Bayesian traction force estimation using cell boundary-dependent force priors.

Understanding the principles of cell migration necessitates measurements of the forces generated by cells. In traction force microscopy (TFM), fluorescent beads are placed on a substrate's surface and the substrate strain caused by the cell traction force is observed as displacement of the beads. Mathematical analysis can estimate traction force from bead displacement. However, most algorithms estimate substrate stresses independently of cell boundary, which results in poor estimation accuracy in low-density bead environments. To achieve accurate force estimation at low density, we proposed a Bayesian traction force estimation (BTFE) algorithm that incorporates cell-boundary-dependent force as a prior. We evaluated the performance of the proposed algorithm using synthetic data generated with mathematical models of cells and TFM substrates. BTFE outperformed other methods, especially in low-density bead conditions. In addition, the BTFE algorithm provided a reasonable force estimation using TFM images from the experiment.

A hybrid in silico/in-cell controller for microbial bioprocesses with process-model mismatch.

Bioprocess optimization using mathematical models is prevalent, yet the discrepancy between model predictions and actual processes, known as process-model mismatch (PMM), remains a significant challenge. This study proposes a novel hybrid control system called the hybrid in silico/in-cell controller (HISICC) to address PMM by combining model-based optimization (in silico feedforward controller) with feedback controllers utilizing synthetic genetic circuits integrated into cells (in-cell feedback controller). We demonstrated the efficacy of HISICC using two engineered Escherichia coli strains, TA1415 and TA2445, previously developed for isopropanol (IPA) production. TA1415 contains a metabolic toggle switch (MTS) to manage the competition between cell growth and IPA production for intracellular acetyl-CoA by responding to external input of isopropyl ß-D-1-thiogalactopyranoside (IPTG). TA2445, in addition to the MTS, has a genetic circuit that detects cell density to autonomously activate MTS. The combination of TA2445 with an in silico controller exemplifies HISICC implementation. We constructed mathematical models to optimize IPTG input values for both strains based on the two-compartment model and validated these models using experimental data of the IPA production process. Using these models, we evaluated the robustness of HISICC against PMM by comparing IPA yields with two strains in simulations assuming various magnitudes of PMM in cell growth rates. The results indicate that the in-cell feedback controller in TA2445 effectively compensates for PMM by modifying MTS activation timing. In conclusion, the HISICC system presents a promising solution to the PMM problem in bioprocess engineering, paving the way for more efficient and reliable optimization of microbial bioprocesses.

Decoding cellular deformation from pseudo-simultaneously observed Rho GTPase activities.

Limitations in simultaneously observing the activity of multiple molecules in live cells prevent researchers from elucidating how these molecules coordinate the dynamic regulation of cellular functions. Here, we propose the motion-triggered average (MTA) algorithm to characterize pseudo-simultaneous dynamic changes in arbitrary cellular deformation and molecular activities. Using MTA, we successfully extract a pseudo-simultaneous time series from individually observed activities of three Rho GTPases: Cdc42, Rac1, and RhoA. To verify that this time series encoded information on cell-edge movement, we use a mathematical regression model to predict the edge velocity from the activities of the three molecules. The model accurately predicts the unknown edge velocity, providing numerical evidence that these Rho GTPases regulate edge movement. Data preprocessing using MTA combined with mathematical regression provides an effective strategy for reusing numerous individual observations of molecular activities.

Analyses of Actin Dynamics, Clutch Coupling and Traction Force for Growth Cone Advance.

To establish functional networks, neurons must migrate to their appropriate destinations and then extend axons toward their target cells. These processes depend on the advances of growth cones that located at the tips of neurites. Axonal growth cones generate driving forces by sensing their local microenvironment and modulating cytoskeletal dynamics and actin-adhesion coupling (clutch coupling). Decades of research have led to the identification of guidance molecules, their receptors, and downstream signaling cascades for regulating neuronal migration and axonal guidance; however, the molecular machineries required for generating forces to drive growth cone advance and navigation are just beginning to be elucidated. At the leading edge of neuronal growth cones, actin filaments undergo retrograde flow, which is powered by actin polymerization and actomyosin contraction. A clutch coupling between F-actin retrograde flow and adhesive substrate generates traction forces for growth cone advance. The present study describes a detailed protocol for monitoring F-actin retrograde flow by single speckle imaging. Importantly, when combined with an F-actin marker Lifeact, this technique can quantify 1) the F-actin polymerization rate and 2) the clutch coupling efficiency between F-actin retrograde flow and the adhesive substrate. Both are critical variables for generating forces for growth cone advance and navigation. In addition, the present study describes a detailed protocol of traction force microscopy, which can quantify 3) traction force generated by growth cones. Thus, by coupling the analyses of single speckle imaging and traction force microscopy, investigators can monitor the molecular mechanics underlying growth cone advance and navigation.

