# Schedule for: 20w5074 - Mathematical Models in Biology: from Information Theory to Thermodynamics (Online)

Beginning on Sunday, July 26 and ending Friday July 31, 2020

All times in Banff, Alberta time, MDT (UTC-6).

Monday, July 27
07:55 - 08:00 Introduction and Welcome by BIRS Staff
A brief welcome and introduction by BIRS Staff
(Online)
08:00 - 08:45 Udo Seifert: From Stochastic Thermodynamics to Thermodynamic Inference
Stochastic thermodynamics provides a universal framework for analyzing nano- and micro-sized non-equilibrium systems. Prominent examples are single molecules, molecular machines, colloidal particles in time-dependent laser traps and biochemical networks. Thermodynamic notions like work, heat and entropy can be identified on the level of individual fluctuating trajectories. They obey universal relations like the fluctuation theorem. Thermodynamic inference as a general strategy uses consistency constraints derived from stochastic thermodynamics to infer otherwise hidden properties of non-equilibrium systems. As a paradigm for thermodynamic inference, the thermodynamic uncertainty relation provides a lower bound on the entropy production through measurements of the dispersion of any current in the system. Likewise, it quantifies the cost of temporal precision for biomolecular processes and provides a model-free bound on the thermodynamic efficiency of molecular motors. For a review: U. Seifert, Annu. Rev. Condens. Matter Phys. 10, 171-192, 2019
(Online)
08:45 - 09:15 Open discussion
Moderated by Michael Hinczewski, Case Western Reserve University.
(Online)
09:15 - 09:25 break (Online)
09:30 - 10:15 Sarah Harvey: An Energy-Accuracy Tradeoff in Nonequilibrium Cellular Sensing
Single celled organisms possess extremely sensitive mechanisms for detecting external chemical concentrations through the binding of individual molecules to cell-surface receptors. Here, we combine stochastic thermodynamics, large deviation theory, and information theory to derive fundamental limits on the accuracy with which single receptors can detect external chemical concentrations through energy-consuming nonequilibrium processes. I will give an overview of these calculations, starting with estimation performed by an ideal observer of the entire trajectory of receptor states. We show that in this case, no energy consuming non-equilibrium receptor that can be divided into two pools of bound signaling and unbound non-signaling states can outperform a simple equilibrium two-state receptor. Next, I will discuss an energy-accuracy tradeoff for such general nonequilibrium receptors when the estimation is performed by a simple observation of the duration the receptor is bound. Our tradeoff reveals that the simple observer can only attain the performance of the ideal observer in the limit of large receptor energy consumption and size.
(Online)
10:15 - 10:45 Open discussion
Moderated by Michael Hinczewski (Case Western Reserve University)
(Online)
Tuesday, July 28
08:00 - 08:45 Massimiliano Esposito: Thermodynamics of Biochemical Reaction Networks: Information, Accuracy and Speed
After formulating a nonequilibrium thermodynamics for open chemical reaction networks, the theory will be applied to assess the thermodynamics performance of a dissipative self-assembly scheme. Power-efficiency and noise-dissipation trade-offs will be discussed.
(Online)
08:45 - 09:15 Open discussion
Moderated by Peter Thomas (Case Western Reserve University)
(Online)
09:15 - 11:15 Virtual poster sessions
Poster presenters should prepare 5-6 slides and a five-minute talk. Please submit title and abstract by July 20, 2020 at https://forms.gle/PU7MVZapEhdJU3C58. Ahead of the workshop, the organizers will distribute a list of poster titles and abstracts. Participants will be enabled to circulate at will among the posters with each presenter in a virtual "room".

# Poster Sessions

## Chitaranjan Mahapatra, University of California San Francisco https://ucsf.zoom.us/j/91360527193

### Quantitative studies of autonomic nervous system activities in urinary bladder smooth muscle cells towards bladder overactivities

Abstract

Context: The urinary incontinence (UI) is defined as the involuntary loss of urine and associated with the enhanced spontaneous contractions of the detrusor smooth muscle (DSM). The spontaneously evoked action potentials (sAPs) in DSM cells initiate and modulate these contractions. The DSM is strongly innervated, connecting approximately 16000 afferent and efferent axons from ganglion neurons. It generates sAPs due to the stochastic nature of purinergic neurotransmitter release from the parasympathetic nerve [1].

