Program

Program

12/5(Mon)

Chair: Yuji Hirono

  • 14:30 - 15:10 Cheol-Min Ghim (UNIST)

    • Title: Michaelis-Menten and Beyond: New Insights from Old Wisdom

    • Abstract: Michaelis-Menten (MM) kinetics, sharing its root with other adiabatic approximation schemes such as Born-Oppenheimer or Frank-Condon, has been the de facto standard analytical framework for enzymatic reactions. Despite the popularity and intuitive interpretation for a wide range of applications in biochemistry, biophysics, cell biology, and chemical engineering, the MM rate law and its modified forms stand on the quasi-steady state assumption, which is not necessarily justified under active changes in molecular concentration over time. By relaxing this constraint, I will discuss the generalized rate law where the effective time delay in molecular complex formation provides a key insight into the reaction dynamics. This scheme consistently improves the prediction and understanding of various biochemical processes with transient or rhythmic dynamics, opening a new avenue of applicability beyond the steady state-based approaches.

  • 15:30 - 16:10 Jinsu Kim (POSTECH)

    • Title: Complex balancing and stationary distributions of stochastically modeled reaction networks

    • Abstract: A reaction network is a graphical configuration that can describe many biochemical systems with interactions between species (molecules). If the abundances of the species involved in a reaction network are small, then the randomness inherent in the molecular interactions is important to the system dynamics, and the abundances are modeled stochastically as a jump-by-jump fashion continuous-time Markov chain. In this talk, we will discuss two approaches for exploring stationary distributions of the Markov chains associated with biochemical reaction networks: algebraic and analytic approaches. Especially for the algebraic approach of deriving a closed form of stationary distributions for a stochastic reaction network, we often employ complex balanced steady states of deterministic counterparts. We will discuss how these two models are linked through complex balanced steady states.

  • 16:30 - 17:10 Kevin Thurley (University Hospital Bonn)

    • Title: Towards data-driven mathematical analysis of cell-cell communication in the mammalian immune response

    • Abstract: Cell-to-cell communication networks have critical roles in coordinating diverse organismal processes, such as tissue development or immune cell response. In particular, cytokine-driven differentiation of Th cells into the well-known Th1, Th2, Tfh subtypes, contain multi-layered regulatory circuits in terms of interaction by diffusible ligands. Compared with intracellular signal transduction networks, the function and engineering principles of cell-to-cell communication networks are far less understood. Major complications include: cells are themselves regulated by complex intracellular signaling networks; individual cells are heterogeneous; and importantly, cells are subject to proliferation and cell death, and often show exponential growth at the onset of an immune response. In this talk, I will outline the challenges on the way to data-driven models of immune-cell interactions, and describe our strategy to tackle those challenges. In recent work, we developed a data-annotated model of Th cell dynamics in LCMV infection in mice. Further, we derived measures characterizing cell-cell interaction dynamics in space, and we characterized transcriptomic signatures of cell-cell communication in autoimmune disease using a T cell perturbation protocol. Overall, we found that data-driven modeling and large-scale transcriptomic analysis of immune cell interaction dynamics can open new perspectives on key decision-making processes at the onset and chronification of an immune response.

12/6(Tue)

Chair: Cheol-Min Ghim

  • 10:30 - 11:10 Atsushi Mochizuki (Kyoto University)

    • Title: Biological function and functional module originated in structure of network

    • Abstract: In living cells, chemical reactions are connected by sharing their products and substrates, and form complex network systems. It is considered that control of biological functions are realized by changes in amount/activities of enzymes mediating reactions. In this talk, I present novel mathematical theories to determine behaviors of chemical reaction systems upon changes in amount/activity of enzymes from network structure alone. We found that (1) qualitative responses of chemical concentrations (and reaction fluxes) upon parameter changes are determined from a network structure alone. (2) The nonzero responses are localized in finite extents in a network, and each of the extent is determined by a subnetwork called a "buffering structure". A buffering structure is defined from local topology of the network by an index analogous to the Euler characteristic. Any perturbation on a reaction parameter in a buffering structure does not influence concentrations and fluxes outside the buffering structure. Finally, (3) buffering structures govern the bifurcation of steady stats of reaction networks. The bifurcation behaviors are localized in finite extents in a network, and the extents are determined by buffering structures, again. These results suggest that the buffering structures may be the origin of the modularity in biological functions in network systems. We apply our method to some real networks, including cell-cycle or carbon metabolism systems, and demonstrate how behaviors of biological systems are understood from network structures.

