Congruent qualitative behavior of complete and reconstructed phase space trajectories from biomolecular dynamics simulation

Central to the study of a complex dynamical system is knowledge of its phase space behavior. Experimentally, it is rarely possible to record a system's (multidimensional) phase space variables. Rather, the system is observed via one (or few) scalar-valued signal(s) of emission or response. In dynamical systems analysis, the multidimensional phase space of a system can be reconstructed by manipulation of a one-dimensional signal. The trick is in the construction of a (higher-dimensional) space through the use of a time lag (or delay) on the signal time series. The trajectory in this embedding space can then be examined using phase portraits generated in selected subspaces. By contrast, in computer simulation, one has an embarrassment of riches: direct access to the complete multidimensional phase space variables, at arbitrary time resolution and precision. Here, the problem is one of reducing the dimensionality to make analysis tractable. This can be achieved through linear or nonlinear projection of the trajectory into subspaces containing high information content. This study considers trajectories of the small protein crambin from molecular dynamics simulations. The phase space behavior is examined using principal component analysis on the Cartesian coordinate covariance matrix of 138 dimensions. In addition, the phase space is reconstructed from a one dimensional signal, representing the radius of gyration of the structure along the trajectory. Comparison of low-dimensional phase portraits obtained from the two methods shows that the complete phase space distribution is well represented by the reconstruction. The study suggests that it may be possible to develop a deeper connection between the experimental and simulated dynamics of biomolecules via phase space reconstruction using data emerging from recent advances in single-molecule time-resolved biophysical techniques.     

Changes of Exponential Growth Rates in Relation to Differentiation of Geotrichum candidum in Submerged Culture

Growth and differentiation of the imperfect fungus Geotrichum candidum were followed in submerged cultures containing a simple synthetic glucose salt medium. Uptake of glucose, ammonium and oxygen from the medium were measured during the entire growth perod. In 0.1% glucose the fungus grows with one exponential growth phase until all the glucose has been consumed. The arthrospores are formed in the stationary phase. In 0.5% glucose the growth curve has two exponential growth phases, one with a doubling time of 1.8 h and a second one with a doubling time of 4.9 h. The second exponential growth phase, which starts when less than 15% of the glucose and less than 30% of the ammonium have been consumed, is shown to be the sporulation phase. During this growth phase the oxygen saturation in the culture remained constant at about 50%.     

The pineal gland and seasonal reproductive adjustments

The pineal gland seems to play a major role in controlling and synchronizing circannual reproductive cycles in some mammals. The following scheme is based primarily on experimental evidence compiled using the golden hamster. However, it is probably applicable in one form or another to a number of long day breeding species. When hamsters are kept under natural photoperiodic conditions they exhibit a period of infertility followed by a period of fertility. The entire cycle encompasses approximately one year. The cycle has been divided into 4 distinctive phases: the inhibition phase, the sexually quiescent phase, the restoration phase, and the sexually active phase. During the inhibition phase the decreasing photoperiods in the fall of the year cause activation of the pineal gland and, as a consequence, gonadal regression. The sexually quiescent phase requires an intact pineal gland to maintain the gonads in a non-functional state. The restoration phase, which occurs in the spring of the year, allows the gonads to become recrudescent. This phase of the cycle seems to be light independent. The sexually active phase extends from spring until fall. During this phase the hypothalamo-pituitary-gonadal axis seems to be refractory to inhibition by the pineal gland. Some light is required during the summer months to interrupt the refractory period.     

