them, particularly for scRNA-seq data with high sparsity and variability. To facilitate the use of scLENS, we have developed a user-friendly package that automates the accurate detection of signals from scRNA-seq data, eliminating the need for manual, time-consuming parameter tuning.

Presenter : Minjin Kim

Title : Assessing the transmission potential of mpox in East Asia during 2022-2023: A focus on Taiwan, China, Japan, and South Korea

Abstract :

This study aims to estimate the transmission potential of mpox in East Asia, focusing on the hardest-hit nations: Taiwan, China, Japan, and South Korea. We utilized six phenomenological dynamic growth models to fit the case incidence during the initial 30 epidemic days. The best-fit model was selected to calculate the reproduction number. Additionally, we used the latest case data and a Bayesian framework to compute the instantaneous effective reproduction number by applying the Cori et al. method. During the early phase, China demonstrated the highest estimated reproduction number of 2.89 (95% confidence interval (CI): 1.44–3.33); followed by South Korea, 2.18 (95% CI: 0.96–3.57); Japan, 1.73 (95% CI: 0.66–3.94); and Taiwan, 1.36 (95% CI: 0.71–3.30). However, by June 30, 2023, estimated reproduction number dropped below 1 in all countries: China at 0.05 (95% credible interval (CrI): 0.02–0.10), Japan at 0.32 (95% CrI: 0.15–0.59), South Korea at 0.23 (95% CrI: 0.11–0.42), and Taiwan at 0.41 (95% CrI: 0.31–0.53), indicating the potential decline of the outbreak. Our analysis shows effective containment by each country. It is crucial to sustain the effective management to ensure the ultimate eradication of the outbreak.

Presenter : Dae Wook Kim

Title : Wearable Data Assimilation to Estimate the Circadian Phase

Abstract :

The circadian clock is an internal timer that coordinates the daily rhythms of behavior and physiology, including sleep and hormone secretion. Accurately tracking the state of the circadian clock, or circadian phase, holds immense potential for precision medicine. Wearable devices present an opportunity to estimate the circadian phase in the real world, as they can non-invasively monitor various physiological outputs influenced by the circadian clock. However, accurately estimating circadian phase from wearable data remains challenging, primarily due to the lack of methods that integrate minute-by-minute wearable data with prior knowledge of the circadian phase. To address this issue, we propose a framework that integrates multi-time scale physiological data and estimates the circadian phase, along with an efficient implementation algorithm based on Bayesian inference and a new state space estimation method called the level set Kalman filter. Our study provides a foundation for systematically understanding the real-world dynamics of the circadian clock.

Presenter : Hyukpyo Hong

Title : Inferring delays in partially observed gene regulation processes

Abstract :

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. We develop a simulation-based Bayesian MCMC method 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. Our method is scalable and can be used to analyze other non-Markovian models with hidden components.

Presenter : Minjin Kim

Title : Assessing the transmission potential of mpox in East Asia during 2022-2023: A focus on Taiwan, China, Japan, and South Korea

Abstract :

This study aims to estimate the transmission potential of mpox in East Asia, focusing on the hardest hit nations: Taiwan, China, Japan, and South Korea. We utilized six phenomenological dynamic growth models to fit the case incidence during the initial 30 epidemic days. The best-fit model was selected to calculate. Additionally, we used the latest case data and a Bayesian framework to compute the instantaneous effective reproduction number by applying the Cori et al. method. During the early phase, China demonstrated the highest estimated reproduction number of 2.89 (95% CI: 1.44-3.33); followed by South Korea, 2.18 (95% CI: 0.96-3.57); Japan, 1.73 (95% CI: 0.66-3.94); and Taiwan, 1.36 (95% CI: 0.71-3.30). However, by June 30, 2023, estimated reproduction number dropped below 1.00 in all countries: China at 0.05 (95% credible interval [CrI]: 0.02-0.10), Japan at 0.32 (95% CrI: 0.15-0.59), South Korea at 0.23 (95% CrI: 0.11-0.42), and Taiwan at 0.41 (95% CrI: 0.31-0.53), indicating the potential decline of the outbreak. Our analysis shows effective containment by each country. It is crucial to sustain effective management to ensure the ultimate eradication of the outbreak.