  • 11:30 - 12:10 Yuji Hirono (APCTP/POSTECH)

    • Title: Simplifying complex chemical reaction networks

    • Abstract: Chemical reactions form a large web of networks inside living cells and they are responsible for physiological functions. Understanding the behavior of complex reaction networks is a challenging and interesting task. In this talk, I will introduce a systematic method for simplifying chemical reaction networks. We identify the structural condition under which a subnetwork can be eliminated without altering the steady-state properties of the remaining parts. The condition is solely determined by the structural information and is insensitive to the details of reactions, because of which the method is widely applicable. The techniques of homological algebra are found to be useful in deriving the result.

  • 14:30 - 15:10 Shinya Kuroda (The University of Tokyo)

    • Title: The roles of intra- and inter-cellular variations in cellular information transfer

    • Abstract: Multicellular organisms can adapt to the environment despite heterogeneous responses by individual cells. Heterogeneity in cellular responses has been regarded as noise that reduces accurate information transmission. Cellular heterogeneity consists of intracellular variation, referred to as “intrinsic” noise, which is caused by stochasticity of biochemical reactions, and of intercellular variation, “extrinsic” noise, which is caused by differences in amounts of molecules. I will talk
      1. Inter-cellular variation.
      We found that intercellular variation increases the gradualness of the multicellular dose-response, a phenomenon that we termed the “response diversity effect.” The result is an increase in the capacity of the system to transmit information. This response diversity effect is a previously unappreciated mechanism enabling multicellular organisms to use cell-to-cell variability as information, not noise.
      2. Intra-cellular variation.
      A dendritic spine is a very small structure (~0.1 µm3) of a neuron in our brain that processes input timing information. Why are spines so small that they can contain only small numbers of molecules and reactions inevitably become stochastic? We found that despite such noisy conditions, the spine exhibits robust information against noise transfer using the probability of Ca2+ increase, termed the “small-volume effect” which can be seen in the spine volume, but not in the cell volume. We propose that the small-volume effect is the functional reason why the spine has to be so small.

12/7(Wed)

Chair: Dimitri Loutchko

  • 10:30 - 11:10 Gheorghe Craciun (University of Wisconsin-Madison)

    • Title: Deterministic and stochastic models of reaction networks: persistence and global stability results inspired by thermodynamic principles

    • Abstract: The standard mathematical model for the dynamics of concentrations in biochemical reaction networks is called mass-action kinetics. We describe mass-action kinetics and discuss the connection between special classes of mass-action systems (such as detailed balanced and complex balanced systems) and the Boltzmann equation. We also discuss the connection between the "Global Attractor Conjecture" for complex balanced mass-action systems and Boltzmann's H-theorem.
      We also describe some implications for biochemical mechanisms that implement noise filtering and cellular homeostasis.

  • 11:30 - 12:10 Wasiur R. KhudaBukhsh (The University of Nottingham)

    • Title: Multiscale approximations in chemical reaction networks

    • Abstract: The talk will focus on a particular area of applied mathematics studying chemical reaction networks (CRNs) that describe creation, annihilation, combination or binding, and changes in the physical state of a collection of chemical species. Many prominent examples of intracellular dynamics, genetic switches, and dynamics of population interactions can be modelled by CRNs, where the interacting particles exhibit vastly different intrinsic scales in terms of abundance, or the reactions operate at different time scales varying over many orders of magnitude. The traditional deterministic approach to multiscale approximations used in such situations employs singular perturbation theory, often invoking Tikhonov’s theorem and Fenichel theory. In this talk, I will take a stochastic viewpoint and introduce, with the help of a number of examples, a probabilistic technique to derive multiscale approximations. The talk will be fairly nontechnical, and no prior knowledge biology is required.


