Assessment and consequences of the constant-volume attribute of the four-chambered heart

The constant-volume hypothesis regarding the four-chambered heart states that total pericardial volume remains invariant throughout the cardiac cycle. Previous canine studies have indicated that the pericardial volume remains constant within 5%; however, this hypothesis has not been validated in humans using state-of-the-art technology. The constant-volume hypothesis has several predictable functional consequences, including a relationship between atrial ejection fraction and chamber equilibrium volumes. Using cardiac magnetic resonance (MR) imaging (MRI), we measured the extent to which the constant-volume attribute of the heart is valid, and we tested the accuracy of the predicted relationship between atrial ejection fraction and chamber equilibrium volumes. Eleven normal volunteers and one volunteer with congenital absence of the pericardium were imaged using a 1.5-T MR scanner. A short-axis cine-loop stack covering the entire heart was acquired. The cardiac cycle was divided into 20 intervals. For each slice and interval, pericardial volumes were measured. The slices were stacked and summed, and total pericardial volume as a function of time was determined for each subject. In the normal subjects, chamber volumes at ventricular end diastole, end systole, and diastasis were measured. Pericardial volume remained invariant within 5 +/- 1% in normal subjects; maximum variation occurred near end systole. In the subject with congenital absence of the pericardium, total heart volume, defined by the epicardial surface, varied by 12%. The predictions of the relationship between atrial ejection fraction and chamber equilibrium volumes were well fit by MRI data. In normal subjects, the four-chambered heart is a constant-volume pump within 5 +/- 1%, and constant-volume-based modeling accurately predicts previously unreported physiological relationships.     

IDENTIFICATION OF A CYCLIC AMP-DEPENDENT PROTEIN KINASE IN THE DINOFLAGELLATE AMPHIDINIUM OPERCULATUM

Single cell analysis by flow cytometry is a powerful tool that has been employed to identify many different characteristics of phytoplankton populations. Cell volume is an important physiological component of many cellular processes. We have used a Coulter EPICS XL flow cytometer to measure cell volume in the spheroid dinoflagellate Amphidinium operculatum as a function of forward scatter. Cell volume measurements of this alga were quantified as equivalent spherical diameters from a standard curve obtained with latex beads of known diameter. This parameter was used to monitor cell diameter throughout the cell division cycle. In log phase cultures, A. operculatum showed increasing cell volumes throughout the light phase and a maximum cell volume concurrent with the onset of cell division late in the light phase. The maximum equivalent spherical diameter measured 14 μm, while the minimum equivalent spherical diameter was 10 μm that occurred late in the dark phase. Stationary phase cultures of A. operculatum did not exhibit oscillating cell volumes throughout the diel cycle. Chemical inhibition of the cell cycle using 100 μM olomoucine diminished cell volume changes during the light phase. These results suggest a coupling of size control to the cell division cycle.     

A novel cost function to estimate parameters of oscillatory biochemical systems

Oscillatory pathways are among the most important classes of biochemical systems with examples ranging from circadian rhythms and cell cycle maintenance. Mathematical modeling of these highly interconnected biochemical networks is needed to meet numerous objectives such as investigating, predicting and controlling the dynamics of these systems. Identifying the kinetic rate parameters is essential for fully modeling these and other biological processes. These kinetic parameters, however, are not usually available from measurements and most of them have to be estimated by parameter fitting techniques. One of the issues with estimating kinetic parameters in oscillatory systems is the irregularities in the least square (LS) cost function surface used to estimate these parameters, which is caused by the periodicity of the measurements. These irregularities result in numerous local minima, which limit the performance of even some of the most robust global optimization algorithms. We proposed a parameter estimation framework to address these issues that integrates temporal information with periodic information embedded in the measurements used to estimate these parameters. This periodic information is used to build a proposed cost function with better surface properties leading to fewer local minima and better performance of global optimization algorithms. We verified for three oscillatory biochemical systems that our proposed cost function results in an increased ability to estimate accurate kinetic parameters as compared to the traditional LS cost function. We combine this cost function with an improved noise removal approach that leverages periodic characteristics embedded in the measurements to effectively reduce noise. The results provide strong evidence on the efficacy of this noise removal approach over the previous commonly used wavelet hard-thresholding noise removal methods. This proposed optimization framework results in more accurate kinetic parameters that will eventually lead to biochemical models that are more precise, predictable, and controllable.     