Presenter : Juseong Kim

Title : Understanding the filoviral entry efficiency by an epidemic spreading model

Abstract :

The Filovirus, known for its hemorrhagic fever symptoms and high fatality rates, poses a significant threat, as evident from past outbreak cases. Research findings the crucial role of NPC1, a cellular cholesterol transporter, in the spread of this virus. However, there is a lack of quantitative understanding regarding the impact of structural changes in NPC1 due to single nucleotide polymorphisms (SNPs) on virus infection rates. To address this, we constructed an agent-based SEIR model to quantitatively evaluate the impact of SNPs on infection rates and compared it with experimental plaque analysis. Allowing comparison with experimental data, we provide a quantitative understanding of the variation in infection rates due to the mutation in NPC1. We also contributing to the development of targeted therapeutic strategies in computational biology.

Presenter : Casey Diekman

Title : Inferring Parameters of Pyramidal Neuron Excitability in Mouse Models of Alzheimer’s Disease Using Biophysical Modeling and Deep Learning

Abstract :

The poster is focused on a Deep Hybrid Modeling (DeepHM) framework that combines deep learning with mechanistic modeling. Although mechanistic modeling and machine learning methods are both powerful techniques for approximating biological systems and making accurate predictions from data, when used in isolation these approaches suffer from distinct shortcomings. Model and parameter uncertainty limit mechanistic modeling, whereas machine learning methods disregard the underlying biophysical mechanisms. DeepHM addresses these shortcomings and can identify the distributions of mechanistic modeling parameters coherent to the data. We employed DeepHM to identify which ionic conductances are responsible for the altered excitability properties of CA1 pyramidal neurons in mouse models of Alzheimer’s disease.

Presenter : Venkata Sai Prasanna Chigicherla

Title : Spatial heterogeneity in tumor adhesion qualifies collective cell invasion.

Abstract :

Collective cell invasion (CCI), a canon of most invasive solid tumors, is an emergent property of the interactions between cancer cells and their surrounding extracellular matrix (ECM). However, tumor populations invariably consist of cells expressing variable levels of adhesive proteins that mediate such interactions, disallowing an intuitive understanding of how tumor invasiveness at a multicellular scale is influenced by spatial heterogeneity of cell-cell and cell-ECM adhesion. Here, we have used a Cellular Potts model-based multiscale computational framework that is constructed on the histopathological principles of glandular cancers. In earlier efforts on homogenous cancer cell populations, this framework revealed the relative ranges of interactions, including cell-cell and cell-ECM adhesion that drove collective, dispersed, and mixed multimodal invasion. Here, we constitute a tumor core of two separate cell subsets showing distinct intra- and inter-subset cell-cell or cell-ECM adhesion strengths. These two subsets of cells are arranged to varying extents of spatial intermingling, which we call the heterogeneity index (HI). We observe that low and high inter-subset cell adhesion favors invasion of high HI and low HI intermingled populations with distinct intra-subset cell-cell adhesion strengths, respectively. In addition, for explored values of cell-ECM adhesion strengths, populations with high HI values collectively invade better than those with lower HI values.

Presenter : Hotaka Kaji

Title : Output system can reduce fluctuations

Abstract :

