A Mathematical Model of the Human Circadian System and Its Application to Jet Lag

A mathematical model of the circadian system is described that is appropriate for application to jet lag. The core of the model is a van der Pol equation with an external force. Approximate solutions of this equation in which the external force is composed of a constant and an oscillating term are investigated. They lead to analytical expressions for the amplitude and period of free-running rhythms and for the frequency limits of the entrainment region. The free-running period increases quadratically with stiffness. Both period and amplitude depend on the value of the constant external force. The width of the range of entrainment is mostly determined by the external force, whereas the relative position of this range follows the intrinsic period of the oscillator. Experiments with forced and spontaneous internal desynchronization were evaluated using these analytical expressions, and estimates were obtained for the intrinsic period of the oscillator, its stiffness, and the external force. A knowledge of these model parameters is essential for predictions about circadian dynamics, and there are practical implications for the assessment of the adaptation after rapid transmeridian travel.     

A Mathematical Model of the Human Circadian System and Its Application to Jet Lag

A mathematical model of the circadian system is described that is appropriate for application to jet lag. The core of the model is a van der Pol equation with an external force. Approximate solutions of this equation in which the external force is composed of a constant and an oscillating term are investigated. They lead to analytical expressions for the amplitude and period of free-running rhythms and for the frequency limits of the entrainment region. The free-running period increases quadratically with stiffness. Both period and amplitude depend on the value of the constant external force. The width of the range of entrainment is mostly determined by the external force, whereas the relative position of this range follows the intrinsic period of the oscillator. Experiments with forced and spontaneous internal desynchronization were evaluated using these analytical expressions, and estimates were obtained for the intrinsic period of the oscillator, its stiffness, and the external force. A knowledge of these model parameters is essential for predictions about circadian dynamics, and there are practical implications for the assessment of the adaptation after rapid transmeridian travel.     

Phase response and entrainment: Model computations on their relation using Wever's oscillator model

Abstract

Enright's theory, which explains entrainment as periodically repeated phase response, is applied to Wever's self‐sustained oscillation model of are circadian rhythm and tested by computer simulation. Ranges of phase response and entrainment are compared and the oscillatory behaviour is shown in the phase diagram for the cases of phase response and entrainment. It is shown that Enright's theory is not valid for self‐sustained oscillations in general, but it need not necessarily fail in case of the biological circadian rhythm.     

ProteinVolume: calculating molecular van der Waals and void volumes in proteins

Background

Voids and cavities in the native protein structure determine the pressure unfolding of proteins. In addition, the volume changes due to the interaction of newly exposed atoms with solvent upon protein unfolding also contribute to the pressure unfolding of proteins. Quantitative understanding of these effects is important for predicting and designing proteins with predefined response to changes in hydrostatic pressure using computational approaches. The molecular surface volume is a useful metric that describes contribution of geometrical volume, which includes van der Waals volume and volume of the voids, to the total volume of a protein in solution, thus isolating the effects of hydration for separate calculations.

Results

We developed ProteinVolume, a highly robust and easy-to-use tool to compute geometric volumes of proteins. ProteinVolume generates the molecular surface of a protein and uses an innovative flood-fill algorithm to calculate the individual components of the molecular surface volume, van der Waals and intramolecular void volumes. ProteinVolume is user friendly and is available as a web-server or a platform-independent command-line version.

Conclusions

ProteinVolume is a highly accurate and fast application to interrogate geometric volumes of proteins. ProteinVolume is a free web server available on http://gmlab.bio.rpi.edu. Free-standing platform-independent Java-based ProteinVolume executable is also freely available at this web site.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-015-0531-2) contains supplementary material, which is available to authorized users.     

Transition Between Advance and Delay Responses to Eastbound Transmeridian Flights

In response to eastbound transmeridian flights, which result in zeitgeber phase advance shifts, adaptation of the circadian system to the new time zone by phase delays and advances are observed. The delay response to an advance zeitgeber shift has been called an antidromic response. For the shift at which the transition from an advance to an antidromic response occurs, the term critical shift is introduced.