Mathematical modeling of a minimal protocell with coordinated growth and division

Self-replication is an essential attribute of life but the molecular-level mechanisms involved are not well understood. Cellular self-replication requires not only duplicating all cellular components and doubling volume and membrane area, but also replicating cellular geometry. A whole-cell modeling framework is presented in which an assumed reaction network determines both concentration changes of cellular components and cell geometry. Cell shape is calculated by minimizing membrane-bending energy. Using this framework, simultaneous doubling of volume, surface area, and all components was found to be insufficient to provide mid-cell “pinching” of the parental cell to form two daughter cells. This prompted the design of a minimal protocell that includes a growing shell, a cell-cycle engine, and a contractile ring to enforce cytokinesis. Kinetic parameters were found such that the system exhibited periodic behavior with fundamental aspects of self-replication. This involved simultaneous doubling of all cellular components during a cell cycle, doubling cell volume and membrane area, achieving periodic changes in surface/volume ratio, and forming daughter cells that were geometrically equivalent to each other and to the “newborn” parental cell. The results presented here impact the design of laboratory protocells and the development of a modular strategy for constructing a comprehensive in silico whole-cell model.     

MEASUREMENT OF MICROALGAL CELL VOLUME BY FLOW CYTOMETRY

Single cell analysis by flow cytometry is a powerful tool that has been employed to identify many different characteristics of phytoplankton populations. Cell volume is an important physiological component of many cellular processes. We have used a Coulter EPICS XL flow cytometer to measure cell volume in the spheroid dinoflagellate Amphidinium operculatum as a function of forward scatter. Cell volume measurements of this alga were quantified as equivalent spherical diameters from a standard curve obtained with latex beads of known diameter. This parameter was used to monitor cell diameter throughout the cell division cycle. In log phase cultures, A. operculatum showed increasing cell volumes throughout the light phase and a maximum cell volume concurrent with the onset of cell division late in the light phase. The maximum equivalent spherical diameter measured 14 μm, while the minimum equivalent spherical diameter was 10 μm that occurred late in the dark phase. Stationary phase cultures of A. operculatum did not exhibit oscillating cell volumes throughout the diel cycle. Chemical inhibition of the cell cycle using 100 μM olomoucine diminished cell volume changes during the light phase. These results suggest a coupling of size control to the cell division cycle.     

Computation of steady-state probability distributions in stochastic models of cellular networks

Cellular processes are "noisy". In each cell, concentrations of molecules are subject to random fluctuations due to the small numbers of these molecules and to environmental perturbations. While noise varies with time, it is often measured at steady state, for example by flow cytometry. When interrogating aspects of a cellular network by such steady-state measurements of network components, a key need is to develop efficient methods to simulate and compute these distributions. We describe innovations in stochastic modeling coupled with approaches to this computational challenge: first, an approach to modeling intrinsic noise via solution of the chemical master equation, and second, a convolution technique to account for contributions of extrinsic noise. We show how these techniques can be combined in a streamlined procedure for evaluation of different sources of variability in a biochemical network. Evaluation and illustrations are given in analysis of two well-characterized synthetic gene circuits, as well as a signaling network underlying the mammalian cell cycle entry.     

From START to FINISH: The Influence of Osmotic Stress on the Cell Cycle

The cell cycle is a sequence of biochemical events that are controlled by complex but robust molecular machinery. This enables cells to achieve accurate self-reproduction under a broad range of different conditions. Environmental changes are transmitted by molecular signalling networks, which coordinate their action with the cell cycle. The cell cycle process and its responses to environmental stresses arise from intertwined nonlinear interactions among large numbers of simpler components. Yet, understanding of how these pieces fit together into a coherent whole requires a systems biology approach. Here, we present a novel mathematical model that describes the influence of osmotic stress on the entire cell cycle of S. cerevisiae for the first time. Our model incorporates all recently known and several proposed interactions between the osmotic stress response pathway and the cell cycle. This model unveils the mechanisms that emerge as a consequence of the interaction between the cell cycle and stress response networks. Furthermore, it characterises the role of individual components. Moreover, it predicts different phenotypical responses for cells depending on the phase of cells at the onset of the stress. The key predictions of the model are: (i) exposure of cells to osmotic stress during the late S and the early G2/M phase can induce DNA re-replication before cell division occurs, (ii) cells stressed at the late G2/M phase display accelerated exit from mitosis and arrest in the next cell cycle, (iii) osmotic stress delays the G1-to-S and G2-to-M transitions in a dose dependent manner, whereas it accelerates the M-to-G1 transition independently of the stress dose and (iv) the Hog MAPK network compensates the role of the MEN network during cell division of MEN mutant cells. These model predictions are supported by independent experiments in S. cerevisiae and, moreover, have recently been observed in other eukaryotes.     