Biological oscillators, like circadian rhythms, achieve remarkable precision despite the presence of noise from both internal and external sources. The mechanism by which such precision is maintained is not fully understood, though studies have indicated that oscillator synchronization can decrease period variability (Kori et al. JTB 2012) Moreover, choosing the correct output signals has been linked to more accurate oscillations (Mori & Mikhailov PRE 2016). Mori & Kori suggested that analyzing the variability in periods can also shed light on the coupling strength among synchronized oscillators (Mori & Kori PNAS 2022), typically measured by the coefficient of variation (CV)—the standard deviation of the periods divided by the average of those periods. Experimentally, the periods of these oscillations and their variations are tracked via output systems, which include methods like bioluminescence and fluorescence reporting systems. For instance, Li et al. (Li et al. PNAS 2020) demonstrated the use of a reporter system driven by a clock-controlled promoter affecting the expression of the luciferase gene, which then manifests as daily bioluminescent rhythms. The effect of these output systems on the precision of the oscillations is not yet fully understood. This study introduced a simple mathematical model composed of a feedback oscillator coupled to an output system. Through numerical analysis, we investigated the extent of fluctuations present in both the oscillator and its output. Our results revealed that the transmitted fluctuations are dependent on the protein degradation rate in the output. Additionally, by the theory of analytically obtaining periodic fluctuations of autonomous oscillators [2], we demonstrated that the stochastic variations intrinsic to biological clocks can be managed by appropriately designing the output system. Employing the theoretical constructs established, we introduce a design principle for a universal function aimed at regulating fluctuation, enhancing the precision of biological timekeeping mechanisms.

Presenter : Alan Lindsay

Title : Robustness in cellular signaling through extreme statistics with applications to chemotaxis.

Abstract :

Cells must reliably coordinate responses to noisy external stimuli for proper functionality. In this talk I will present a perspective on this important problem via extreme statistics. The central premise is that when a single stochastic process exhibits large variability (unreliable), the extrema of multiple processes has a remarkably tight distribution (reliable). In this poster I will present some background on extreme statistics followed by specific applications to directional sensing - the process in which cells acquire a direction to move towards a target. In both cases, we find that extreme statistics provide new insights and corroborate experimental observations.

Presenter : Sol Kim

Title : Cost-effectiveness Analysis of Varicella and Herpes Zoster Vaccination in South Korea: A Mathematical Modeling Study

Abstract :

This study assesses the impact of introducing zoster vaccines (ZVL or RZV) for adults alongside a potential two-dose varicella vaccination schedule for children in South Korea. Analyzing four strategies targeting 60-year-olds, with or without a second varicella dose for 4-year-olds, cost-effectiveness was evaluated using a deterministic compartment model over 50 years. Results show that while RZV reduces disease burden and increases QALY gains, ZVL remains more cost-effective initially due to lower costs. However, RZV becomes more cost-effective at higher willingness-to-pay levels (>60.9 million KRW). These findings offer insights for policymakers in formulating optimal vaccination strategies in South Korea.

Presenter : Yeonji Seo

Title : Analyzing the spreading patterns of COVID-19 by temporal motif

Abstract :

The epidemic spread over time, so the epidemic data is appropriate for presentation as a time series. The time series data can be represented in the form of a temporal network comprising nodes and events. The temporal motifs are patterns in the occurrence of events in temporal networks. In this study, we use temporal motifs to analyze the regional spread patterns of COVID-19 in Republic of Korea. The dataset we used is information about COVID-19 confirmed cases in Republic of Korea. The dataset includes information about the residence of the confirmed cases, the reported date, and the infector-infectee pair. A residence denotes each node, and events are the infection events between the infector and the infectee residing in the same or a different residence in the temporal network. We consider up to 3 events temporal motifs in the event sequence. The motifs represented by the one event indicate the occurrence of inter-regional and intra-regional infections. The 2-event temporal motifs indicate an infection pattern involving up to three regions as connected with 2 events. We consider two types of 3-event temporal motifs, namely the big-out star motif and the big-in-star motif. The former represents the spread of infection from the center node, while the latter represents the center node become targeting of infection. Finally, we obtain the following findings. First, the 3-event motifs are observed dominantly in the increasing number of confirmed cases. Second, when the epidemic spreads widely, occurrences of 3-node motifs tend to increase. Third, the 1-event motifs can be related to the timing of the COVID-19 spreading nationwide. Lastly, the center nodes in big-out-star and big-in-star spreading patterns are mostly situated in populous regions. These findings can identify patterns that affect the epidemic spreading and might help mitigate it.

