Targeting Proteases for Treating COVID-19.

The unprecedented pandemic of coronavirus disease 2019 (COVID-19) demands effective treatment for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection. The infection of SARS-CoV-2 critically depends on diverse viral or host proteases, which mediate viral entry, viral protein maturation, as well as the pathogenesis of the viral infection. Endogenous and exogenous agents targeting for proteases have been proved to be effective toward a variety of viral infections ranging from HIV to influenza virus, suggesting protease inhibitors as a promising antiviral treatment for COVID-19. In this Review, we discuss how host and viral proteases participated in the pathogenesis of COVID-19 as well as the prospects and ongoing clinical trials of protease inhibitors as treatments.

Activation and synchronization of the oscillatory morphodynamics in multicellular monolayer.

Oscillatory morphodynamics provides necessary mechanical cues for many multicellular processes. Owing to their collective nature, these processes require robustly coordinated dynamics of individual cells, which are often separated too distantly to communicate with each other through biomaterial transportation. Although it is known that the mechanical balance generally plays a significant role in the systems' morphologies, it remains elusive whether and how the mechanical components may contribute to the systems' collective morphodynamics. Here, we study the collective oscillations in the Drosophila amnioserosa tissue to elucidate the regulatory roles of the mechanical components. We identify that the tensile stress is the key activator that switches the collective oscillations on and off. This regulatory role is shown analytically using the Hopf bifurcation theory. We find that the physical properties of the tissue boundary are directly responsible for synchronizing the oscillatory intensity and polarity of all inner cells and for orchestrating the spatial oscillation patterns inthe tissue.

Information processing in bacteria: memory, computation, and statistical physics: a key issues review.

Living systems have to constantly sense their external environment and adjust their internal state in order to survive and reproduce. Biological systems, from as complex as the brain to a single E. coli cell, have to process these data in order to make appropriate decisions. How do biological systems sense external signals? How do they process the information? How do they respond to signals? Through years of intense study by biologists, many key molecular players and their interactions have been identified in different biological machineries that carry out these signaling functions. However, an integrated, quantitative understanding of the whole system is still lacking for most cellular signaling pathways, not to say the more complicated neural circuits. To study signaling processes in biology, the key thing to measure is the input-output relationship. The input is the signal itself, such as chemical concentration, external temperature, light (intensity and frequency), and more complex signals such as the face of a cat. The output can be protein conformational changes and covalent modifications (phosphorylation, methylation, etc), gene expression, cell growth and motility, as well as more complex output such as neuron firing patterns and behaviors of higher animals. Due to the inherent noise in biological systems, the measured input-output dependence is often noisy. These noisy data can be analysed by using powerful tools and concepts from information theory such as mutual information, channel capacity, and the maximum entropy hypothesis. This information theory approach has been successfully used to reveal the underlying correlations between key components of biological networks, to set bounds for network performance, and to understand possible network architecture in generating observed correlations. Although the information theory approach provides a general tool in analysing noisy biological data and may be used to suggest possible network architectures in preserving information, it does not reveal the underlying mechanism that leads to the observed input-output relationship, nor does it tell us much about which information is important for the organism and how biological systems use information to carry out specific functions. To do that, we need to develop models of the biological machineries, e.g. biochemical networks and neural networks, to understand the dynamics of biological information processes. This is a much more difficult task. It requires deep knowledge of the underlying biological network-the main players (nodes) and their interactions (links)-in sufficient detail to build a model with predictive power, as well as quantitative input-output measurements of the system under different perturbations (both genetic variations and different external conditions) to test the model predictions to guide further development of the model. Due to the recent growth of biological knowledge thanks in part to high throughput methods (sequencing, gene expression microarray, etc) and development of quantitative in vivo techniques such as various florescence technology, these requirements are starting to be realized in different biological systems. The possible close interaction between quantitative experimentation and theoretical modeling has made systems biology an attractive field for physicists interested in quantitative biology. In this review, we describe some of the recent work in developing a quantitative predictive model of bacterial chemotaxis, which can be considered as the hydrogen atom of systems biology. Using statistical physics approaches, such as the Ising model and Langevin equation, we study how bacteria, such as E. coli, sense and amplify external signals, how they keep a working memory of the stimuli, and how they use these data to compute the chemical gradient. In particular, we will describe how E. coli cells avoid cross-talk in a heterogeneous receptor cluster to keep a ligand-specific memory. We will also study the thermodynamic costs of adaptation for cells to maintain an accurate memory. The statistical physics based approach described here should be useful in understanding design principles for cellular biochemical circuits in general.