Objectives: The aim of this current study is to understand the putative relationship between the fluctuating ion channel conductances and stochastically release of ATP in generating sAPs.

Methods: The neurotransmitter current was considered as an independent excitatory conductance in the model where gex(t) and Eex are the one-variable stochastic process conductance and the reversal potential respectively. In addition, Dex and λ1(t) are known as the diffusion coefficients and Gaussian white noise. The point-conductance is incorporated into a single DSM cell model based on single cylindrical compartment [2]. Fitting procedures were based on the Nelder-Mead minimization method with a tolerance of 1%. To have a good estimate of the coefficient of variation, the histograms of inter-spike intervals (ISIs) were fitted by a gamma distribution.

Results: The elicited AP consists an after depolarization and after hyperpolarization phase. The AP peak amplitude and duration are about 5 mV and 40 ms respectively. Then, the random injection of point process model is conducted to elicit a series of sAPs and depolarization for 5 second. The membrane resting potential is held at ─ 50 mV with a 3 mV of fluctuation. The stochastically depolarization up to 20 mV activates the T-type Ca2+ channel first and then the L-type Ca2+ channel to generate action potential.

Conclusions: The T-type Ca2+ channel blocker can be used as a new phrmacologicl target for UI. In addition, a extended multidimensional models will aid our understanding of DSM electrical and contractile function, providing windows of insight into the factors that govern excitability and contraction in both normal and unstable bladder, in turn shedding light on such phenomena as bladder overactivity and its underlying mechanisms.

1. Young, John S., En Meng, Tom C. Cunnane, and Keith L. Brain. ""Spontaneous purinergic neurotransmission in the mouse urinary bladder."" The Journal of physiology 586, no. 23 (2008): 5743-5755.
2. Mahapatra, Chitaranjan, Keith L. Brain, and Rohit Manchanda. ""A biophysically constrained computational model of the action potential of mouse urinary bladder smooth muscle."" PloS one 13, no. 7 (2018): e0200712.

## Purushottam Dixit, University of Florida https://ufl.zoom.us/j/98516349839

### Endocytosis-based mechanism of memory in cellular signaling networks

Abstract

Detecting relative rather than absolute changes in extracellular signals enables cells to make decisions in constantly fluctuating environments. It is currently not well understood how mammalian signaling networks store the memories of past stimuli and subsequently use them to compute relative signals, that is perform fold change detection. Using the growth factor-activated PI3K-Akt signaling pathway, we develop here computational and analytical models, and experimentally validate a novel non-transcriptional mechanism of relative sensing in mammalian cells. This mechanism relies on a new form of cellular memory, where cells effectively encode past stimulation levels in the abundance of cognate receptors on the cell surface. The surface receptor abundance is regulated by background signal-dependent receptor endocytosis and down-regulation. We show the robustness and specificity of relative sensing for two physiologically important ligands, epidermal growth factor (EGF) and hepatocyte growth factor (HGF), and across wide ranges of background stimuli. Our results suggest that similar mechanisms of cell memory and fold change detection may be important in diverse signaling cascades and multiple biological contexts.

## Hammed Olawale Fatoyinbo, Massey University, New Zealand https://massey.zoom.us/j/4621313515

### Pattern formation in gap-junction coupled smooth muscle cells

Abstract

Electro-mechanical coupling (EMC) is a physiological process that relates the generation of electrical signals to contraction and relaxation of muscle cells. It may arise under the influence of external source (such as agonists) or spontaneous activity of the ion channels. Spontaneous oscillatory behaviour in muscle cells is known as pacemaker dynamics. Motivated by this cellular behaviour, we investigate the formation of spatiotemporal patterns in a model of electrically coupled smooth muscle cells. By varying model parameters, we identify transitions between types of excitability of a model of a smooth muscle cell. And numerical simulations of a model of a lattice of electrically coupled cells in one spatial dimension showed that the patterns can bifurcate from stable patterns, including travelling fronts and pulses, to spatiotemporal chaos.