Basic Proline-Rich Protein-Mediated Microtubules Are Essential for Lobe Growth and Flattened Cell Geometry.

Complex cell shapes are generated first by breaking symmetry, and subsequent polar growth. Localized bending of anticlinal walls initiates lobe formation in the epidermal pavement cells of cotyledons and leaves, but how the microtubule cytoskeleton mediates local cell growth, and how plant pavement cells benefit from adopting jigsaw puzzle-like shapes, are poorly understood. In Arabidopsis (Arabidopsis thaliana), the basic Pro-rich protein (BPP) microtubule-associated protein family comprises seven members. We analyzed lobe morphogenesis in cotyledon pavement cells of a BPP1;BPP2;BPP5 triple knockout mutant. New image analysis methods (MtCurv and BQuant) showed that anticlinal microtubule bundles were significantly reduced and cortical microtubules that fan out radially across the periclinal wall did not enrich at the convex side of developing lobes. Despite these microtubule defects, new lobes were initiated at the same frequency as in wild-type cells, but they did not expand into well-defined protrusions. Eventually, mutant cells formed nearly polygonal shapes and adopted concentric microtubule patterns. The mutant periclinal cell wall bulged outward. The radius of the calculated inscribed circle of the pavement cells, a proposed proxy for maximal stress in the cell wall, was consistently larger in the mutant cells during cotyledon development, and correlated with an increase in cell height. These bpp mutant phenotypes provide genetic and cell biological evidence that initiation and growth of lobes are distinct morphogenetic processes, and that interdigitated cell geometry effectively suppresses large outward bulging of pavement cells.

Sensing of substratum rigidity and directional migration by fast-crawling cells.

Living cells sense the mechanical properties of their surrounding environment and respond accordingly. Crawling cells detect the rigidity of their substratum and migrate in certain directions. They can be classified into two categories: slow-moving and fast-moving cell types. Slow-moving cell types, such as fibroblasts, smooth muscle cells, mesenchymal stem cells, etc., move toward rigid areas on the substratum in response to a rigidity gradient. However, there is not much information on rigidity sensing in fast-moving cell types whose size is ∼10 µm and migration velocity is ∼10 µm/min. In this study, we used both isotropic substrata with different rigidities and an anisotropic substratum that is rigid on the x axis but soft on the y axis to demonstrate rigidity sensing by fast-moving Dictyostelium cells and neutrophil-like differentiated HL-60 cells. Dictyostelium cells exerted larger traction forces on a more rigid isotropic substratum. Dictyostelium cells and HL-60 cells migrated in the "soft" direction on the anisotropic substratum, although myosin II-null Dictyostelium cells migrated in random directions, indicating that rigidity sensing of fast-moving cell types differs from that of slow types and is induced by a myosin II-related process.

Computational Methods for Estimating Molecular System from Membrane Potential Recordings in Nerve Growth Cone.

Biological cells express intracellular biomolecular information to the extracellular environment as various physical responses. We show a novel computational approach to estimate intracellular biomolecular pathways from growth cone electrophysiological responses. Previously, it was shown that cGMP signaling regulates membrane potential (MP) shifts that control the growth cone turning direction during neuronal development. We present here an integrated deterministic mathematical model and Bayesian reversed-engineering framework that enables estimation of the molecular signaling pathway from electrical recordings and considers both the system uncertainty and cell-to-cell variability. Our computational method selects the most plausible molecular pathway from multiple candidates while satisfying model simplicity and considering all possible parameter ranges. The model quantitatively reproduces MP shifts depending on cGMP levels and MP variability potential in different experimental conditions. Lastly, our model predicts that chloride channel inhibition by cGMP-dependent protein kinase (PKG) is essential in the core system for regulation of the MP shifts.

Diagnosis by Volatile Organic Compounds in Exhaled Breath from Lung Cancer Patients Using Support Vector Machine Algorithm.

