Mikiya Otsuji

A Mass Conserved Reaction–Diffusion System Captures Properties of Cell Polarity

Cell polarity is a general cellular process that can be seen in various cell types such as migrating neutrophils and Dictyostelium cells. The Rho small GTP(guanosine 5′-tri phosphate)ases have been shown to regulate cell polarity; however, its mechanism of emergence has yet to be clarified. We first developed a reaction–diffusion model of the Rho GTPases, which exhibits switch-like reversible response to a gradient of extracellular signals, exclusive accumulation of Cdc42 and Rac, or RhoA at the maximal or minimal intensity of the signal, respectively, and tracking of changes of a signal gradient by the polarized peak. The previous cell polarity models proposed by Subramanian and Narang show similar behaviors to our Rho GTPase model, despite the difference in molecular networks. This led us to compare these models, and we found that these models commonly share instability and a mass conservation of components. Based on these common properties, we developed conceptual models of a mass conserved reaction–diffusion system with diffusion–driven instability. These conceptual models retained similar behaviors of cell polarity in the Rho GTPase model. Using these models, we numerically and analytically found that multiple polarized peaks are unstable, resulting in a single stable peak (uniqueness of axis), and that sensitivity toward changes of a signal gradient is specifically restricted at the polarized peak (localized sensitivity). Although molecular networks may differ from one cell type to another, the behaviors of cell polarity in migrating cells seem similar, suggesting that there should be a fundamental principle. Thus, we propose that a mass conserved reaction–diffusion system with diffusion-driven instability is one of such principles of cell polarity.

Tracking of intertissue migration reveals the origins of tumor-infiltrating monocytes

Significance Solid tumors contain large numbers of immune cells, including monocytes and monocyte-derived macrophages that promote tumor progression. During tumor development, monocytes accumulate in the spleen. However, the influence of spleen cells on tumor growth remains controversial. Here, we used novel methods for tracking intertissue migration and monitoring hematopoiesis to show that during tumor development the bone marrow dramatically accelerates production of monocytes, rapidly transferring many of these newly formed cells to a reservoir in the spleen. However, these spleen monocytes are less able than their bone marrow counterparts to enter the tumor and make only a minor contribution to the tumor-infiltrating monocyte population. These findings clarify the roles of the spleen and bone marrow in cancer development. Myeloid cells such as monocytes and monocyte-derived macrophages promote tumor progression. Recent reports suggest that extramedullary hematopoiesis sustains a sizable reservoir of tumor-infiltrating monocytes in the spleen. However, the influence of the spleen on tumor development and the extent to which spleen monocytes populate the tumor relative to bone marrow (BM) monocytes remain controversial. Here, we used mice expressing the photoconvertible protein Kikume Green-Red to track the redistribution of monocytes from the BM and spleen, and mice expressing fluorescent ubiquitination-based cell-cycle indicator proteins to monitor active hematopoiesis in these tissues. In mice bearing late-stage tumors, the BM, besides being the major site of monocyte production, supplied the expansion of the spleen reservoir, replacing 9% of spleen monocytes every hour. Deployment of monocytes was equally rapid from the BM and the spleen. However, BM monocytes were younger than those in the spleen and were 2.7 times more likely to migrate into the tumor from the circulation. Partly as a result of this intrinsic difference in migration potential, spleen monocytes made only a minor contribution to the tumor-infiltrating monocyte population. At least 27% of tumor monocytes had traveled from the BM in the last 24 h, compared with only 2% from the spleen. These observations highlight the importance of the BM as the primary hematopoietic tissue and monocyte reservoir in tumor-bearing mice, despite the changes that occur in the spleen monocyte reservoir during tumor development.

A Conceptual Molecular Network for Chemotactic Behaviors Characterized by Feedback of Molecules Cycling Between the Membrane and the Cytosol

Simulations and observations of migrating cells suggest a model for feedback loops that regulate chemotaxis. Understanding Navigation Cells that migrate up a gradient of chemoattractant, a process known as chemotaxis, do so by producing membrane protrusions called pseudopods. Various models have been proposed to describe how pseudopods form and drive cell movement and navigation. Otsuji et al. performed simulations of migrating cells and observed cells undergoing chemotaxis, enabling them to develop a conceptual model to explain pseudopod formation. Their model is based on two interacting molecules, “A” and “B,” such that A promotes membrane protrusion (and pseudopod formation), whereas B promotes membrane retraction. A and B cycle between the membrane and the cytosol, and they have diffusion rates that are slower in the membrane than in the cytosol. Instabilities in the model, based on differential diffusion, combine to promote competition between potential pseudopods, such that one is favored; such instabilities also lead to the periodic splitting of a pseudopod into two “peaks,” only one of which persists. The surviving pseudopods often exhibit an alternating left-right pattern that aids migration. Although the environment through which a cell migrates is likely more complex than the model assumes, this general model suggests a simple explanation for pseudopod formation and cell migration. Cell chemotaxis has been characterized as the formation of a front-back axis that is triggered by a gradient of chemoattractant; however, chemotaxis is accompanied by more complicated behaviors. These include migration in a straight line with a stable axis [the stable single-axis (SSA) pattern] and repeated splitting of the leading edge of the cell into two regions, followed by the “choice” of one of these as the new leading edge [the split and choice (S&C) pattern]. Indeed, transition between these two behaviors can be observed in individual cells. However, the conceptual framework of the network of signaling molecules that generates these patterns remains to be clarified. We confirmed theoretically that a system that has positive and negative feedback loops involving the reciprocal cycling between the membrane and the cytosol of molecules that promote membrane protrusion or retraction generates SSA and S&C patterns of migratory behavior under similar conditions. We also predicted properties of the instabilities of such a system, which are essential for the generation of these behaviors, and we verified their existence in chemotaxing cells. Our research provides a simple model of network structure for chemotactic behaviors, including cell polarization.