An Optimal Free Energy Dissipation Strategy of the MinCDE Oscillator in Regulating Symmetric Bacterial Cell Division.

Sustained molecular oscillations are ubiquitous in biology. The obtained oscillatory patterns provide vital functions as timekeepers, pacemakers and spacemarkers. Models based on control theory have been introduced to explain how specific oscillatory behaviors stem from protein interaction feedbacks, whereas the energy dissipation through the oscillating processes and its role in the regulatory function remain unexplored. Here we developed a general framework to assess an oscillator's regulation performance at different dissipation levels. Using the Escherichia coli MinCDE oscillator as a model system, we showed that a sufficient amount of energy dissipation is needed to switch on the oscillation, which is tightly coupled to the system's regulatory performance. Once the dissipation level is beyond this threshold, unlike stationary regulators' monotonic performance-to-cost relation, excess dissipation at certain steps in the oscillating process damages the oscillator's regulatory performance. We further discovered that the chemical free energy from ATP hydrolysis has to be strategically assigned to the MinE-aided MinD release and the MinD immobilization steps for optimal performance, and a higher energy budget improves the robustness of the oscillator. These results unfold a novel mode by which living systems trade energy for regulatory function.

Lateral density of receptor arrays in the membrane plane influences sensitivity of the E. coli chemotaxis response.

In chemotactic bacteria, transmembrane chemoreceptors, CheA and CheW form the core signalling complex of the chemotaxis sensory apparatus. These complexes are organized in extended arrays in the cytoplasmic membrane that allow bacteria to respond to changes in concentration of extracellular ligands via a cooperative, allosteric response that leads to substantial amplification of the signal induced by ligand binding. Here, we have combined cryo-electron tomographic studies of the 3D spatial architecture of chemoreceptor arrays in intact E. coli cells with computational modelling to develop a predictive model for the cooperativity and sensitivity of the chemotaxis response. The predictions were tested experimentally using fluorescence resonance energy transfer (FRET) microscopy. Our results demonstrate that changes in lateral packing densities of the partially ordered, spatially extended chemoreceptor arrays can modulate the bacterial chemotaxis response, and that information about the molecular organization of the arrays derived by cryo-electron tomography of intact cells can be translated into testable, predictive computational models of the chemotaxis response.

Adapt locally and act globally: strategy to maintain high chemoreceptor sensitivity in complex environments.

In bacterial chemotaxis, several types of ligand-specific receptors form mixed clusters, wherein receptor-receptor interactions lead to signal amplification and integration. However, it remains unclear how a mixed receptor cluster adapts to individual stimuli and whether it can differentiate between different types of ligands. Here, we combine theoretical modeling with experiments to reveal the adaptation dynamics of the mixed chemoreceptor cluster in Escherichia coli. We show that adaptation occurs locally and is ligand-specific: only the receptor that binds the external ligand changes its methylation level when the system adapts, whereas other types of receptors change methylation levels transiently. Permanent methylation crosstalk occurs when the system fails to adapt accurately. This local adaptation mechanism enables cells to differentiate individual stimuli by encoding them into the methylation levels of corresponding types of chemoreceptors. It tunes each receptor to its most responsive state to maintain high sensitivity in complex environments and prevents saturation of the cluster by one signal.

Condensation of FtsZ filaments can drive bacterial cell division.