Monitoring exhaled breath is a very attractive, noninvasive screening technique for early diagnosis of diseases, especially lung cancer. However, the technique provides insufficient accuracy because the exhaled air has many crucial volatile organic compounds (VOCs) at very low concentrations (ppb level). We analyzed the breath exhaled by lung cancer patients and healthy subjects (controls) using gas chromatography/mass spectrometry (GC/MS), and performed a subsequent statistical analysis to diagnose lung cancer based on the combination of multiple lung cancer-related VOCs. We detected 68 VOCs as marker species using GC/MS analysis. We reduced the number of VOCs and used support vector machine (SVM) algorithm to classify the samples. We observed that a combination of five VOCs (CHN, methanol, CH3CN, isoprene, 1-propanol) is sufficient for 89.0% screening accuracy, and hence, it can be used for the design and development of a desktop GC-sensor analysis system for lung cancer.

Fast-crawling cell types migrate to avoid the direction of periodic substratum stretching.

To investigate the relationship between mechanical stimuli from substrata and related cell functions, one of the most useful techniques is the application of mechanical stimuli via periodic stretching of elastic substrata. In response to this stimulus, Dictyostelium discoideum cells migrate in a direction perpendicular to the stretching direction. The origins of directional migration, higher migration velocity in the direction perpendicular to the stretching direction or the higher probability of a switch of migration direction to perpendicular to the stretching direction, however, remain unknown. In this study, we applied periodic stretching stimuli to neutrophil-like differentiated HL-60 cells, which migrate perpendicular to the direction of stretch. Detailed analysis of the trajectories of HL-60 cells and Dictyostelium cells obtained in a previous study revealed that the higher probability of a switch of migration direction to that perpendicular to the direction of stretching was the main cause of such directional migration. This directional migration appears to be a strategy adopted by fast-crawling cells in which they do not migrate faster in the direction they want to go, but migrate to avoid a direction they do not want to go.

Actin Migration Driven by Directional Assembly and Disassembly of Membrane-Anchored Actin Filaments.

Actin and actin-associated proteins migrate within various cell types. To uncover the mechanism of their migration, we analyzed actin waves, which translocate actin and actin-associated proteins along neuronal axons toward the growth cones. We found that arrays of actin filaments constituting waves undergo directional assembly and disassembly, with their polymerizing ends oriented toward the axonal tip, and that the lateral side of the filaments is mechanically anchored to the adhesive substrate. A combination of live-cell imaging, molecular manipulation, force measurement, and mathematical modeling revealed that wave migration is driven by directional assembly and disassembly of actin filaments and their anchorage to the substrate. Actin-associated proteins co-migrate with actin filaments by interacting with them. Furthermore, blocking this migration, by creating an adhesion-free gap along the axon, disrupts axonal protrusion. Our findings identify a molecular mechanism that translocates actin and associated proteins toward the cell's leading edge, thereby promoting directional cell motility.

Hes7 3'UTR is required for somite segmentation function.

A set of genes in the posterior end of developing mouse embryos shows oscillatory expression, thereby regulating periodic somite segmentation. Although the mechanism for generating oscillation has extensively been clarified, what regulates the oscillation period is still unclear. We attempted to elongate the oscillation period by increasing the time to transcribe Hes7 in this research. We generated knock-in mice, in which a large intron was inserted into Hes7 3'UTR. The exogenous intron was unexpectedly not properly spliced out and the transcripts were prematurely terminated. Consequently, Hes7 mRNA lost its 3'UTR, thereby reducing the amount of Hes7 protein. Oscillation was damped in the knock-in embryos and periodic somite segmentation does not occur properly. Thus, we demonstrated that Hes7 3'UTR is essential to accumulate adequate amounts of Hes7 protein for the somite segmentation clock that orchestrates periodic somite formation.

Experimental comparison of classification methods for key kinase identification for neurite elongation.

Kinases in a developing neuron play important roles in elongating a neurite with their complex interactions. To elucidate the effect of each kinase on neurite elongation and regeneration from a small set of experiments, we applied machine learning methods to synthetic datasets based on a biologically feasible model. The result showed the ridged partial least squares (RPLS) algorithm performed better than other standard algorithms such as naive Bayes classifier, support vector machines and random forest classification. This suggests the effectiveness of dimension reduction done in RPLS.

A single-molecule approach to DNA replication in Escherichia coli cells demonstrated that DNA polymerase III is a major determinant of fork speed.