Chair: Chuang Xu

  • 14:30 - 15:10 Jaekyoung Kim (IBS/KAIST)

    • Title: Modeling and Inference for Biological Systems with Hidden Components

    • Abstract: Despite dramatic advances in experimental techniques, many facets of intracellular dynamics remain hidden, or can be measured only indirectly. In this talk, I will describe strategies to develop mathematical models with hidden parts: replacement of hidden components with either time delay and quasi-steady-state. Then, I will illustrate how the simplification with the time delay can be used to understand the processes of protein synthesis, which involves multiple steps such as transcription, translation, folding and maturation, but typically whose intermediates proteins cannot be measured. Furthermore, I will illustrate how the simplification with the quasi-steady-state can be used to develop an accurate method to estimate drug clearance, which occurs in multiple steps of metabolism, which greatly improved the canonical approach used in more than 65,000 published papers for last 30 years. Finally, I will describe an inference method, GOBI (General Model-based Inference), that identifies hidden regulatory biochemical connections from timeseries data. This method adopts the advantage of model-free inference methods (broad applicability) and model-based inference methods (accuracy).

  • 15:30 - 16:10 Ugur Cetiner (Harvard medical school)

    • Title: Reformulating non-equilibrium steady-states and generalised Hopfield discrimination

    • Abstract: Despite substantial progress in non-equilibrium physics, steady-state (s.s.) probabilities remain intractable to analysis. For a Markov process, s.s. probabilities can be expressed in terms of transition rates using the Matrix-Tree theorem (MTT) in the graph-based linear framework. The MTT reveals that, away from equilibrium, s.s. probabilities become globally dependent on all rates, with expressions growing exponentially in the system size. This overwhelming complexity and lack of thermodynamic interpretation have greatly impeded analysis. Here, we show that s.s. probabilities are proportional to the average of exp(−S(P)), where S(P) is the entropy generated along minimal paths, P, in the graph, and the average is taken over a probability distribution on spanning trees. Assuming Arrhenius rates, this "arboreal" distribution becomes Boltzmann-like, with the energy of a tree being its total edge barrier energy. This reformulation offers a thermodynamic interpretation that smoothly generalises equilibrium statistical mechanics and reorganises the expression complexity: the number of distinct minimal-path entropies depends on the entropy production index, a new graph-theoretic measure of non-equilibrium complexity, not on graph size. We demonstrate the power of this reformulation by extending Hopfield's analysis of discrimination by kinetic proofreading to any graph with index 1. We derive a general formula for the error ratio and use it to show that local energy dissipation can yield optimal discrimination through global synergy.

  • 16:30 - 17:10 Ryusuke Hamazaki (RIKEN)

    • Title: Speed limits in nonequilibrium dynamics — From population biology to macroscopic quantum transitions —

    • Abstract: Speed of state transitions is a crucial concept for understanding nonequilibrium dynamics in nature. While extensive studies investigated fundamental bounds for such speed, i.e., speed limits, they were mainly limited to linear dynamics and small systems. In this talk, I present new types of speed limits that are relevant for (i) nonlinear population dynamics and (ii) macroscopic transitions.
      In the first part, we show that a speed limit based on classical Fisher information is obtained for the proportion of types in general nonlinear population dynamics [1]. We argue that our speed limit is regarded as a generalization of Fisher's fundamental theorem of natural selection in evolution theory. Furthermore, we find a critical scaling form of the speeds near a bifurcation, a unique phenomenon in nonlinear dynamics. We discuss that the associated critical exponents have nontrivial bounds that are dependent only on the bifurcation structure.
      In the second part, we show useful speed limits for macroscopic transitions [2], where the conventional speed limits become divergent and meaningless. We derive a convergent tighter bound employing the local conservation law of probability: it is described by the gradient term of the observable and the probability current. We apply our speed limit to classical stochastic systems to provide a bound based on the entropy production rate, which is better than the previous literature. We finally discuss how our framework can be applied to quantum macroscopic transitions.
      [1] K. Adachi, R. Iritani, and R. Hamazaki, Communications Physics 5 (1), 1-7 (2022).
      [2] R. Hamazaki, PRX Quantum 3 (2), 020319 (2022).