Forces are important in biological systems for accomplishing key cell functions, such as motility, organelle transport, and cell division. Currently, known force generation mechanisms typically involve motor proteins. In bacterial cells, no known motor proteins are involved in cell division. Instead, a division ring (Z-ring) consists of mostly FtsZ, FtsA, and ZipA is used to exerting a contractile force. The mechanism of force generation in bacterial cell division is unknown. Using computational modeling, we show that Z-ring formation results from the colocalization of FtsZ and FtsA mediated by the favorable alignment of FtsZ polymers. The model predicts that the Z-ring undergoes a condensation transition from a low-density state to a high-density state and generates a sufficient contractile force to achieve division. FtsZ GTP hydrolysis facilitates monomer turnover during the condensation transition, but does not directly generate forces. In vivo fluorescence measurements show that FtsZ density increases during division, in accord with model results. The mechanism is akin to van der Waals picture of gas-liquid condensation, and shows that organisms can exploit microphase transitions to generate mechanical forces.

Improved Prediction of Body Mass Index in Real-World Administrative Healthcare Claims Databases.

INTRODUCTION: To continue closing the gap between the predictive modeling and its real-world application, we report a new data-to-prediction pipeline that advanced the state-of-the-art predictive performance of body mass index (BMI) classifications by integrating siloed claims databases via a common data model. METHODS: This study adapted the ensemble-based methodology of the baseline prediction model and focused on removing the silos in the claims databases. We applied the Super Learner machine learning algorithm (SLA) to learn a combined dataset consisting of 50% data from the Optum Date of Death database and 50% data from the IBM MarketScan Commercial Claims and Encounters (CCAE), and omitted the commonly used one-hot-encoding step and used multi-categorical variables directly in the feature engineering process. These developments were then optimized via a standard cross-validation scheme and the performance was evaluated on a holdout test set. RESULTS: Sociodemographic and clinical characteristics were used with (denoted as SLA1) and without (denoted as SLA2) baseline BMI values to predict BMI classifications (≥ 30, ≥ 35, and ≥ 40 kg/m2). Although the newly implemented SLA1 performed similarly to the previous model, with the area under the receiver operating characteristic curve (ROC AUC) being approximately 88% for all BMI classifications, specificity ranging from 90% to 96%, and accuracy ranging from 88% to 93%. The new SLA2 achieved consistently better performance on all metrics across all BMI classes. In particular, the new SLA2 achieved 77-79% in ROC AUC, increasing from the previously reported level (73%). Its specificity improved to the range of 76-90% from 71-86%. Its accuracy improved to the range of 77-86% from 73-80%. Its recall (i.e., sensitivity) improved to the range of 64-78% from 60-76%. CONCLUSIONS: This study demonstrates dramatic improvements in the prediction of BMI across classifications using integrated databases in a common data model for the generation of real-world evidence.

Dynamics of the bacterial flagellar motor: the effects of stator compliance, back steps, temperature, and rotational asymmetry.

The rotation of a bacterial flagellar motor (BFM) is driven by multiple stators tethered to the cell wall. Here, we extend a recently proposed power-stroke model to study the BFM dynamics under different biophysical conditions. Our model explains several key experimental observations and reveals their underlying mechanisms. 1), The observed independence of the speed at low load on the number of stators is explained by a force-dependent stepping mechanism that is independent of the strength of the stator tethering spring. Conversely, without force-dependent stepping, an unrealistically weak stator spring is required. 2), Our model with back-stepping naturally explains the observed absence of a barrier to backward rotation. Using the same set of parameters, it also explains BFM behaviors in the high-speed negative-torque regime. 3), From the measured temperature dependence of the maximum speed, our model shows that stator-stepping is a thermally activated process with an energy barrier. 4), The recently observed asymmetry in the torque-speed curve between counterclockwise- and clockwise-rotating BFMs can be quantitatively explained by the asymmetry in the stator-rotor interaction potentials, i.e., a quasilinear form for the counterclockwise motor and a quadratic form for the clockwise motor.