Alteration of the physical and chemical structure of the primary cell wall of growth-limited plant cells adapted to osmotic stress

Cells of tobacco (Nicotiana tabacum L.) adapted to grow in severe osmotic stress of 428 millimolar NaCl (−23 bar) or 30% polyethylene glycol 8000 (−28 bar) exhibit a drastically altered growth physiology that results in slower cell expansion and fully expanded cells with volumes only one-fifth to one-eighth those of unadapted cells. This reduced cell volume occurs despite maintenance of turgor pressures sometimes severalfold higher than those of unadapted cells. This report and others (NM Iraki et al [1989] Plant Physiol 90: 000-000 and 000-000) document physical and biochemical alterations of the cell walls which might explain how adapted cells decrease the ability of the wall to expand despite diversion of carbon used for osmotic adjustment away from synthesis of cell wall polysaccharides. Tensile strength measured by a gas decompression technique showed empirically that walls of NaCl-adapted cells are much weaker than those of unadapted cells. Correlated with this weakening was a substantial decrease in the proportion of crystalline cellulose in the primary cell wall. Even though the amount of insoluble protein associated with the wall was increased relative to other wall components, the amount of hydroxyproline in the insoluble protein of the wall was only about 10% that of unadapted cells. These results indicate that a cellulosic-extensin framework is a primary determinant of absolute wall tensile strength, but complete formation of this framework apparently is sacrificed to divert carbon to substances needed for osmotic adjustment. We propose that the absolute mass of this framework is not a principal determinant of the ability of the cell wall to extend.     

A connectionist model of development.

We present a phenomenological modeling framework for development. Our purpose is to provide a systematic method for discovering and expressing correlations in experimental data on gene expression and other developmental processes. The modeling framework is based on a connectionist or "neural net" dynamics for biochemical regulators, coupled to "grammatical rules" which describe certain features of the birth, growth, and death of cells, synapses and other biological entities. We outline how spatial geometry can be included, although this part of the model is not complete. As an example of the application of our results to a specific biological system, we show in detail how to derive a rigorously testable model of the network of segmentation genes operating in the blastoderm of Drosophila. To further illustrate our methods, we sketch how they could be applied to two other important developmental processes: cell cycle control and cell-cell induction. We also present a simple biochemical model leading to our assumed connectionist dynamics which shows that the dynamics used is at least compatible with known chemical mechanisms.     

A membrane model of plant cell extension

A theory is presented for the mechanics of plant cell wall extension and is based on the analogy of the cell wall with a membrane structure made of material capable of large non-linear deformations. These wall deformations may be elastic, elastic-plastic or visco-elastic. Mathematical analyses of such membrane structures show that there is, generally, a critical internal pressure at which dimensional instability occurs. This instability is characterized by a sudden drop in internal pressure accompanied by a large increase in the physical proportions of the membrane structure. The theory proposes that cell wall extension occurs when the cell turgor pressure reaches this critical instability value. The cell wall thus stretched is fixed by biochemical synthesis of wall material. Osmotic regulation re-establishes the turgor pressure and the instability cycle repeats itself as long as the critical instability pressure of the cell is below the osmotic pressure of the cell contents. Equalization of these pressures stops cell extension. The rate of cell extension depends on the frequency of the instability cycle and is thus dependent on the various rate processes associated with the instability cycle. The theory appears to be able to explain most of the known facts regarding cell extension such as the influence of temperature and the action of some growth substances.     