Effect of rapidity of phase separation on the efficiency of cell fractionation by partitioning in aqueous two-phase systems

Partitioning in two-polymer aqueous phase systems is an established method for the separation, purification and characterization of biomaterials. Because of the relatively slow settling rates of these phases, a consequence of the slight difference in density between them, effort has been directed to speeding up phase separation by various means (e.g., the development of a thin-layer countercurrent distribution apparatus). This has resulted in the more rapid processing of materials. Unlike soluble materials, biological particulates (e.g., cells) generally partition between one of the bulk phases and the interface. The mechanism of cell partitioning involves cell-specific adsorption to droplets of one phase suspended in the other, subsequent to phase mixing, and the delivery of adsorbed cells to the bulk interface as the droplets settle. In this communication we show, using erythrocytes as a model, that speeding up phase separation is counterproductive when partitioning cells and results in reduced efficiency of their separation or subfractionation. The most likely reason for this result is that increasing the speed of phase settling removes the droplets of one phase suspended in the other more rapidly than cells can attach to them, thereby interfering with the mechanism whereby cells partition.     

Nucleoid structure and partition in Methanococcus jannaschii: an archaeon with multiple copies of the chromosome.

We measured different cellular parameters in the methanogenic archaeon Methanococcus jannaschii. In exponential growth phase, the cells contained multiple chromosomes and displayed a broad variation in size and DNA content. In most cells, the nucleoids were organized into a thread-like network, although less complex structures also were observed. During entry into stationary phase, chromosome replication continued to termination while no new rounds were initiated: the cells ended up with one to five chromosomes per cell with no apparent preference for any given DNA content. Most cells in stationary phase contained more than one genome equivalent. Asymmetric divisions were detected in stationary phase, and the nucleoids were found to be significantly more compact than in exponential phase.     

Spatial and temporal structure of phase synchronization of spontaneous alpha EEG activity

Spatiotemporal characteristics of spontaneous alpha EEG activity patterns are analyzed in terms of large-scale phase synchronization. During periods with strong phase synchronization over the entire scalp, phase patterns take either of two forms; one is a gradual phase shift between frontal and occipital regions and the other is a stepwise pattern with a sudden phase shift in the central region. The former is regarded as a traveling wave of electrocortical activity, of which the direction of propagation is predominantly from anterior to posterior in three out of four subjects, and opposite in the remaining one. The other activity pattern observed may correspond to a standing wave composed of two traveling waves propagating in opposite directions. The duration distributions of these patterns have similar forms within a subject, which suggests that they share the same mechanism for their generation.     

Bovine papilloma virus plasmids replicate randomly in mouse fibroblasts throughout S phase of the cell cycle

Bovine papilloma virus (BPV) replicates as a multicopy nuclear plasmid in mouse fibroblasts. Using fluorescence activated cell sorting and mitotic selection procedures, we show that the replication of BPV occurs throughout S phase of the cell cycle and that replication is confined to S phase. After one round of chromosomal DNA replication, almost one quarter of BPV plasmids have replicated more than once, while a similar number of plasmids have not replicated at all. While multiple forms of BPV exist in the cell, all forms show the same pattern of replication. These results are consistent with a model in which BPV plasmids are chosen at random for replication throughout, and only during, S phase and support the view that the completion of S phase is a specifically activated event in the cell cycle rather than simply the end of one round of chromosomal DNA replication.     

Effects of carbohydrate headgroups on the stability of induced cubic phases in binary mixtures of glycolipids

This paper is part in a series of papers, investigating the influence of carbohydrate headgroups on the mesogenic properties of glycolipids. While previous papers focussed on the synthesis and mesogenic properties of the pure compounds, we will discuss here our results obtained with binary mixtures. Mixtures of compounds, one forming a lamellar phase and the other one a columnar phase in their pure state, displayed always an induced cubic phase. The stability of this induced cubic phase depends significantly on the structure of the carbohydrate headgroup of both components. Thus it was possible to derive structure–property relationships by comparison of the phase diagrams that have been obtained, if the carbohydrate headgroup of one component was changed systematically. We observed an interesting effect of galactose headgroups which might be of great biological importance. Furthermore, the observed kind of kinetic of the S_A→cub transition might also be of great biological relevance.     