The replisome catalyses DNA synthesis at a DNA replication fork. The molecular behaviour of the individual replisomes, and therefore the dynamics of replication fork movements, in growing Escherichia coli cells remains unknown. DNA combing enables a single-molecule approach to measuring the speed of replication fork progression in cells pulse-labelled with thymidine analogues. We constructed a new thymidine-requiring strain, eCOMB (E. coli for combing), that rapidly and sufficiently incorporates the analogues into newly synthesized DNA chains for the DNA-combing method. In combing experiments with eCOMB, we found the speed of most replication forks in the cells to be within the narrow range of 550-750 nt s(-1) and the average speed to be 653 ± 9 nt s(-1) (± SEM). We also found the average speed of the replication fork to be only 264 ± 9 nt s(-1) in a dnaE173-eCOMB strain producing a mutant-type of the replicative DNA polymerase III (Pol III) with a chain elongation rate (300 nt s(-1) ) much lower than that of the wild-type Pol III (900 nt s(-1) ). This indicates that the speed of chain elongation by Pol III is a major determinant of replication fork speed in E. coli cells.

Conversion of a signal into forces for axon outgrowth through Pak1-mediated shootin1 phosphorylation.

Soluble guidance cues can direct cellular protrusion and migration by modulating adhesion and cytoskeletal dynamics. Actin filaments (F-actins) polymerize at the leading edge of motile cells and depolymerize proximally [1, 2]; this, together with myosin II activity, induces retrograde flow of F-actins [3-5]. It has been proposed that the traction forces underlying cellular motility may be regulated by the modulation of coupling efficiency between F-actin flow and the extracellular substrate via "clutch" molecules [6-10]. However, how cell signaling controls the coupling efficiency remains unknown. Shootin1 functions as a linker molecule that couples F-actin retrograde flow and the substrate at neuronal growth cones to promote axon outgrowth [11]. Here we show that shootin1 is located at a critical interface, transducing a chemical signal into traction forces for axon outgrowth. We found that a chemoattractant, netrin-1, positively regulates traction forces at axonal growth cones via Pak1-mediated shootin1 phosphorylation. This phosphorylation enhanced the interaction between shootin1 and F-actin retrograde flow, thereby promoting F-actin-substrate coupling, force generation, and concomitant filopodium extension and axon outgrowth. These results suggest that dynamic actin-substrate coupling can transduce chemical signals into mechanical forces to control cellular motility and provide a molecular-level description of how this transduction may occur.

Dynamic regulation of myosin light chain phosphorylation by Rho-kinase.

Myosin light chain (MLC) phosphorylation plays important roles in various cellular functions such as cellular morphogenesis, motility, and smooth muscle contraction. MLC phosphorylation is determined by the balance between activities of Rho-associated kinase (Rho-kinase) and myosin phosphatase. An impaired balance between Rho-kinase and myosin phosphatase activities induces the abnormal sustained phosphorylation of MLC, which contributes to the pathogenesis of certain vascular diseases, such as vasospasm and hypertension. However, the dynamic principle of the system underlying the regulation of MLC phosphorylation remains to be clarified. Here, to elucidate this dynamic principle whereby Rho-kinase regulates MLC phosphorylation, we developed a mathematical model based on the behavior of thrombin-dependent MLC phosphorylation, which is regulated by the Rho-kinase signaling network. Through analyzing our mathematical model, we predict that MLC phosphorylation and myosin phosphatase activity exhibit bistability, and that a novel signaling pathway leading to the auto-activation of myosin phosphatase is required for the regulatory system of MLC phosphorylation. In addition, on the basis of experimental data, we propose that the auto-activation pathway of myosin phosphatase occurs in vivo. These results indicate that bistability of myosin phosphatase activity is responsible for the bistability of MLC phosphorylation, and the sustained phosphorylation of MLC is attributed to this feature of bistability.

The period of the somite segmentation clock is sensitive to Notch activity.

The number of vertebrae is defined strictly for a given species and depends on the number of somites, which are the earliest metameric structures that form in development. Somites are formed by sequential segmentation. The periodicity of somite segmentation is orchestrated by the synchronous oscillation of gene expression in the presomitic mesoderm (PSM), termed the "somite segmentation clock," in which Notch signaling plays a crucial role. Here we show that the clock period is sensitive to Notch activity, which is fine-tuned by its feedback regulator, Notch-regulated ankyrin repeat protein (Nrarp), and that Nrarp is essential for forming the proper number and morphology of axial skeleton components. Null-mutant mice for Nrarp have fewer vertebrae and have defective morphologies. Notch activity is enhanced in the PSM of the Nrarp(-/-) embryo, where the ~2-h segmentation period is extended by 5 min, thereby forming fewer somites and their resultant vertebrae. Reduced Notch activity partially rescues the Nrarp(-/-) phenotype in the number of somites, but not in morphology. Therefore we propose that the period of the somite segmentation clock is sensitive to Notch activity and that Nrarp plays essential roles in the morphology of vertebrae and ribs.