Presenter : 김태홍/Taehong Kim

Title : Total Quasi Steady State Approximation for Identical Bisubstrate Enzymes

Abstract :

Typically, Hill kinetics is used to analyze the kinetics of bisubstrate enzymes with identical substrates. However, since Hill kinetics is based on the standard quasi-steady state approximation (sQSSA), it shows unreliable behavior at high enzyme concentrations. Thus, we suggest an alternative model based on total quasi-steady state approximation (tQSSA), where the slow manifold is given as a cubic equation between the concentration of the enzyme-substrate complex and the total substrate concent

Presenter : 차재윤 (Jaeyun Cha)

Title : Total Quasi Steady State Approximation for Identical Bisubstrate Enzymes

Abstract :

Presenter : Gugyoung Kim

Title : Oscillating synchronization order parameter of the Kuramoto model with inertia

Abstract :

Coupled oscillators with inertia are commonly observed in a variety of natural systems, including biological rhythms, brain waves, and power grid systems with alternating current. The governing equations of these systems are often described by second-order Kuramoto models. The distribution of natural frequencies, representing the interplay between power demand and generation in power-grid systems or the intrinsic rhythms generated by cells, significantly influences the synchronization stability of their respective systems. It has been well known that hysteresis in the second-order Kuramoto model manifests itself with accompanying the discontinuous transition for the uniform and Lorentzian distributions of the natural frequency. In addition, the previous research has discovered that the secondary synchronization groups of the whirling oscillators at large inertia emerge irregularly when the coupling strength $K$ increases. In this study, we investigate the region of $K$ where the secondary group appears, with the natural frequency distributed from the normal distribution (having the fatter tails than the previous Lorentzian one), together with considering the initial condition dependency. We find that the standard deviation of the synchronization order parameter $r$ plays an important role in detecting the emergence of the secondary groups. The large deviation implies the existence of the giant cluster of the synchronization and the small but nonnegligible clusters. With the aid of an appropriate visualization, we confirm the existence of the globally synchronized and desynchronized oscillators (which are the ordinary classification) and secondary synchronized groups with different angular velocity. At low $K$ and high $K$ with a small deviation of $r$, either the desynchronized or global synchronized state is observed without the secondary group. At an intermediate $K$ with a large deviation of $r$, the secondary groups can be detected. We expect that the multiple formations of synchronization groups will contribute to understanding the problems that arise in many applications dealing with synchronization phenomena in real world.

Presenter : Sanjeev Kumar

Title : Mathematical Models and Analysis of Growing Tumor and Treatments with Chemotherapy and Immunotherapy

Abstract :

Mathematical models have various techniques for cancer therapy such as virotherapy, immunotherapy, chemotherapy, radiotherapy, drug and vaccine therapy and many other scientific solutions to analyze the dynamics of cancer cells. Mathematical models help to analyze the behavior of tumor and these mathematical models are designed by ordinary differential equations and solved by a system of equations. This system also includes the interaction between growing tumor cells and the host immune system help to understand the dynamics of tumor growth cells and cells in the immune system including natural killer cells, dendritic cells, and cytotoxic CD8+ T cells combined with drug and vaccine intervention to these cells. This model of a control function represents the application of natural killer cells combined with CD8+ T cell treatment to the system. The numerical solutions are obtained from Runge-Kutta’s 4th-ordered method. Some external terms are used that help to control tumor growth and these term also help with drug and vaccine intervention. The graphical results help to analyze the cell’s growth, decreasing cells after adding external terms, and control by drug and vaccine.