Immunofluorescence study of fimbrial phase variation in Escherichia coli KS71

An immunofluorescence assay was developed to study fimbrial phase variation in a pyelonephritogenic Escherichia coli strain, KS71. By using fluorochrome-labeled antibodies specific for either P, type-1C, or type-1 fimbriae of strain KS71, it was shown that in a broth culture of strain KS71 the fimbrial types mostly occurred on different cells. Only 9% of the cells carried more than one fimbrial type. The KS71 cell population was fractionated into subpopulations expressing only one of the fimbrial types or lacking fimbriae. Immunofluorescence assay of the subpopulations revealed a rapid phase variation in fimbrial synthesis. Kinetic analyses of a nonfimbriated cell population suggested that a change from one fimbrial phase to another was not totally random.     

Analysis of the replication pattern of Chinese hamster chromosomes using 5-bromodeoxyuridine suppression of 33258 Hoechst fluorescence

Chinese hamster fibroblasts were synchronized and given 5-bromodeoxyuridine for DNA synthesis except during one hour of the S phase when thymidine was present in the medium. In the next mitosis, chromosomes stained with 33258 Hoechst were banded in appearance when photographed by fluorescence microscopy. The bright regions corresponded to the chromosome segments replicated during the thymidine exposure in the S phase. The segments replicated together during any one hour produced three distinct patterns which were characteristic of early, middle, and late S phase. Most of the fluorescent regions corresponded in size and position with G-bands of these chromosomes. There was no correlation between the staining behavior of a band in G-band procedure and its time-of-replication, i.e., both light and dark G-bands were replicated during early, middle, and late S phase. However, it appears that all of the DNA within a single band is replicated together within one third of the S phase.     

The influence of protein-lipid interactions on the order-disorder conformational transitions of the hydrocarbon chain.

The phases of simple systems involving one type of protein (lysozyme or cytochrome c) and one type of lipid (phosphatidic acid) have been characterized by X-ray crystallography, chemical analysis and spin-labeling technique as a function of temperature. They are of the lamellar type with alternative protein monolayers and lipid bilayers. According to the pH, two types of lamellar phases are obtained, one where the lipid-protein interactions are mainly hydrophobic, the other where they are electrostatic. In both cases, a phase transition occurs as temperature is lowered, between a high temperature phase, where all the lipids are in the liquid-like state, and another phase where some lipid chains are rigid. In the case of the phases with electrostatic interaction, it is shown that the onset of the order-disorder transition is shifted towards low temperature as compared with the homologous lipid-water phase and that the protein content of the phase decreases as the ratio of the liquid to rigid hydrocarbon chains decreases. This leads us to suggest that in the systems studied in this work the proteins interact only with lipid in the liquid-like state. In the case of the phases with hydrophobic interaction, it is shown that the extent of hydrophobic interaction between protein and lipid increases as the unsaturation of the hydrocarbon chains increases. The onset of the order-disorder transition shows a greater shift towards low temperature than the one observed in the case of the phase with electrostatic interaction.     

Optimal sample size allocation and go/no‐go decision rules for phase II/III programs where several phase III trials are performed

The conduct of phase II and III programs is costly, time‐consuming and, due to high failure rates in late development stages, risky. There is a strong connection between phase II and III trials as the go/no‐go decision and the sample size chosen for phase III are based on the results observed in phase II. An integrated planning of phase II and III is therefore reasonable. The success of phase II/III programs crucially depends on the allocation of the resources to phase II and III in terms of sample size and the rule applied to decide whether to stop or to proceed with phase III. Recently, a utility‐based approach was proposed, where optimal planning of phase II/III programs is achieved by taking fixed and variable costs of the drug development program and potential gains after a successful launch into account. However, this method is restricted to programs with a single phase III trial, while regulatory authorities usually require statistical significance in two or more phase III trials. We present a generalization of this procedure to programs where two or more phase III trials are performed. Optimal phase II sample sizes and go/no‐go decision rules are provided for time‐to‐event outcomes and cases, where at least one, two, or three phase III trials need to be successful. Different drug development program strategies (e.g. one large vs. two phase III trials) are compared within these different cases. Application to practical examples typically met in oncology trials illustrates the proposed method.     