## Zahmeeth Sakkaff, Argonne National Laboratory https://zoom.us/j/3759876374

### Molecular Communication Based on Cell Metabolism: A Case Study with Human Gut Microbes

Abstract

Understanding the complete mechanisms behind the cell's interaction with the environment is one of the challenging research problems. Molecular Communication is, studying information propagation through molecules in the biological domain, and coding and information theory, a mathematical theory to quantify information, are paving the way for understanding the ins and outs of these mechanisms. In this poster, both concepts are applied to model and quantify the information flow from the cell's environment into the internal state of the cell's metabolism, intermediate, and the end-to-end. We characterized the cell metabolism into two-channel abstractions: the enzyme expression regulation and the metabolic reaction network. The composition of these two channels together quantifies the information flow in the end-to-end molecular communication system, where the exchange of metabolites and growth of the cell is modeled as a function of the input chemical compounds in its environment. Based on these abstractions, the potential of cell metabolism is characterized and quantified in terms of the information-and communication-centric mutual information parameter to understand the limits in the fine-tuning and controllability of the behavior of natural biological cell communication that has many applications such as on the Internet of Bio-Nano Things, health, environment, and defense. We performed simulations and present numerical results of our proposed models using the standard processes of genome-scale modeling and flux balance analysis on two important human gut microbes: Bacteroides thetaiotaomicron and Methanobrevibacter smithii. We also introduce signal constellation concepts on mutual information values to generate an input signal constellation diagram with a reduced number of symbols possible for each combination of compounds to avoid input redundancy.

## Thomas Schneider, National Institutes of Health, National Cancer Institute https://ubc.zoom.us/j/69779588078?

### Restriction enzymes use a 24 dimensional coding space to recognize 6 base long DNA sequences

Abstract

We show that restriction enzymes apparently use the famous Leech Lattice to code precise DNA recognition. The Leech Lattice is a way of packing spheres in 24 dimensions and it is the best sphere packing known. The spheres are generated by thermal noise interfering with the molecules.

## Peter Rogan, University of Western Ontario https://westernuniversity.zoom.us/j/96493840237

### A proposed molecular mechanism for pathogenesis of severe RNA-viral pulmonary infections

Abstract

Certain viruses encoded with RNA genomes can cause severe pulmonary complications in a subset of infected patients, in some cases leading to death. We suggest that viral release may be accelerated by programmed cell death, precipitated by depletion of host RNA binding proteins (RBPs) that recognize specific viral sequences, destabilizing nuclear transcripts, and causing widespread chromosome damage. Interactions between RBPs and individual sequences in the SARS-CoV-2, influenza A (H3N1), HIV-1, and dengue genomes were analyzed by information theory. Viral genomes are proposed to sequester RBPs, especially SRSF1 and RNPS1, as they replicate, through their binding affinity for these proteins. Ordinarily, binding of these RBPs stabilizes nascent host transcripts, preventing them from annealing to chromosomal templates and forming R-loops. These proteins also contribute to mRNA splicing, which eliminates long intronic sequences, and is itself is antagonistic to R-loop formation. Strong RBP binding sites present and abundant in multiple viral genomes were identified with robust, information theory-based binding site models that we derived from Clip-Seq data. RBP binding sites in viral genomes and transcriptomes of human type II pneumocytes were used to estimate the stoichiometry of sites in replicated viral genomes that compete with and significantly prevent recognition of binding sites in human RNAs. Chromosomal breakage occurs when an excessive number of unresolved, RBP deficient R-loops collide with incoming replication forks, overwhelming DNA repair machinery. We found that influenza and dengue-infected cells in some individuals unexpectedly induce mRNAs encoding DNA repair and apoptotic proteins. R-loop-induced apoptosis could release significant quantities of membrane-associated viral particles into neighboring alveoli, infect adjacent pneumocytes and other tissues, rapidly compromise lung function and cause other symptoms.

## Michael Vennettilli, Purdue University https://pitt.zoom.us/j/95432512014

### Precision of Protein Thermometry

Abstract

Temperature sensing is a ubiquitous cell behavior, but the fundamental limits to the precision of temperature sensing are poorly understood. We find that, unlike in chemical concentration sensing, the precision of temperature sensing is not limited by extrinsic fluctuations in the temperature field itself. Instead, precision is limited by the intrinsic copy number, turnover, and binding kinetics of temperature-sensitive proteins. Developing a model based on the canonical TlpA protein, we find that a cell can estimate temperature to within 1% in the experimentally observed response time of one minute.

