Comparative thermodynamic elucidation of the structural stability of thermophilic proteins

Differential scanning calorimetry, circular dichroism, and visible absorption spectrophotometry were employed to elucidate the structural stability of thermophilic phycocyanin derived from Cyanidium caldarium, a eucaryotic organism which contains a nucleus, grown in acidic conditions (pH 3.4) at 54°C. The obtained results were compared with those previously reported for thermophilic phycocyanin derived from Synechococcus lividus, a procaryote containing no organized nucleus, grown in alkaline conditions (pH 8.5) at 52°C. The temperature of thermal unfolding (t_d) was found to be comparable between C. caldarium (73°C) and S. lividus (74°C) phycocyanins. The apparent free energy of unfolding (ΔG_[urea]=0) at zero denaturant (urea) concentration was also comparable: 9.1 and 8.7 kcal/mole for unfolding the chromophore part of the protein, and 5.0 and 4.3 kcal/mole for unfolding the apoprotein part of the protein, respectively. These values of t_d and ΔG_[urea]=0 were significantly higher than those previously reported for mesophilic Phormidium luridum phycocyanin (grown at 25°C). These findings revealed that relatively higher values of t_d and ΔG_[urea]=0 were characteristics of thermophilic proteins. In contrast, the enthalpies of completed unfolding (ΔH_d) and the half-completed unfolding (ΔH_d)1/2 for C. caldarium phycocyanin were much lower than those for S. lividus protein (89 versus 180 kcal/mole and 62 versus 115 kcal/mole, respectively). Factors contributing to a lower ΔH_d in C. caldarium protein and the role of charged groups in enhancing the stability of thermophilic proteins were discusse.     

Mathematical model indicates nonlinearity of noradrenaline effect on rat renal artery

The aim of this work is to present the efficacy of a previously introduced computational procedure, developed for evaluation of vascular responsiveness. On this reason, as an example a common study of noradrenaline (NA) effect on a rat renal artery under in vitro conditions was arbitrarily selected. The response of the arterial segment to NA doses (0.1-10 microg) was digitally recorded on a PC and employed to develop mathematical model of NA effect. Using the model, the following NA effect variables were determined: the vessel sensitivity parameter, mean effect time and rate constant, respectively, characterizing the effect intensity, duration, and regression and also classic response variables: the maximal effect and time of the maximal effect. The two-way analysis of variance followed by Bonferroni's test revealed a significant influence of the increasing NA dose on the vessel sensitivity parameter and mean effect time. These findings indicated nonlinearity of processes underlying NA effect on the rat renal artery over the given range of NA doses. The procedure exemplified has the potential for use as an effective adjunct to routine studies of vascular responsiveness as it enables the extraction of meaningful information which cannot by obtained by common manual evaluation procedures.     

Mathematical model for adaptive evolution of populations based on a complex domain

A mutation is ultimately essential for adaptive evolution in all populations. It arises all the time, but is mostly fixed by enzymes. Further, most do consider that the evolution mechanism is by a natural assortment of variations in organisms in line for random variations in their DNA, and the suggestions for this are overwhelming. The altering of the construction of a gene, causing a different form that may be communicated to succeeding generations, produced by the modification of single base units in DNA, or the deletion, insertion, or rearrangement of larger units of chromosomes or genes. This altering is called a mutation. In this paper, a mathematical model is introduced to this reality. The model describes the time and space for the evolution. The tool is based on a complex domain for the space. We show that the evolution is distributed with the hypergeometric function. The Boundedness of the evolution is imposed by utilizing the Koebe function.     

Mathematical model of cardiac mechanogram rhythmicity (based on mollusc heart)

1. The time course of force development by the heart is modelled by Gompertz kinetics from the product of two terms: a cumulative increase in relative number of activated "contractile units", and an exponential decrease in contractile force. 2. For each beat, an "initial condition" is specified by an "intrinsic tension" parameter, and a specific rate of change of tension; cardioactive agents change these specifications. 3. Depending on parameter values, heartbeats are predicted that are constant, or in which the frequency, amplitude and baseline tension are appropriate to inhibited or augmented cardiac activity.     