Presenter : 김보연 (Boyeon Kim)

Title : Evaluating the Impact of Chemoprophylaxis Discontinuation on Malaria in the Republic of Korea Army: A Mathematical Modeling Study

Abstract :

Since the re-emergence of P. vivax malaria in Korea in 1993, there has been a significant rise in the number of civilian and military cases. Chemoprophylaxis was introduced in 1997 in response to the rapid increase in malaria cases. After these efforts, P.vivax malaria was diagnosed in 41 (10.6%) military patients in 2020, a significant drop from 180 (29.9%) in 2016. This change underlines the need to assess chemoprophylaxis's ongoing impact and effectiveness. We built a mathematical model to simulate different scenarios, including the continuation and discontinuation of chemoprophylaxis. It employs two parameter estimation approaches, Maximum Likelihood Estimation (MLE) and Bayesian Estimation, to calibrate the model to data. Our cost-benefit analysis explores the financial and health implications of various chemoprophylaxis strategies. The results indicate that maintaining the current chemoprophylaxis coverage at 55% or restoring it to the 2021 level of 100% is more beneficial than stopping it altogether. In addition, we conducted uncertainty quantification to address the stochasticity of malaria transmission. This comprehensive evaluation highlights the importance of strategic decisions in malaria control and chemoprophylaxis's effectiveness in reducing the disease's incidence among the military.

Presenter : Daniel Glazar

Title : A joint model of T2/FLAIR tumor volume dynamics and progression-free survival to make individual dynamic predictions for patients with recurrent high-grade glioma

Abstract :

Introduction Patients with recurrent high-grade glioma (rHGG) have poor prognosis with median progression-free survival (PFS) and overall survival (OS) of <6 and <12 months, respectively. However, there is wide heterogeneity in responses to treatment, suggesting a clinical need for prognostic models to aid clinicians as clinical decision tools for protocol personalization. Bayesian data analysis can exploit individual patient follow-up to dynamically predict risk of progression and suggest adaptive follow-up and treatment protocol tailored to the individual patient. Materials & Methods We developed a joint model describing tumor response dynamics and PFS for rHGG patients. The developed model was then calibrated to longitudinal tumor volumes delineated from T2/FLAIR MRIs and interval-censored time-to-progression (TTP) of 52 rHGG patients. We performed a leave-one-out cross validation (LOOCV) to predict patient-specific PFS across landmark times and time horizons. Individual dynamic predictions of PFS were evaluated using area under the receiver operating characteristics curve (AUC) and Brier score (BS). Comparisons were made with a null Cox proportional hazards (CPH) model. Results The developed joint model recapitulated patient-specific tumor response dynamics well with R2=0.87. In a LOOCV, individual dynamic predictions of PFS with time horizon to the next observed MRI performed with 7.2% improvement in AUC, but 7.6% drop in BS compared to the null CPH model. Setting different time horizons to 60, 90, and 120 days led to predictive performances of 14.9–16.7% improvement in AUC and 1.2% drop to 1.9% improvement in BS, compared to the null CPH model. Conclusion Here, we developed, calibrated, and evaluated a joint model to dynamically predict patient-specific T2/FLAIR tumor volume and PFS of rHGG patients. Potential directions for future research include inclusion of competing risks (e.g., new lesion, clinical deterioration, increase in enhancing volume), prospective evaluation on an external cohort, and propagation of uncertainty in population parameters.

Presenter : Torkel Loman

Title : Catalyst: Fast and Flexible Modeling of Reaction Networks

Abstract :

We introduce Catalyst.jl, a flexible and feature-filled Julia library for modeling and high-performance simulation of chemical reaction networks (CRNs). Catalyst supports simulating stochastic chemical kinetics (jump process), chemical Langevin equation (stochastic differential equation), and reaction rate equation (ordinary differential equation) representations for CRNs. Through comprehensive benchmarks, we demonstrate that Catalyst simulation runtimes are often one to two orders of magnitude faster than other popular tools. More broadly, Catalyst acts as both a domain-specific language and an intermediate representation for symbolically encoding CRN models as Julia-native objects. This enables a pipeline of symbolically specifying, analyzing, and modifying CRNs; converting Catalyst models to symbolic representations of concrete mathematical models; and generating compiled code for numerical solvers. Leveraging ModelingToolkit.jl and Symbolics.jl, Catalyst models can be analyzed, simplified, and compiled into optimized representations for use in numerical solvers. Finally, we demonstrate Catalyst’s broad extensibility and composability by highlighting how it can compose with a variety of Julia libraries, and how existing open-source biological modeling projects have extended its intermediate representation.