## Afeez Abidemi, Universiti Teknologi Malaysia https://us04web.zoom.us/j/5546482140

### Assessing the Role of Human Movement and Effect of Control Measures on Dengue Fever Spread in Connected Patches: From Modelling to Simulation

Abstract

Dengue is a mosquito-borne viral disease endemic in many areas across the globe. The role of human movement and heterogeneity in populations have long been recognised as driving forces in dengue disease spread. Hence, there is the need to better understand the impact of human movement on dengue disease transmission, and the impact of combined efforts of various control measures in reducing the disease prevalence in the population. In this work, a two-patch model featuring human, aquatic and adult mosquito populations to investigate the impact of host mobility on dengue disease transmission between two spatial locations is proposed. The model incorporates three patch-specific control measures, namely, personal protection, larvicide and adulticide controls to gain insights into the effect of their combined efforts on the spatial dissemination of the disease in the populations. The basic reproductive number, $\mathcal R_0$, of the model is derived through the next generation matrix method. Comparison theorem is used to prove the global asymptotic stability of the model. Qualitative analysis of the model reveals that the biologically realistic disease-free equilibrium is both locally and globally asymptotically stable when $\mathcal R_0<1$, and it is unstable otherwise. The simulated results indicate that human movement between patches can increase or decrease dengue disease prevalence in the population, and the disease burden can be reduced significantly, or even eliminated, in the interacting human and mosquito populations through the implementation of combined efforts of the three control interventions under consideration.

## Alexander Moffett, York University https://yorku.zoom.us/j/94190656675

### The Fitness Value of Information with Delayed Phenotype Switching

Abstract

The ability of organisms to accurately sense their environment and respond accordingly is critical for evolutionary success. However, exactly how the sensory ability influences fitness is a topic of active research, while the necessity of a time delay between when unreliable environmental cues are sensed and when organisms can mount a response has yet to be explored at any length. Accounting for this delay in phenotype response in models of population growth, we find that a critical error probability can exist under certain environmental conditions: an organism with a sensory system with any error probability less than the critical value can achieve the same long-term growth rate as an organism with a perfect sensing system. The existence of this critical error probability could have several important evolutionary consequences, primarily that sensory systems operating at the non-zero critical error probability may be evolutionarily optimal.

## Yeeren Low, McGill University https://mcgill.zoom.us/j/91974319487

### Data-driven modeling of T cell morphodynamics during migration

Abstract

T cells can spontaneously migrate rapidly through the extracellular matrix using an "amoeboid" mechanism, which is believed to aid their search for antigens. While modeling and experiments have in part addressed motility parameters and the impact of matrix characteristics, the morphodynamics during locomotion remains not well understood. We consider a data-driven approach using low–spatial resolution time-lapse fluorescence microscopy videos of activated T cells migrating in collagen matrix. We analyze the resulting cell shapes by using an autoencoder to extract a low-dimensional "shape space". We find time-irreversible motion in shape space, as expected from Purcell's theorem for a swimmer at low Reynolds number. We also find evidence of distinct signatures of turning behavior as a result of cell–matrix interactions. Our statistical analysis allows us to generate artificial trajectories of cells and their shapes using a coarse-grained morphology. This approach confers the possibility of inferring predictive dynamical laws which would inform biophysical models of cell morphology during migration and interaction with the environment, together with the impact of experimental conditions such as addition of chemokine, matrix characteristics, or cellular manipulations.

## Tenglong Wang, Case Western Reserve University https://cwru.zoom.us/j/93074196380

### The price of information transfer in living cells

Abstract

Survival for living cells depends in part on accurate and responsive signaling: the ability to collect enough information about the micro-environment to make decisions in response to external stimuli such nutrients, hormones, and toxic agents. This capacity to react to extracellular cues developed early in evolutionary history, and is now seen at all levels of biological organization, from chemotaxis in unicellular organisms to the pathways that regulate cell differentiation and disease in multicellular life. Despite the resulting diversity of biochemical networks that implement this signaling, information theory provides a powerful universal framework to quantify the amount of information transferred through a network, allowing comparisons between different systems. Over the last decade a remarkable experimental consensus has emerged from such comparisons: studies of both prokaryotic and eukaryotic signaling pathways have found they can transmit at most 1 to 3 bits of information, with typical results clustering near the lower end of that range. These values refer to mutual information (MI) between pathway input (concentrations of a molecule representing the signal) and the output (concentrations of a downstream molecule produced by the network, sampled either at a single or multiple time points).