Mathematical model of the effect of glucocorticoids on the movement and proliferation kinetics of mammalian lymphocytes

Effect of glucocorticoids on proliferation, death and migration of T-lymphocytes was studied by mathematical methods. A model of the interaction between hormone and thymus T1-lymphocytes is proposed which imitates involution of lymphoid tissue under stress. There were constructed models of migrations of free and radioactive chromium labeled lymphocytes in lymphoid and non-lymphoid organs, blood and lymph at arbitrary concentration of glucocorticoids in the blood. Possible mechanisms of immunodepression due to increased hormone concentrations in the organism are discussed.     

Mathematical model for carbohydrate energy metabolism. Mechanism of the Pasteur effect

The simple mathematical model based on the stoichiometric structure of carbohydrate metabolism and the only allosteric regulation presented, i. e. activation of phosphofructokinase by AMP, was used to study the mechanism of the Pasteur effect, e. g. interrelationship of glycolysis, the Krebs cycle and H-transporting shuttles at varying rates of oxidative phosphorylation and ATPase load. It was shown that the mechanism of the Pasteur effect is based on the presence of two negative feed-back mechanisms in carbohydrate metabolism, namely by the level of ATP in glycolysis and by the level of mitochondrial NADH in the Krebs cycle and H-transporting shuttles. It was also shown that the value and sign of the Pasteur effect depend on the level of ATPase load. The role of this phenomenon in stabilization of ATP in the cell is discussed. The effects of changes in the allosteric properties of phosphofructokinase and low activity of H-transporting shuttles on the Pasteur effect was studied. It was shown that the low values of the pasteur effect in tumour tissues are mainly determined by an insufficient activity of oxidative phosphorylation.     

Mathematical model for an evolutive and hierarchical living system, based on the theory of categories

The notion of an evolutive hierarchical system proposed here retains the following characteristics of some natural systems, like living organisms: they have an internal organization consisting of more or less complex components with interrelations; they maintain their organization in time although their components are changing; they may be studied at several complexity levels (e.g., molecular, cellular, ...). The idea is to model the state of the system at a given instant by a category, the state transition by a functor, a complex object by the (direct) limit of a pattern of linked objects (its own organization). The emergence of new properties for a complex object is measured, and a development process is described.     

Mathematical model of a simultaneous combined effect of ionizing radiation and hyperthermia

A mathematical model has been proposed suggesting that the synergistic action of a combination of ionizing radiation and hyperthermia is conditioned by additional lethal damages arising from the interaction of "sub-lesions" induced by both agents. The model describes quantitatively the synergism of the combined action of the agents used and predicts the maximal value of the synergistic effect and conditions in which it can be achieved.     

The thermodynamic stability of nanoconstructions based on the double-stranded DNA molecules

The temperature stability of nanoconstructions formed by double-stranded DNA molecules fixed in the structure of their liquid crystalline dispersions and cross-linked by nanobridges was determined. It was shown that the heating of nanoconstructions is accompanied by a decrease in the amplitude of the negative bands in the CD spectrum both at lambda approximately 310 and lambda approximately 505 nm. Temperature "melting curves" were derived and characterzed by T(M) values. The T(M) values at lambda approximately 310 and lambda approximately 505 nm coincided with each other but differed from the T(M) value characteristic of the DNA cholesteric liquid crystalline dispersion.     

Mathematical model for chemotherapeutic drug efficacy in arresting tumour growth based on the cancer stem cell hypothesis

OBJECTIVE: Cancer stem cells have been identified as the growth root for various malignant tumours and are thought to be responsible for cancer recurrence following treatment. MATERIALS AND METHODS: Here, a predictive mathematical model for the cancer stem cell hypothesis is used to understand tumour responses to chemotherapeutic drugs and judge the efficacy of treatments in arresting tumour growth. The impact of varying drug efficacies on different abnormal cell populations is investigated through the kinetics associated with their decline in response to therapy. RESULTS AND CONCLUSIONS: The model predicts the clinically established 'dandelion phenomenon' and suggests that the best response to chemotherapy occurs when a drug targets abnormal stem cells. We compare continuous and periodic drug infusion. For the latter, we examine the relative importance of the drug cell-kill rate and the mean time between successive therapies, to identify the key attributes for successful treatment.     