MinC spatially controls bacterial cytokinesis by antagonizing the scaffolding function of FtsZ.

BACKGROUND: Cytokinesis in bacteria is mediated by a cytokinetic ring, termed the Z ring, which forms a scaffold for recruitment of other cell-division proteins. The Z ring is composed of FtsZ filaments, but their organization in the Z ring is poorly understood. In Escherichia coli, the Min system contributes to the spatial regulation of cytokinesis by preventing the assembly of the Z ring away from midcell. The effector of the Min system, MinC, inhibits Z ring assembly by a mechanism that is not clear. RESULTS: Here, we report that MinC controls the scaffolding function of FtsZ by antagonizing the mechanical integrity of FtsZ structures. Specifically, MinC antagonizes the ability of FtsZ filaments to be in a solid-like gel state. MinC is a modular protein whose two domains (MinC(C) and MinC(N)) synergize to inhibit FtsZ function. MinC(C) interacts directly with FtsZ polymers to target MinC to Z rings. MinC(C) also prevents lateral interactions between FtsZ filaments, an activity that seems to be unique among cytoskeletal proteins. Because MinC(C) is inhibitory in vivo, it suggests that lateral interactions between FtsZ filaments are important for the structural integrity of the Z ring. MinC(N) contributes to MinC activity by weakening the longitudinal bonds between FtsZ molecules in a filament leading to a loss of polymer rigidity and consequent polymer shortening. On the basis of our results, we develop the first computational model of the Z ring and study the effects of MinC. CONCLUSIONS: Control over the scaffolding activity of FtsZ probably represents a universal regulatory mechanism of bacterial cytokinesis.

Competitive coordination of the dual roles of the Hedgehog co-receptor in homophilic adhesion and signal reception.

Hedgehog (Hh) signaling patterns embryonic tissues and contributes to homeostasis in adults. In Drosophila, Hh transport and signaling are thought to occur along a specialized class of actin-rich filopodia, termed cytonemes. Here, we report that Interference hedgehog (Ihog) not only forms a Hh receptor complex with Patched to mediate intracellular signaling, but Ihog also engages in trans-homophilic binding leading to cytoneme stabilization in a manner independent of its role as the Hh receptor. Both functions of Ihog (trans-homophilic binding for cytoneme stabilization and Hh binding for ligand sensing) involve a heparin-binding site on the first fibronectin repeat of the extracellular domain. Thus, the Ihog-Ihog interaction and the Hh-Ihog interaction cannot occur simultaneously for a single Ihog molecule. By combining experimental data and mathematical modeling, we determined that Hh-Ihog heterophilic interaction dominates and Hh can disrupt and displace Ihog molecules involved in trans-homophilic binding. Consequently, we proposed that the weaker Ihog-Ihog trans interaction promotes and stabilizes direct membrane contacts along cytonemes and that, as the cytoneme encounters secreted Hh ligands, the ligands trigger release of Ihog from trans Ihog-Ihog complex enabling transport or internalization of the Hh ligand-Ihog-Patched -receptor complex. Thus, the seemingly incompatible functions of Ihog in homophilic adhesion and ligand binding cooperate to assist Hh transport and reception along the cytonemes.

Polymerization and bundling kinetics of FtsZ filaments.

FtsZ is a tubulin homolog essential for prokaryotic cell division. In living bacteria, FtsZ forms a ringlike structure (Z-ring) at the cell midpoint. Cell division coincides with a gradual contraction of the Z-ring, although the detailed molecular structure of the Z-ring is unknown. To reveal the structural properties of FtsZ, an understanding of FtsZ filament and bundle formation is needed. We develop a kinetic model that describes the polymerization and bundling mechanism of FtsZ filaments. The model reveals the energetics of the FtsZ filament formation and the bundling energy between filaments. A weak lateral interaction between filaments is predicted by the model. The model is able to fit the in vitro polymerization kinetics data of another researcher, and explains the cooperativity observed in FtsZ kinetics and the critical concentration in different buffer media. The developed model is also applicable for understanding the kinetics and energetics of other bundling biopolymer filaments.