For the study of critical shifts, a flight experiment across nine time zones and numerical simulations of a van der Pol equation have been evaluated. The interest is focussed on the determination of a range for critical abrupt shifts. An abrupt shift means that the ensemble of zeitgebers including geophysical zeitgebers and the rest-activity cycle is shifted immediately in the new time zone. The range of critical advance shifts has been estimated to reach from + 7 to + 10 hr. In the literature, results were reported which would imply a much wider range. The discussion of these observations shows that the actual shifts were presumably not abrupt in the quoted experiments.

The consequences of critical shifts for jet lag symptoms are investigated. If reduced circadian amplitudes and long times taken for the resynchronization contribute to the feeling of jet lag, the symptoms will be worst for shifts close to the critical one, as numerical simulations revealed. Manipulations of such shifts with the aim to alleviate jet lag are discussed.     

A circadian rhythm of thermal preference in the ant Camponotus mus: masking and entrainment by temperature cycles

Abstract. Along a stable temperature gradient and under a LD 12:12 h cycle, nurse workers of the ant Camponotus mus Roger 1863 (Hymenoptera: Formicidae) select for the brood two different temperatures daily: 30.8°C at the middle of the light period (circadian phase = 90°), and 27.5°C 8 h later, during the dark period (circadian phase = 210°), this rhythm being of endogenous nature.When a 24 h temperature cycle was superimposed along the thermal gradient, so that the immobile brood experienced a temperature transition as they receive when translocated by nurses (8 h at 30.8°C and 16 h at 27.5°C), no brood translocations occurred.The thermal cycle masked the rhythm of brood translocation when temperature fitted the daily pattern expected by nurses.When the same temperature cycle was presented with a phase-advance, nurses did not tolerate the early thermal increase and removed the brood as temperature rose.However, when workers experienced this new phase relationship between light and temperature cycles for more than 10 days, brood translocations were suppressed.Records under constant conditions of light and temperature indicated that the overt rhythm was locked-on to the expected early increase in temperature, so that the temperature cycle dominated over the LD cycle in resetting brood-carrying activity.     

Bioluminescent kinase strips: A novel approach to targeted and flexible kinase inhibitor profiling

In addition to target efficacy, drug safety is a major requirement during the drug discovery process and is influenced by target specificity. Therefore, it is imperative that every new drug candidate be profiled against various liability panels that include protein kinases. Here, an effective methodology to streamline kinase inhibitor profiling is described. An accessible standardized profiling system for 112 protein kinases covering all branches of the kinome was developed. This approach consists of creating different sets of kinases and their corresponding substrates in multi-tube strips. The kinase stocks are pre-standardized for optimal kinase activity and used for inhibitor profiling using a bioluminescent ADP detection assay. We show that these strips can routinely generate inhibitor selectivity profiles for small or broad kinase family panels. Lipid kinases were also assembled in strip format and profiled together with protein kinases. We identified two specific PI3K inhibitors that have off-target effects on CK2 that were not reported before and would have been missed if compounds were not profiled against lipid and protein kinases simultaneously. To validate the accuracy of the data generated by this method, we confirmed that the inhibition potencies observed are consistent with published values produced by more complex technologies such as radioactivity assays.     

A novel PCR-based approach for the detection and classification of potential cellulolytic fungal strains isolated from museum items and surrounding indoor environment

Aims: To develop a novel PCR‐based method able to detect potential cellulolytic filamentous fungi and to classify them exploiting the amplification of the cellobiohydrolase gene (cbh‐I) and its polymorphism. Methods and Results: A mixed approach including the combination of (i) fungal cultivation and isolation, (ii) classification of fungal isolates through the amplification of the cbh gene using a fluorescently labelled primer (f‐CBH‐PCR) and (iii) final fungal identification based on amplification and sequencing of the ITS1‐5.8S rDNA‐ITS2 region of the selected fungal strains was developed. By this approach, it was possible to screen 77 fungal strains belonging to 14 genera and 26 species. Conclusions: The f‐CBH‐PCR permitted the discrimination of fungal species, producing typical f‐CBH profiles. Significance and Impact of the Study: In this study, the cbh gene was used as a preliminary classification tool able to differentiate among themselves the fungal members isolated from indoor museum items and surrounding environment. Such mixed approach consented the fast identification of all isolated fungal strains. The f‐CBH‐PCR method demonstrated its discrimination power, and it can be considered as a new molecular system suitable for the classification of fungal strains isolated from different environments.     