A Dynamic Gene Regulatory Network Model That Recovers the Cyclic Behavior of Arabidopsis thaliana Cell Cycle

Cell cycle control is fundamental in eukaryotic development. Several modeling efforts have been used to integrate the complex network of interacting molecular components involved in cell cycle dynamics. In this paper, we aimed at recovering the regulatory logic upstream of previously known components of cell cycle control, with the aim of understanding the mechanisms underlying the emergence of the cyclic behavior of such components. We focus on Arabidopsis thaliana, but given that many components of cell cycle regulation are conserved among eukaryotes, when experimental data for this system was not available, we considered experimental results from yeast and animal systems. We are proposing a Boolean gene regulatory network (GRN) that converges into only one robust limit cycle attractor that closely resembles the cyclic behavior of the key cell-cycle molecular components and other regulators considered here. We validate the model by comparing our in silico configurations with data from loss- and gain-of-function mutants, where the endocyclic behavior also was recovered. Additionally, we approximate a continuous model and recovered the temporal periodic expression profiles of the cell-cycle molecular components involved, thus suggesting that the single limit cycle attractor recovered with the Boolean model is not an artifact of its discrete and synchronous nature, but rather an emergent consequence of the inherent characteristics of the regulatory logic proposed here. This dynamical model, hence provides a novel theoretical framework to address cell cycle regulation in plants, and it can also be used to propose novel predictions regarding cell cycle regulation in other eukaryotes.     

Climate change,phenological shifts,eco-evolutionary responses and population viability: toward a unifying predictive approach

The debate on emission targets of greenhouse gasses designed to limit global climate change has to take into account the ecological consequences. One of the clearest ecological consequences is shifts in phenology. Linking these shifts to changes in population viability under various greenhouse gasses emission scenarios requires a unifying framework. We propose a box-in-a-box modeling approach that couples population models to phenological change. This approach unifies population modeling with both ecological responses to climate change as well as evolutionary processes. We advocate a mechanistic embedded correlative approach, where the link from genes to population is established using a periodic matrix population model. This periodic model has several major advantages: (1) it can include complex seasonal behaviors allowing an easy link with phenological shifts; (2) it provides the structure of the population at each phase, including the distribution of genotypes and phenotypes, allowing a link with evolutionary processes; and (3) it can incorporate the effect of climate at different time periods. We believe that the way climatologists have approached the problem, using atmosphere–ocean coupled circulation models in which components are gradually included and linked to each other, can provide a valuable example to ecologists. We hope that ecologists will take up this challenge and that our preliminary modeling framework will stimulate research toward a unifying predictive model of the ecological consequences of climate change.     

Non-invasive analysis of cell cycle dynamics in single living cells with Raman micro-spectroscopy

Raman micro-spectroscopy is a laser-based technique which enables rapid and non-invasive biochemical analysis of cells and tissues without the need for labels, markers or stains. Previous characterization of the mammalian cell cycle using Raman micro-spectroscopy involved the analysis of suspensions of viable cells and individual fixed and/or dried cells. Cell suspensions do not provide cell-specific information, and fixing/drying can introduce artefacts which distort Raman spectra, potentially obscuring both qualitative and quantitative analytical results. In this article, we present Raman spectral characterization of biochemical changes related to cell cycle dynamics within single living cells in vitro. Raman spectra of human osteosarcoma cells synchronized in G(0)/G(1), S, and G(2)/M phases of the cell cycle were obtained and multivariate statistics applied to analyze the changes in cell spectra as a function of cell cycle phase. Principal components analysis identified spectral differences between cells in different phases, indicating a decrease in relative cellular lipid contribution to Raman spectral signatures from G(0)/G(1) to G(2)/M, with a concurrent relative increase in signal from nucleic acids and proteins. Supervised linear discriminant analysis of spectra was used to classify cells according to cell cycle phase, and exhibited 97% discrimination between G(0)/G(1)-phase cells and G(2)/M-phase cells. The non-invasive analysis of live cell cycle dynamics with Raman micro-spectroscopy demonstrates the potential of this approach to monitoring biochemical cellular reactions and processes in live cells in the absence of fixatives or labels.     

Temporal and spatial oscillations in bacteria

Oscillations pervade biological systems at all scales. In bacteria, oscillations control fundamental processes, including gene expression, cell cycle progression, cell division, DNA segregation and cell polarity. Oscillations are generated by biochemical oscillators that incorporate the periodic variation in a parameter over time to generate an oscillatory output. Temporal oscillators incorporate the periodic accumulation or activity of a protein to drive temporal cycles such as the cell and circadian cycles. Spatial oscillators incorporate the periodic variation in the localization of a protein to define subcellular positions such as the site of cell division and the localization of DNA. In this Review, we focus on the mechanisms of oscillators and discuss the design principles of temporal and spatial oscillatory systems.     