Derivation of recruitment function from the pressure-volume curve in an acute lung injury model.

Lung volume changes involve the recruitment of collapsed alveoli and the expansion of already opened alveoli. This study aimed to determine the alveolar recruitment function by using a mathematical model from a pressure-volume curve (P-V curve). We assumed a lung model as VL=R(P)V0f(P), where R recruitment function is the fraction of recruited alveoli, V0 is the resting lung volume at FRC of a fully recruited lung, and f(P) corresponds to the normalized compliance function of the lungs open to ventilation. Seven white rabbits were subjected to saline-lavage lung injury, and P-V curves were calculated using the slow inflation technique. We obtained the P-R curve from the P-V curve, and two curves were differently shaped after lung injury. We concluded that the recruitment function was obtained from the P-V curve and that the P-R curve estimated the recruitment and derecruitment status.

Half-Logistic Function Model for First Half of Descending Phase of Cardiomyocyte Cytoplasmic Ca2+ Concentration ([Ca2+]i)-Time Curve (CaTCIII) in Isolated Aequorin-Injected Mouse Left Ventricular Papillary Muscle

BACKGROUND Myocardial contraction and relaxation are regulated by increases and decreases in cytoplasmic calcium concentration ([Ca(2+)]i). In previous studies, we found that a half-logistic (h-L) function, which represents a half-curve of a symmetrical sigmoid logistic function with a boundary at the inflection point, curve-fits the first half of the ascending phase and the second half of the descending phase of the [Ca(2+)]i transient curve better than a mono-exponential (m-E) function. In the present study, we investigated the potential application of an h-L function to analyse the first half of the descending phase of CaTC (CaTCIII). METHODS The [Ca(2+)]i was measured using the Ca(2+)-sensitive aequorin, which was microinjected into 15 isolated mouse left ventricular (LV) papillary muscles. The observed CaTCIII data in the interval from the point corresponding to the peak [Ca(2+)]i to the point corresponding to dCa/dtmin was curve-fitted using the h-L and m-E function equations by the least-squares method. RESULTS The mean correlation coefficient (r) values of the h-L and m-E function best curve-fits for 11 CaTCIIIs were 0.9986 and 0.9982, respectively. The Z transformation of h-L r (3.64 ± 0.45) was larger than that of m-E r (3.50 ± 0.33) (p < 0.05). CONCLUSIONS The h-L function can evaluate most CaTCIIIs more accurately than the m-E function in isolated aequorin-injected mouse LV papillary muscle. The three calculated h-L parameters i.e., amplitude constant, time constant, and non-zero asymptote, are more reliable indices than m-E for evaluating the magnitude and time course of the change in the decrease in [Ca(2+)]i. KEY WORDS Ca(2+) transient; Half-logistic amplitude constant; Half-logistic non-zero asymptote; Half-logistic time constant; Myocardial Ca(2+) handling.

Temperature-dependent inotropic and lusitropic indices based on half-logistic time constants for four segmental phases in isovolumic left ventricular pressure–time curve in excised, cross-circulated canine heart

Varying temperature affects cardiac systolic and diastolic function and the left ventricular (LV) pressure-time curve (PTC) waveform that includes information about LV inotropism and lusitropism. Our proposed half-logistic (h-L) time constants obtained by fitting using h-L functions for four segmental phases (Phases I-IV) in the isovolumic LV PTC are more useful indices for estimating LV inotropism and lusitropism during contraction and relaxation periods than the mono-exponential (m-E) time constants at normal temperature. In this study, we investigated whether the superiority of the goodness of h-L fits remained even at hypothermia and hyperthermia. Phases I-IV in the isovolumic LV PTCs in eight excised, cross-circulated canine hearts at 33, 36, and 38 °C were analyzed using h-L and m-E functions and the least-squares method. The h-L and m-E time constants for Phases I-IV significantly shortened with increasing temperature. Curve fitting using h-L functions was significantly better than that using m-E functions for Phases I-IV at all temperatures. Therefore, the superiority of the goodness of h-L fit vs. m-E fit remained at all temperatures. As LV inotropic and lusitropic indices, temperature-dependent h-L time constants could be more useful than m-E time constants for Phases I-IV.