A novel approach to the establishment of dual cultures of pearl millet and Sclerospora graminicola

Dual cultures were successfully established using malformed florets of pearl millet infected with Sclerospora graminicola, the downy mildew pathogen. A higher proportion (86%) of calli from malformed florets formed dual cultures on Murashige and Skoog's (MS) medium with 2 mg 1^-1 of 2,4-dichlorophenoxy acetic acid (2,4-d), compared to shoot tips (25%). Fungal mycelium covered the entire surface of the callus within 30 days of placement of explants on the MS medium with 2 mg 1^-1 of 2,4-d. The infected calli also differentiated and produced plantlets when transferred to MS medium without 2,4-d.     

A novel approach to the analysis of specificity, clonality, and frequency of HIV-specific T cell responses reveals a potential mechanism for control of viral escape

Escape from the CD8(+) T cell response through epitope mutations can lead to loss of immune control of HIV replication. Theoretically, escape from CD8(+) T cell recognition is less likely when multiple TCRs target individual MHC/peptide complexes, thereby increasing the chance that amino acid changes in the epitope could be tolerated. We studied the CD8(+) T cell response to six immunodominant epitopes in five HIV-infected subjects using a novel approach combining peptide stimulation, cell surface cytokine capture, flow cytometric sorting, anchored RT-PCR, and real-time quantitative clonotypic TCR tracking. We found marked variability in the number of clonotypes targeting individual epitopes. One subject recognized a single epitope with six clonotypes, most of which were able to recognize and lyse cells expressing a major epitope variant that arose. Additionally, multiple clonotypes remained expanded during the course of infection, irrespective of epitope variant frequency. Thus, CD8(+) T cells comprising multiple TCR clonotypes may expand in vivo in response to individual epitopes, and may increase the ability of the response to recognize virus escape mutants.     

Phase locking,period doubling bifurcations and chaos in a mathematical model of a periodically driven oscillator: A theory for the entrainment of biological oscillators and the generation of cardiac dysrhythmias

A mathematical model for the perturbation of a biological oscillator by single and periodic impulses is analyzed. In response to a single stimulus the phase of the oscillator is changed. If the new phase following a stimulus is plotted against the old phase the resulting curve is called the phase transition curve or PTC (Pavlidis, 1973). There are two qualitatively different types of phase resetting. Using the terminology of Winfree (1977, 1980), large perturbations give a type 0 PTC (average slope of the PTC equals zero), whereas small perturbations give a type 1 PTC. The effects of periodic inputs can be analyzed by using the PTC to construct the Poincaré or phase advance map. Over a limited range of stimulation frequency and amplitude, the Poincaré map can be reduced to an interval map possessing a single maximum. Over this range there are period doubling bifurcations as well as chaotic dynamics. Numerical and analytical studies of the Poincaré map show that both phase locked and non-phase locked dynamics occur. We propose that cardiac dysrhythmias may arise from desynchronization of two or more spontaneously oscillating regions of the heart. This hypothesis serves to account for the various forms of atrioventricular (AV) block clinically observed. In particular 22 and 42 AV block can arise by period doubling bifurcations, and intermittent or variable AV block may be due to the complex irregular behavior associated with chaotic dynamics.     

A pentavalent single-domain antibody approach to tumor antigen discovery and the development of novel proteomics reagents

Proteomics research has delivered many novel tumor targets. However, due to key limitations, it does not specifically identify targets that are most accessible for drug delivery, such as cell-surface antigens. A novel tumor antigen discovery platform based on screening a single domain antibody (sdAb) library against tumor cells and subsequently identifying the corresponding antigens of the isolated antibodies is described. An sdAb, AFAI, specific for non-small cell lung carcinoma (A549 cell line) was isolated from a phage library derived from the heavy chain antibody repertoire of a llama. The homopentamerization property of a non-toxic verotoxin B-subunit was exploited to make the ES1 pentabody, a pentameric form of AFAI. Pentamerization improved the binding of the AFAI to A549 cells dramatically and greatly facilitated antigen identification by a Western blotting/mass spectrometry approach. The antigen of ES1, which is present only in the hydrophobic, not in the hydrophilic, fraction of A549 cellular proteins, was identified as carcinoembryonic antigen-related cell adhesion molecule 6 (CEA6). CEA6 was observed to be acidic and highly glycosylated, and to exist in multiple glycoforms. The results show that the platform described here should find wide application in antigen discovery, and demonstrated that the pentabodies are very useful immunological reagents for proteomics.     