12/8(Thu)

Chair: Atsushi Mochizuki

  • 10:30 - 11:10 Radek Erban (University of Oxford)

    • Title: Chemical Reaction Networks: Systematic Design, Noise Control and Limit Cycles

    • Abstract: Chemical reaction networks describe interactions between biochemical species. Two types of mathematical models of reaction systems will be considered: (i) deterministic models which are written in terms of reaction rate equations (i.e. ordinary differential equations (ODEs) for concentrations of biochemical species involved); and (ii) stochastic models of reaction networks, given in terms of the Gillespie stochastic simulation algorithm, which provides more detailed information about the simulated system than ODEs. I will discuss methods for systematic design of relatively simple reaction systems with exotic dynamical behaviour, including applications to synthetic biology and DNA computing. Considering deterministic models of reaction networks, I will present examples of reaction systems with multiple oscillating solutions or systems whose deterministic models (based on reaction rate equations) undergo specific bifurcations. Since reaction networks in biological applications often involve species at low-copy numbers, stochastic effects may become a significant part of the dynamics. In such circumstances, tools for controlling the intrinsic noise in the system are needed for a successful network design. To this end, the so-called noise control algorithm will be presented. The algorithm structurally modifies any given reaction network under the mass action kinetics, in such a way that controllable state-dependent noise is introduced into the stochastic dynamics, while the deterministic dynamics (based on reaction rate equations) are preserved. I will present reaction networks with noise-induced oscillations and multi-stability.
      References:
      [1] Radek Erban and Hye Won Kang, "Chemical Systems with Limit Cycles", submitted, available as https://arxiv.org/abs/2211.05755 (2022)
      [2] Radek Erban and S. Jonathan Chapman, "Stochastic Modelling of Reaction-Diffusion Processes", Cambridge Texts in Applied Mathematics, Cambridge University Press (2020)
      [3] Tomislav Plesa, Konstantinos Zygalakis, David Anderson and Radek Erban, "Noise control for molecular computing", Journal of the Royal Society Interface, Volume 15, Number 144, 20180199 (2018)

  • 11:30 - 12:10 Chuang Xu (The University of Hawaiʻi at Mānoa)

    • Title: Structural classification of stochastic reaction networks with applications

    • Abstract: Many real-world phenomena are modelled as reaction networks, ranging from molecular biology, chemistry, biophysics, genetics and social sciences. When molecule counts of species are in low copy numbers, reaction networks are modelled as continuous time Markov chains (CTMCs), and termed as stochastic reaction networks. In practice, parameters in a reaction system are usually unknown. One can use a directed graph, so-called reaction graph, to represent a reaction network. A fundamental question in reaction network theory is to deduce qualitative dynamics of a reaction network purely from the associated reaction graph independent of the reaction parameters. In order to capture the dynamics of a stochastic reaction network, it demands to first analyze the underlying structure of the state space of CTMCs whose Q-matrix in common is generated from a stochastic reaction network. In this talk, I will introduce the recent work on classification of states of stochastic reaction networks with applications to some biological systems. This talk is based on a joint work with Mads C. Hansen and Carsten Wiuf.


Chair: Jinsu Kim

  • 14:30 - 15:10 Tetsuya J. Kobayashi (The University of Tokyo)

    • Title: Information Geometry of Equilibrium and Nonequilibrium Chemical Reaction Networks