Effect of counterions on the influence of dodecyltrimethylammonium halides on thermotropic phase behaviour of phosphatidylcholine bilayers

Effects of dodecyltrimethylammonium chloride (DTAC), dodecyltrimethylammonium bromide (DTAB) and dodecyltrimethylammonium iodide (DTAI) on thermotropic phase behaviour of phosphatidylcholine bilayers as well as on 1H NMR spectra were studied. In order to enhance the effect of counterions on water structure two series of experiments were performed. In the first one the surfactants were added to the water phase and in the other one directly to lipid phase (a mixed film was formed). The effects of particular surfactants on the main phase-transition temperature were more pronounced when they were added to the water phase (1st method) instead of the lipid phase (2nd method). Furthermore, in the case of the first method the transitions were found asymmetrical while in the second method nearly symmetrical. It is suggested that surfactant-poor and surfactant-rich domains are formed when surfactants are added to the water phase.     

NMR on-line monitoring of esterification catalyzed by cutinase

A nuclear magnetic resonance (NMR) method has been developed to monitor on-line lipase-catalyzed esterification reactions without the need to sample the reaction medium. The technique, through (1)H NMR, measures the concentrations of alcohol, ester, hydroxylic hydrogens in the organic phase, and hydroxylic hydrogens in the aqueous phase, if any. Also, the chemical shift evolution of the two types of hydroxylic hydrogens has been followed, providing information on water content of the organic phase and on the appearance of a distinct aqueous phase. As far as (13)C NMR is concerned, it has been possible to measure, first the acid and the ester concentrations in the carbonyl region, and second, the alcohol and the ester concentrations in the methylene region. All (1)H and (13)C results are in agreement with one another. Furthermore, NMR allows for the choice of detection zone. Preliminary studies on the solid phase proved the presence of much more water in the solid phase than in the organic phase, and also gave evidence of the existence of two types of esters, one in the organic phase, mainly associated with the acid, and the other one not associated with the acid, most probably entrapped within the solid enzyme.     

Kinetic studies on mammalian cytochrome c modified with 2-hydroxy-5-hydroxy-5-nitrobenzyl bromide.

The reduction of 2-hydroxy-5-nitrobenzyl tryptophyl cytochrome c by the chromous ion was studied by stopped-flow techniques. At pH6.5 the reduction of 2-hydroxy-5-nitrobenzyl tryptophyl cytochrome c is complex, showing the presence of three distinct phases. Two chromium concentration-dependent phases are observed (1.1 X 10(5) M-1-S-1, phase 1; 1.25 X 10(4)M-1-S-1, phase 2) and one slow first-order process (0.25S-1, phase 3). A comparison of the static and kinetic difference spectra, along with the data from the reduction of the reoxidized reduced protein, suggests that the slow chromium concentration-independent phase is due to a slow conformational event after fast reduction of the NO2 group. The rates of the chromium concentration-dependent phases show a marked variation with pH above 7.5. The activation energies for the three processes were also measured at 33.2, 38.6 and 69.7 kJ-mol-1 for phases 1, 2 and 3 respectively. The reaction of reduced 2-hydroxy-5-nitrobenzyl tryptophyl cytochrome c with CO was foollowed by means of both stopped-flow and flash photolysis. The combination with CO at pH 6.8 as measured in stopped-flow experiments showed two phases, one CO-dependent phase (phase 2, 2.4 X 10(2)M-1-S-1) and one CO-independent phase (phase 1, 0.015S-1). Investigation of the pH-dependence of the phases showed both the rates and amounts of each phase to be pH-invariant. CO recombination, after photolytic removal, was found to be biphasic; a CO-dependent phase (phase 2, 2.4 X 10(2)M-1-S-1) and a CO-independent phase (phase 1, 1.0s-1) were observed. A tentative model which can accommodate these observations is proposed.     