Surfactosomes: a novel approach to the reconstitution and 2-D crystallisation of membrane proteins

The formation of vesicle-like structures (termed surfactosomes) and lamellar sheets from solutions containing ammonium perfluoroocanoate (APFO) is illustrated using conventional and cryo-transmission electron microscopy. It is shown how this detergent can be used for the solubilisation, reconstitution, and 2-D crystallisation of membrane proteins as demonstrated for the major protein of the membrane sector of the V-type H⁺-ATPase (16-kDa protein). Electron microscopical analysis of 2-D crystals of the 16-kDa protein (a = b = 13.0 ± 0.2 nm with γ = 90° and p4 projection symmetry) revealed a unit cell comprising four dimeric complexes of the 16-kDa protein the significance of which is discussed.     

A novel approach to overcome temozolomide resistance in glioma and melanoma: Inactivation of MGMT by gene therapy

Malignant glioma is the most common primary brain tumor. Malignant melanoma is the most malignant of skin tumor. The two malignancies are poorly responsive to conventional treatment regimens such as chemotherapy. Temozolomide (TMZ) is a DNA-alkylating agent used for the treatment of glioma, astrocytoma, and melanoma. Resistance to alkylating agents such as TMZ correlates with increased expression of DNA repair protein O6-methylguanine-DNA methyltransferase (MGMT). Several studies in animal models have demonstrated that decreasing MGMT level with gene therapy could overcome TMZ resistance and enhance tumor cell death. In the present review, we provide an overview of recent advances in this field.     

A novel computer modeling approach to the structures of small bioactive peptides: The structure of gonadotropin releasing hormone

A novel computer modeling approach suitable for the structure analysis of small bioactive peptides has been developed. This approach involves identification of conformational patterns in protein structure data bank based on the sequence homology with the bioactive peptide. The models built on the basis of this homology and having common conformational patterns are analyzed under the structural constraints derived from the activity data of various synthetic analogs of the peptide. Application of this procedure to the gonadotropin releasing hormone (GnRH) resulted in a library of possible structures for GnRH, 9 among which shared a common β-turn. Further analysis of the structures containing the β-turn motif, in the context of the structure–activity data, led to a model for the active conformation of GnRH. The topology of the putative receptor binding site of the hormone is defined by a contiguous surface formed through an appropriate juxtaposition of the N-terminal pGlu¹ the guanidyl group of Arg⁸, aromatic side chain of Trp³, and the Gly¹⁰-NH₂ at the C-terminal end. ©Wiley-Liss, Inc.     

A new analytical approach to landscape genetic modelling: least-cost transect analysis and linear mixed models

Landscape genetics aims to assess the effect of the landscape on intraspecific genetic structure. To quantify interdeme landscape structure, landscape genetics primarily uses landscape resistance surfaces (RSs) and least-cost paths or straight-line transects. However, both approaches have drawbacks. Parameterization of RSs is a subjective process, and least-cost paths represent a single migration route. A transect-based approach might oversimplify migration patterns by assuming rectilinear migration. To overcome these limitations, we combined these two methods in a new landscape genetic approach: least-cost transect analysis (LCTA). Habitat-matrix RSs were used to create least-cost paths, which were subsequently buffered to form transects in which the abundance of several landscape elements was quantified. To maintain objectivity, this analysis was repeated so that each landscape element was in turn regarded as migration habitat. The relationship between explanatory variables and genetic distances was then assessed following a mixed modelling approach to account for the nonindependence of values in distance matrices. Subsequently, the best fitting model was selected using the statistic. We applied LCTA and the mixed modelling approach to an empirical genetic dataset on the endangered damselfly, Coenagrion mercuriale. We compared the results to those obtained from traditional least-cost, effective and resistance distance analysis. We showed that LCTA is an objective approach that identifies both the most probable migration habitat and landscape elements that either inhibit or facilitate gene flow. Although we believe the statistical approach to be an improvement for the analysis of distance matrices in landscape genetics, more stringent testing is needed.