The central question we explore in this work is to what extent the fundamental information scale is shaped by the energy requirements of the underlying biochemical signaling networks. In order to transmit information, these networks necessarily need to operate out of equilibrium, fueled by processes like ATP hydrolysis that consume energetic resources. To investigate the question, we focus on one of the canonical signaling circuits in biology, the kinase-phosphatase “push-pull loop”, which often forms a basic unit of more complicated signaling cascades. We derive the relationships between three facets of the system: i) the MI between the input (active kinase) and output (phosphorylated substrate) molecular populations; ii) the timescales over which the input signal varies; and iii) the energy requirements, expressed in terms of chemical potential of ATP hydrolysis and the rate of ATP consumption. In fact, taking advantage of results from optimal noise filter theory, we derive a remarkably simple analytical relationship that describes the tradeoffs between minimum ATP rate, the MI, and the maximum characteristic signal frequency (the so-called bandwidth) which the push-pull network can handle. Verified via extensive numerical simulations across the whole gamut of enzymatic parameters, this relation is a novel theoretical prediction that can be directly tested in future experiments.

## Alexander Strang, Case Western Reserve University https://cwru.zoom.us/j/91570713229

### The Discrete Helmholtz-Hodge Decomposition, Linear Thermodynamics, and the Weak Rotation Expansion

Abstract

The discrete Helmholtz-Hodge Decomposition (HHD) decomposes an edge flow on a graph into two components, a conservative component and a rotational component. The HHD can be applied to discrete-space continuous-time Markov chains with reversible transitions to construct analogies with statistical thermodynamics, and to understand steady-state behavior near detailed balance. We show that, in the limit when the rotational component is small, the steady-state and steady-state fluxes can be expanded in the strength of rotation, and that each term in these expansion satisfies a recursively defined HHD equation. Convergence of the expansion and consequences are discussed.

(Online)
Wednesday, July 29
08:00 - 08:45 Thomas Ouldridge (Addenbrooke): Non-Equilibrium Thermodynamics of Catalytic Information Processing
Catalytic motifs are ubiquitous in cellular information-processing systems, from kinase signalling networks to the central dogma of molecular biology. This ubiquity results from the ability of catalysts to channel chemical free energy into far-from-equilibrium information-bearing states, allowing them to perform non-trivial computational operations. This power, however, comes at a price. At a fundamental level, the need to create non-equilibrium outputs sets thermodynamic constraints on these systems. At a practical level, catalysts must carefully balance kinetic and thermodynamic factors to ensure that the desired non-equilibrium output is actually reached. The complexity of this task explains the comparatively slow progress made with engineering synthetic non-equilibrium information-processing systems, as opposed to synthetic systems that form complex equilibrium assemblies. I will present our latest work - both theoretical and experimental - aimed at overcoming this challenge to engineer non-equilibrium catalytic systems for information processing.
(Online)
08:45 - 09:15 Open discussion
Moderated by Andrew Eckford (York University)
(Online)
09:15 - 09:30 break (Online)
09:30 - 10:15 Ilka Bischofs: Information Processing by Bacterial Quorum Sensing Systems
Bacteria can communicate with each other by means of diffusive signaling molecules to coordinate their behaviors. The term “quorum sensing” denotes a cell-density dependent regulation of population-level behavior and is typically used to describe the sensory function of these signaling systems. I will give an overview of the diversity of different quorum sensing architectures and explain how architecture could affect information processing. I will then focus on a particular type of so-called pump-probe signaling architectures and demonstrate that they could serve other functions than classical quorum sensing. Finally, I will introduce our attempts to determine network parameters using a FRET-based reporter system in order to quantitatively describe signal processing in B. subtilis with the help of a phenomenological model.
(Online)
10:15 - 10:45 Open discussion
Moderated by Andrew Eckford (York University)
(Online)
10:45 - 11:30 Conclusion, Poster Prizes, and Farewell (Online)