Robust polarity establishment occurs via an endocytosis-based cortical corralling mechanism

Formation of a stable polarity axis underlies numerous biological processes. Here, using high-resolution imaging and complementary mathematical modeling we find that cell polarity can be established via the spatial coordination of opposing membrane trafficking activities: endocytosis and exocytosis. During polarity establishment in budding yeast, these antagonistic processes become apposed. Endocytic vesicles corral a central exocytic zone, tightening it to a vertex that establishes the polarity axis for the ensuing cell cycle. Concomitantly, the endocytic system reaches an equilibrium where internalization events occur at a constant frequency. Endocytic mutants that failed to initiate periodic internalization events within the corral displayed wide, unstable polarity axes. These results, predicted by in silico modeling and verified by high resolution in vivo studies, identify a requirement for endocytic corralling during robust polarity establishment.     

Osmotic loading of spherical gels: a biomimetic study of hindered transport in the cell protoplasm

Osmotic loading of cells has been used to investigate their physicochemical properties as well as their biosynthetic activities. The classical Kedem-Katchalsky framework for analyzing cell response to osmotic loading, which models the cell as a fluid-filled membrane, does not generally account for the possibility of partial volume recovery in response to loading with a permeating osmolyte, as observed in some experiments. The cell may be more accurately represented as a hydrated gel surrounded by a semi-permeable membrane, with the gel and membrane potentially exhibiting different properties. To help assess whether this more elaborate model of the cell is justified, this study investigates the response of spherical gels to osmotic loading, both from experiments and theory. The spherical gel is described using the framework of mixture theory. In the experimental component of the study alginate is used as the model gel, and is osmotically loaded with dextran solutions of various concentrations and molecular weight, to verify the predictions from the theoretical analysis. Results show that the mixture framework can accurately predict the transient and equilibrium response of alginate gels to osmotic loading with dextran solutions. It is found that the partition coefficient of dextran in alginate regulates the equilibrium volume response and can explain partial volume recovery based on passive transport mechanisms. The validation of this theoretical framework facilitates future investigations of the role of the protoplasm in the response of cells to osmotic loading.     

Control of cell division in Paramecium tetraurelia. Effects of abrupt changes in nutrient level on accumulation of macronuclear DNA and cell mass

In the cell cycle of Paramecium there are three points of interaction between cell growth-related processes and the processes of macronuclear DNA replication and cell division: initiation of DNA synthesis, regulation of the rates of growth and DNA accumulation, and initiation of cell division. This study examines the regulation of the latter two processes by analysis of the response of each to abrupt changes in nutrient level brought about either by transferring dividing cells from a steady-state chemostat culture to medium with unlimited food, or by transferring well-fed dividing cells to exhausted medium. The rates of DNA accumulation and cell growth respond quickly to changes in nutrient level. The amounts of these cell components accumulated during the cell cycle following a shift in nutrient level are typical of those occurring during equilibrium growth under post-shift conditions. Commitment to division occurs at a fixed interval prior to fission that is similar in well-fed and nutrient-limited cells. Initiation of cell division in Paramecium is associated with accumulation of a threshold DNA increment, whose level is largely independent of nutritive conditions. The amount of DNA accumulated during the cell cycle varies with nutritional conditions because the rates of growth and DNA accumulation are affected by nutrient level; slowly growing cells accumulated relatively little DNA during the fixed interval between commitment to cell division and fission.     

Cell cycle and apoptosis: Common pathways to life and death

Programmed cell death, or apoptosis, is a highly regulated process used to eliminate unwanted or damaged cells from multicellular organisms. The morphology of cells undergoing apoptosis is similar to cells undergoing both normal mitosis and an aberrant form of mitosis called mitotic catastrophe. During each of these processes, cells release substrate attachments, lose cell volume, condense their chromatin, and disassemble the nuclear lamina. The morphological similarities among cells undergoing these processes suggest that the underlying biochemical changes also may be related. The susceptibility of cells to apoptosis frequently depends on the differentiation state of the cell. Additionally, cell cycle checkpoints appear to link the cell cycle to apoptosis. Deregulation of the cell cycle components has been shown to induce mitotic catastrophe and also may be involved in triggering apoptosis. Some apoptotic cells express abnormal levels of cell cycle proteins and often contain active Cdc2, the primary kinase active during mitosis. Although cell cycle components may not be involved in all forms of apoptosis, in many instances cell proliferation and cell death may share common pathways.