Biochemical Timekeeping Via Reentrant Phase Transitions

Appreciation for the role of liquid–liquid phase separation in the functional organization of cellular matter has exploded in recent years. More recently there has been a growing effort to understand the principles of heterotypic phase separation, the demixing of multiple proteins and nucleic acids into a single functional condensate. A phase transition is termed reentrant if it involves the transformation of a system from one state into a macroscopically similar or identical state via at least two phase transitions elicited by variation of a single parameter. Reentrant liquid–liquid phase separation can occur when the condensation of one species is tuned by another. Reentrant phase transitions have been modeled in vitro using protein and RNA mixtures. These biochemical studies reveal two features of reentrant phase separation that are likely important to functional cellular condensates: (1) the ability to generate condensates with layered functional topologies, and (2) the ability to generate condensates whose composition and duration are self-limiting to enable a form of biochemical timekeeping. We relate these biochemical studies to potential cellular examples and discuss how layered topologies and self-regulation may impact key biological processes.     

Parathyroid hormone-activated calcium channels in an osteoblast-like clonal osteosarcoma cell line. cAMP-dependent and cAMP-independent calcium channels

Changes in free cytosolic calcium were measured in UMR-106 cells in response to parathyroid hormone (PTH) stimulation. Bovine PTH-(1-34) induced an increase in [Ca2+]i with the contour of the rise in [Ca2+]i occurring in three successive phases: a rapid increase in [Ca2+]i occurring within seconds, rapid decrement in [Ca2+]i to near-resting levels within 1 min, and slow increment in [Ca2+]i. Phase one and phase three increases in [Ca2+]i were dependent on medium calcium. The phase one rise in [Ca2+]i was inhibitable by the calcium channel blockers lanthanum and verapamil. Only the phase one rise in [Ca2+]i was blocked by preincubation of the cells with the phorbol ester, phorbol 12-myristate 13-acetate. This channel was also blocked when cellular cAMP levels were increased prior to PTH stimulation. The phase two decrement of [Ca2+]i was due to the rapid inactivation of the phase one calcium channel. The phase three rise in [Ca2+]i was mediated by cellular cAMP levels. This cAMP-dependent Ca2+ channel was insensitive to pretreatment of the cells with phorbol diesters and showed low sensitivity to Ca2+ channel blockers. It is concluded that UMR-106 cells respond to PTH stimulation by the activation of a cAMP-independent Ca2+ channel. This channel rapidly inactivates. The subsequent PTH-dependent increase in cellular cAMP is followed by activation of a cAMP-dependent Ca2+ channel resulting in a slow rise in [Ca2+]i.     

The influence of protein-lipid interactions on the order-disorder conformational transitions of the hydrocarbon chain

The phases of simple systems involving one type of protein (lysozyme or cytochrome $\text{c}$) and one type of lipid (phosphatidic acid) have been characterized by X-ray crystallography, chemical analysis and spin-labeling technique as a function of temperature. They are of the lamellar type with alternative protein monolayers and lipid bilayers. According to the pH, two types of lamellar phases are obtained, one where the lipid-protein interactions are mainly hydrophobic, the other where they are electrostatic. In both cases, a phase transition occurs as temperature is lowered, between a high temperature phase, where all the lipids are in the liquid-like state, and another phase where some lipid chains are rigid. In the case of the phases with electrostatic interaction, it is shown that the onset of the order-disorder transition is shifted towards low temperature as compared with the homologous lipid-water phase and that the protein content of the phase decreases as the ratio of the liquid to rigid hydrocarbon chains decreases. This leads us to suggest that in the systems studied in this work the proteins interact only with lipid in the liquid-like state. In the case of the phases with hydrophobic interaction, it is shown that the extent of hydrophobic interaction between protein and lipid increases as the unsaturation of the hydrocarbon chains increases. The onset of the order-disorder transition shows a greater shift towards low temperture than the one observed in the case of the phase with electrostatic interaction.