    • Abstract: Cells are the basic units of all living things, and their functions are realized by circuits and networks of chemical reactions. Understanding the mechanism of how various cellular functions are implemented by chemical reaction networks (CRN) is the central challenge in biophysics and quantitive biology. Among various aspects of CRN, its thermodynamic property is particularly important because most of the biological functions are energy-consuming nonequilibrium phenomena. However, even though the equilibrium chemical thermodynamics and kinetics of chemical reactions were founded more than one century ago, the nonequilibrium theory of CRN is still immature. One reason is the nonlinearity in the constitutive equation between chemical force and flux, which prevents us from associating the tangent and cotangent spaces of the dynamics with the usual inner product structure.
      In this work, we employ the fact that the nonlinear relation between chemical force and flux can be captured by Legendre transformation induced by the dissipation function (1). By combining another Legendre duality between molecular densities and chemical potential spaces (2,3), the equilibrium and nonequilibrium CRNs are characterized and also generalized by the generalized gradient and non-gradient flow defined on the two Legendre dual spaces linked by the algebraic structure of CRN. The geometry of the generalized flow can be effectively grasped by information geometry, the geometry of the convex Legendre duality. We show how equilibrium and nonequilibrium aspects of CRNs can be dissected by the generalized Helmholtz projections in information geometry (4). We mention the relation of this geometric structure to Otto calculus in Wasserstein geometry, network thermodynamics, and discrete differential form (4). If possible, we want to discuss potential applications of this structure not only for CRN but also for other phenomena and problems (5,6).
      (1) T.J. Kobayashi et al, Hessian Geometry of Nonequilibrium Chemical Reaction Networks and Generalized Entropy Production Decompositions, Phys. Rev. Res. 033208, (2022)
      (2) Y.Sughiyama et al, A Hessian Geometric Structure of Chemical Thermodynamic Systems with Stoichiometric Constraints, Phys. Rev. Res, 033065, (2022)
      (3) T. J. Kobayashi et al, Kinetic Derivation of the Hessian Geometric Structure in Chemical Reaction Systems, Phys Rev. Res, 033066, (2022)
      (4) T. J. Kobayashi et al, Information Geometry of Dynamics on Graphs and Hypergraphs , arXiv:2211.14455, (2022)
      (5) Y.Sughiyama et al, Chemical thermodynamics for growing systems, Phys. Rev. Res., 033191 (2022)
      (6) D. Loutchko et al, Riemannian Geometry of Optimal Driving and Thermodynamic Length and its Application to Chemical Reaction Networks, Phys Rev. Res., 043049 (2022).

  • 15:30 - 16:10 Jinwoo Jang (POSTECH)

    • Title: Kinetic Models for Semiflexible Polymers in a Half-plane

    • Abstract: In this talk, we introduce a derivation of a kinetic equation for semi-flexible polymers. The equation describes the limiting behavior of a N-segment discrete chain via the continuum-limit. In the half-plane, we also present a formal derivation of the trapping boundary condition by assuming the energy-minimizing transition of a segment at the boundary.

  • 16:30 - 17:10 Kyemyung Park (UNIST)

    • Title: How do T cells distinguish self vs. non-self?: reconciling microscopic randomness and macroscopic determinism through multiscale regulations

    • Abstract: T cells provide effective host protection while limiting autoimmunity. The genetic loci of T cell receptors (TCR) responsible for recognizing peptide antigens undergo random rearrangement during T cell maturation, giving rise to a diverse TCR repertoire. Self-reactive T cells are thought to be removed through thymic selections, and some of them are differentiated to regulatory T cells (Tregs) with immune suppressive phenotypes to ensure immune homeostasis (being reactive to foreign antigens yet tolerant to self-antigens). However, accumulating evidence suggests that a sizable fraction of peripheral conventional T cells (Tconvs) can be activated in response to self-antigens presented by peripheral dendritic cells. These self-activated T cells are typically suppressed by Tregs. Separate lines of evidence illustrate that the peripheral maintenance of a homeostatic Treg population in secondary lymphoid organs (SLOs) is dependent on a cytokine, IL-2, and a major source of IL-2 is likely these self-activated CD4+ Tconvs. These findings illustrate that we still lack an integrated quantitative understanding encompassing the inevitable leakage of self-reactive T cells out of the molecular and cellular random processes and the formation of robust decision boundaries between tolerance and the full-blown response of T cells. Here, utilizing multiscale modeling approaches, I propose a view that the peripheral self-reactivity of T cells is indeed an integral part of immune homeostasis, ensuring a dynamical equilibrium between self-activated T cells and Tregs, typically operating well below thresholds that could result in clonal expansion and subsequent autoimmunity. This exemplifies how a biological system suffering/utilizing random noises at the microscopic scale eventually achieves robust and predictable physiologic behavior at the macroscopic level through multiscale regulations, yet sometimes goes awry, causing diseases.