Systems biology of symmetry breaking during neuronal polarity formation.

Polarization, in which a single axon and multiple dendrites are formed, is crucial for neuronal functions, and symmetry breaking is the initial step of this process. Accumulating studies have revealed a number of molecules that act asymmetrically in neurons, and thereby regulate neuronal polarity. Thus, one of the major goals of current research is to understand how asymmetric signals are generated during the symmetry-breaking step. Current models of neuronal symmetry breaking generally involve "local activation" for induction of axon outgrowth and "global inhibition" to suppress formation of multiple axons and can be categorized into "one-takes-all" and "activator-inhibitor" models. Both types of model incorporate a positive feedback loop to execute local activation, but differ in the manner of global inhibition. Quantitative experimentation combined with computational modeling is a powerful strategy in systems biology, and analyses in this direction have begun to yield a more profound understanding of how neurons break their symmetry during polarity formation.

A diffusion-based neurite length-sensing mechanism involved in neuronal symmetry breaking.

Although there has been significant progress in understanding the molecular signals that change cell morphology, mechanisms that cells use to monitor their size and length to regulate their morphology remain elusive. Previous studies suggest that polarizing cultured hippocampal neurons can sense neurite length, identify the longest neurite, and induce its subsequent outgrowth for axonogenesis. We observed that shootin1, a key regulator of axon outgrowth and neuronal polarization, accumulates in neurite tips in a neurite length-dependent manner; here, the property of cell length is translated into shootin1 signals. Quantitative live cell imaging combined with modeling analyses revealed that intraneuritic anterograde transport and retrograde diffusion of shootin1 account for its neurite length-dependent accumulation. Our quantitative model further explains that the length-dependent shootin1 accumulation, together with shootin1-dependent neurite outgrowth, constitutes a positive feedback loop that amplifies stochastic fluctuations of shootin1 signals, thereby generating an asymmetric signal for axon specification and neuronal symmetry breaking.

Sprouty4, an FGF inhibitor, displays cyclic gene expression under the control of the notch segmentation clock in the mouse PSM.

BACKGROUND: During vertebrate embryogenesis, somites are generated at regular intervals, the temporal and spatial periodicity of which is governed by a gradient of fibroblast growth factor (FGF) and/or Wnt signaling activity in the presomitic mesoderm (PSM) in conjunction with oscillations of gene expression of components of the Notch, Wnt and FGF signaling pathways. PRINCIPAL FINDINGS: Here, we show that the expression of Sprouty4, which encodes an FGF inhibitor, oscillates in 2-h cycles in the mouse PSM in synchrony with other oscillating genes from the Notch signaling pathway, such as lunatic fringe. Sprouty4 does not oscillate in Hes7-null mutant mouse embryos, and Hes7 can inhibit FGF-induced transcriptional activity of the Sprouty4 promoter. CONCLUSIONS: Thus, periodic expression of Sprouty4 is controlled by the Notch segmentation clock and may work as a mediator that links the temporal periodicity of clock gene oscillations with the spatial periodicity of boundary formation which is regulated by the gradient of FGF/Wnt activity.

Quantification of local morphodynamics and local GTPase activity by edge evolution tracking.

Advances in time-lapse fluorescence microscopy have enabled us to directly observe dynamic cellular phenomena. Although the techniques themselves have promoted the understanding of dynamic cellular functions, the vast number of images acquired has generated a need for automated processing tools to extract statistical information. A problem underlying the analysis of time-lapse cell images is the lack of rigorous methods to extract morphodynamic properties. Here, we propose an algorithm called edge evolution tracking (EET) to quantify the relationship between local morphological changes and local fluorescence intensities around a cell edge using time-lapse microscopy images. This algorithm enables us to trace the local edge extension and contraction by defining subdivided edges and their corresponding positions in successive frames. Thus, this algorithm enables the investigation of cross-correlations between local morphological changes and local intensity of fluorescent signals by considering the time shifts. By applying EET to fluorescence resonance energy transfer images of the Rho-family GTPases Rac1, Cdc42, and RhoA, we examined the cross-correlation between the local area difference and GTPase activity. The calculated correlations changed with time-shifts as expected, but surprisingly, the peak of the correlation coefficients appeared with a 6-8 min time shift of morphological changes and preceded the Rac1 or Cdc42 activities. Our method enables the quantification of the dynamics of local morphological change and local protein activity and statistical investigation of the relationship between them by considering time shifts in the relationship. Thus, this algorithm extends the value of time-lapse imaging data to better understand dynamics of cellular function.