Hedgehog mediated degradation of Ihog adhesion proteins modulates cell segregation in Drosophila wing imaginal discs.

The Drosophila Hedgehog receptor functions to regulate the essential downstream pathway component, Smoothened, and to limit the range of signaling by sequestering Hedgehog protein signal within imaginal disc epithelium. Hedgehog receptor function requires both Patched and Ihog activity, the latter interchangeably encoded by interference hedgehog (ihog) or brother of ihog (boi). Here we show that Patched and Ihog activity are mutually required for receptor endocytosis and degradation, triggered by Hedgehog protein binding, and causing reduced levels of Ihog/Boi proteins in a stripe of cells at the anterior/posterior compartment boundary of the wing imaginal disc. This Ihog spatial discontinuity may contribute to classically defined cell segregation and lineage restriction at the anterior/posterior wing disc compartment boundary, as suggested by our observations that Ihog activity mediates aggregation of otherwise non-adherent cultured cells and that loss of Ihog activity disrupts wing disc cell segregation, even with downstream genetic rescue of Hedgehog signal response.

Energy dissipation drives the gradient signal amplification through an incoherent type-1 feed-forward loop.

We present here the analytical relation between the gain of eukaryotic gradient sensing network and the associated thermodynamic cost. By analyzing a general incoherent type-1 feed-forward loop, we derive the gain function (G) through the reaction network and explicitly show that G depends on the nonequilibrium factor (0≤γ≤1 with γ=0 and 1 representing irreversible and equilibrium reaction systems, respectively), the Michaelis constant (K_{M}), and the turnover ratio (r_{cat}) of the participating enzymes. We further find the maximum possible gain is intrinsically determined by K_{M}/G_{max}=(1/K_{M}+2)/4. Our model also indicates that the dissipated energy (measured by -lnγ), from the intracellular energy-bearing bioparticles (e.g., ATP), is used to generate a force field F_{γ}∝(1-sqrt[γ]) that reshapes and disables the effective potential around the zero gain region, which leads to the ultrasensitive response to external chemical gradients.

Mechanochemical regulation of oscillatory follicle cell dynamics in the developing Drosophila egg chamber.

During tissue elongation from stage 9 to stage 10 in Drosophila oogenesis, the egg chamber increases in length by ∼1.7-fold while increasing in volume by eightfold. During these stages, spontaneous oscillations in the contraction of cell basal surfaces develop in a subset of follicle cells. This patterned activity is required for elongation of the egg chamber; however, the mechanisms generating the spatiotemporal pattern have been unclear. Here we use a combination of quantitative modeling and experimental perturbation to show that mechanochemical interactions are sufficient to generate oscillations of myosin contractile activity in the observed spatiotemporal pattern. We propose that follicle cells in the epithelial layer contract against pressure in the expanding egg chamber. As tension in the epithelial layer increases, Rho kinase signaling activates myosin assembly and contraction. The activation process is cooperative, leading to a limit cycle in the myosin dynamics. Our model produces asynchronous oscillations in follicle cell area and myosin content, consistent with experimental observations. In addition, we test the prediction that removal of the basal lamina will increase the average oscillation period. The model demonstrates that in principle, mechanochemical interactions are sufficient to drive patterning and morphogenesis, independent of patterned gene expression.

The cost of sensitive response and accurate adaptation in networks with an incoherent type-1 feed-forward loop.