12/9(Fri)

Chair: Jaekyoung Kim

  • 11:00 - 12:00 George Sugihara (Scripps Institution of Oceanography) (online, jointly hosted with IBS Biomedical Math Online Colloquium)

    • Title: Taming Complexity in Data-Limited Nonlinear Nonequilibrium Settings

    • Abstract: Since before the time of Aristotle and the natural philosophers, reductionism has played a foundational role in western scientific thought. The premise of reductionism is that systems can be broken down into constituent pieces and studied independently, then reassembled to understand the behavior of the system as a whole. It embodies the classical linear perspective. This approach has been successful in developing basic physical laws and especially in engineering where linear analysis dominates and systems are purposefully designed that way. However, reductionism is not universally applicable for natural complex systems where behavior is driven, not by a few factors acting independently, but by complex interactions between many components acting together and changing in time.
      Nonlinearity in living systems means that its parts are interdependent – variables do not act in a mutually independent manner; rather they interact, and as a consequence associations (correlations) between them will change as the overall system context (state) changes. This problem is highlighted when extrapolating the results of single-factor experiments to nature, and surely contributes to the frustrating disconnect between experimental findings and clinical outcomes in drug trials. Indeed, while everyone knows Berkeley’s 1710 dictum “correlation does not imply causation” few realize that for nonlinear systems the converse “causation does not imply correlation” is also true. This conundrum runs counter to deeply ingrained heuristic thinking that is at the basis of modern science. Biological systems (esp. ecosystems) are particularly perverse on this issue by exhibiting mirage correlations that can continually cause us to rethink relationships we thought we understood.
      Here we examine a minimalist paradigm, empirical dynamics (EDM), for studying non-linear systems and a method (CCM) that can detect causality when there is no correlation among variables. It is a data-driven approach that uses time series to study a system holistically by reconstructing its attractor – a geometric object that embodies the rules of a full set of equations for the system. The ideas are intuitive and will be illustrated with examples from genetics, ecology and epidemiology.

List of poster presentations

  • Seong-Gyu Yang (APCTP)

    • Title: The role of self-regulation in ecological systems

  • Jia Yin Lee (University of Nottingham)

    • Title: Pattern formation in a nonlocal Lotka-Volterra system

  • Dimitri Loutchko (The University of Tokyo)

    • Title: Riemannian Geometry of Chemical Reaction Networks and its Applications to Optimal Driving and Sensitivity

  • Federico Girotti (University of Nottingham)

    • Title: Concentration Inequalities for Output Statistics of Quantum Markov Processes

  • Yeongjin Kim (POSTECH)

    • Title: Active Diffusion of Self-Propelled Particles in a Flexible Polymer Networks

  • Atsuki Hishida (Kyoto University)

    • Title: Analyzing the effect of structural modification of chemical reaction networks on dynamics

  • Candan Celik (IBS)

    • Title: Attenuation of noise in a structured gene expression model

  • Hyukpyo Hong (IBS)

    • Title: Network translation allows for revealing long-term dynamics of stochastic reaction networks

  • Hyun Kim (IBS)

    • Title: Improved clustering algorithm on single-cell RNA seq data based on random matrix theory and clustering stability

  • Yuhei Yamauchi (Kyoto University)

    • Title: Independent regulation of the G1-S and G2-M transitions realized by topology of the cell cycle network

  • Seho Park (IBS)

    • Title: General model-based casual inference overcomes the curse of synchrony and indirect effect

  • Yun Min Song (IBS)

    • Title: Combined multiple transcriptional repression mechanisms generate ultrasensitivity and oscillations

  • Jinyoung Kim (POSTECH)

    • Title: Stochastic aggregation models in 2D and 3D spaces to describe Liquid-Liquid Phase Separation (LLPS)

  • Hyeontae Jo (IBS)

    • Title: Nonparametric inference method for intracellular signaling dynamics via deep learning

  • Seokjoo Chae (IBS)

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