The incoherent type-1 feed-forward loop (I1-FFL) is ubiquitous in biological regulatory circuits. Although much is known about the functions of the I1-FFL motif, the energy cost incurred in the network and how it affects the performance of the network have not been investigated. Here, we study a generic I1-FFL enzymatic reaction network modelled after the GEF-GAP-Ras pathway responsible for chemosensory adaptation in eukaryotic cells. Our analysis shows that the I1-FFL network always operates out of equilibrium. Continuous energy dissipation is necessary to drive an internal phosphorylation-dephosphorylation cycle that is crucial in achieving strong short-time response and accurate long-time adaptation. In particular, we show quantitatively that the energy dissipated in the I1-FFL network is used (i) to increase the system's initial response to the input signals; (ii) to enhance the adaptation accuracy at steady state; and (iii) to expand the range of such accurate adaptation. Moreover, we find that the energy dissipation rate, the catalytic speed and the maximum adaptation accuracy in the I1-FFL network satisfy the same energy-speed-accuracy relationship as in the negative-feedback-loop (NFL) networks. Because the I1-FFL and NFL are the only two basic network motifs that enable accurate adaptation, our results suggest that a universal cost-performance trade-off principle may underlie all cellular adaptation processes independent of the detailed biochemical circuit architecture.

The energy-speed-accuracy tradeoff in sensory adaptation.

Adaptation is the essential process by which an organism becomes better suited to its environment. The benefits of adaptation are well documented, but the cost it incurs remains poorly understood. Here, by analysing a stochastic model of a minimum feedback network underlying many sensory adaptation systems, we show that adaptive processes are necessarily dissipative, and continuous energy consumption is required to stabilize the adapted state. Our study reveals a general relation among energy dissipation rate, adaptation speed and the maximum adaptation accuracy. This energy-speed-accuracy relation is tested in the Escherichia coli chemosensory system, which exhibits near-perfect chemoreceptor adaptation. We identify key requirements for the underlying biochemical network to achieve accurate adaptation with a given energy budget. Moreover, direct measurements confirm the prediction that adaptation slows down as cells gradually de-energize in a nutrient-poor medium without compromising adaptation accuracy. Our work provides a general framework to study cost-performance tradeoffs for cellular regulatory functions and information processing.

Chapter 23: Stochastic modeling methods in cell biology.

Stochastic methods have been a staple for understanding complex systems in chemistry and physics. In the biological context, they are useful for understanding phenomena ranging from molecular-level fluctuations to cellular movement. We review the basic formalism behind stochastic methods and outline how they can be implemented for quantifying gene expression, movement of molecular motors, and the dynamics of cytoplasmic components. We show that stochastic methods are quantitative checks for proposed molecular mechanisms and can pose new questions for experiments. Structural information of cellular components can be incorporated into stochastic models to reveal new biological insights.

Z-ring force and cell shape during division in rod-like bacteria.

The life cycle of bacterial cells consists of repeated elongation, septum formation, and division. Before septum formation, a division ring called the Z-ring, which is made of a filamentous tubulin analog, FtsZ, is seen at the mid cell. Together with several other proteins, FtsZ is essential for cell division. Visualization of strains with GFP-labeled FtsZ shows that the Z-ring contracts before septum formation and pinches the cell into two equal halves. Thus, the Z-ring has been postulated to act as a force generator, although the magnitude of the contraction force is unknown. In this article, we develop a mathematical model to describe the process of growth and Z-ring contraction in rod-like bacteria. The elasticity and growth of the cell wall is incorporated in the model to predict the contraction speed, the cell shape, and the contraction force. With reasonable parameters, the model shows that a small force from the Z-ring (8 pN in Escherichia coli) is sufficient to accomplish division.

Flexible light-chain and helical structure of F-actin explain the movement and step size of myosin-VI.

Myosin-VI is a dimeric isoform of unconventional myosins. Single molecule experiments indicate that myosin-VI and myosin-V are processive molecular motors, but travel toward opposite ends of filamentous actin. Structural studies show several differences between myosin-V and VI, including a significant difference in the light-chain domain connecting the motor domains. Combining the measured kinetics of myosin-VI with the elasticity of the light chains, and the helical structure of F-actin, we compare and contrast the motility of myosin-VI with myosin-V. We show that the elastic properties of the light-chain domain control the stepping behavior of these motors. Simple models incorporating the motor elastic energy can quantitatively capture most of the observed data. Implications of our result for other processive motors are discussed.