Mathematical model of the dynamics of psychotherapy

The success of psychotherapy depends on the nature of the therapeutic relationship between a therapist and a client. We use dynamical systems theory to model the dynamics of the emotional interaction between a therapist and client. We determine how the therapeutic endpoint and the dynamics of getting there depend on the parameters of the model. Previously Gottman et al. used a very similar approach (physical-sciences paradigm) for modeling and making predictions about husband–wife relationships. Given that this novel approach shed light on the dyadic interaction between couples, we have applied it to the study of the relationship between therapist and client. The results of our computations provide a new perspective on the therapeutic relationship and a number of useful insights. Our goal is to create a model that is capable of making solid predictions about the dynamics of psychotherapy with the ultimate intention of using it to better train therapists.     

Mathematical model of the male urinary tract

The paper presents a simplified (but not trivial) mathematical model of the interaction between the urine flow and the male urethra and bladder, respectively. Urine is assumed to be a Newtonian fluid. The flow is considered to be non-stationary, isothermal and turbulent. The urethra and bladder wall, featuring elastic properties, experience large displacements and strains. The dynamic forces are included in the urethra wall motion. When fully extended the urethra attains the shape of an axisymetric tube. An iterative method based on the uncoupled approach is developed.     

A thermodynamic model for the self-association of human spectrin

The self-association of human spectrin at 28.8 degrees C in 0.11 M salt (pH 7.5) has been studied by means of sedimentation equilibrium. Coincidence of omega function plots as a function of total spectrin concentration (0-2 g/L) indicated that equilibrium was achieved and that no significant concentration of solute was incapable of participating in the self-association reaction. On the basis of the root-mean-square deviation of the fits and the randomness of the residuals, the behavior can be described equally well, either by a cooperative isodesmic model, in which K12 approximately 2 x 10(6) M-1 and all other K approximately 10(6) M-1, or by an attenuated scheme in which K(i-1)i approximately (3.5 x 10(6)/i M-1. The returned values of the second virial coefficient, B, for both these models fall within the range calculated from the charge and Stokes radius of spectrin. A mechanism for spectrin self-association consistent with both schemes is proposed in which spectrin heterodimers undergo a reversible opening at the self-association interface. These open heterodimers then undergo indefinite self-association to form a series of open-chain oligomers in dynamic equilibrium with closed-loop oligomers.     

Atypical effect of salts on the thermodynamic stability of human prion protein

Prion diseases are associated with the conversion of cellular prion protein, PrPC, into a misfolded oligomeric form, PrPSc. Previous studies indicate that salts promote conformational conversion of the recombinant prion protein into a PrPSc-like form. To gain insight into the mechanism of this effect, here we have studied the influence of a number of salts (sodium sulfate, sodium fluoride, sodium acetate, and sodium chloride) on the thermodynamic stability of the recombinant human prion protein. Chemical unfolding studies in urea show that at low concentrations (below approximately 50 mm), all salts tested significantly reduced the thermodynamic stability of the protein. This highly unusual response to salts was observed for both the full-length prion protein as well as the N-truncated fragments huPrP90-231 and huPrP122-231. At higher salt concentrations, the destabilizing effect was gradually reversed, and salts behaved according to their ranking in the Hofmeister series. The present data indicate that electrostatic interactions play an unusually important role in the stability of the prion protein. The abnormal effect of salts is likely because of the ion-induced destabilization of salt bridges (Asp144-Arg148 and/or Asp147-Arg151) in the extremely hydrophilic helix 1. Contrary to previous suggestions, this effect is not due to the interaction of ions with the glycine-rich flexible N-terminal region of the prion protein. The results of this study suggest that ionic species present in the cellular environment may control the PrPC to PrPSc conversion by modulating the thermodynamic stability of the native PrPC isoform.     

The effect of aminoglycoside antibiotics on the thermodynamic properties of liposomal vesicles

Liposomes are ideal drug-delivery systems because they can alter the pharmacokinetic characteristics and biodistribution profile of the incorporated bioactive molecule. The effect of the aminoglycoside antibiotics, gentamicin (GN), tobramycin (TOB), and amikacin (AMI), on the thermodynamic properties of multilamellar vesicles composed of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) was studied by using differential scanning calorimetry (DSC), electron paramagnetic resonance (EPR), and ³¹P nuclear magnetic resonance (NMR) spectroscopy. The relationship between the structure of aminoglycoside antibiotics and their effect on the physical properties of the liposomal bilayers was investigated. The incorporation of the drugs was achieved and an osmotic gradient created by controlling the mole ratio of the drug inside to that outside of the DPPC vesicles so that [drug_{inside DPPC}]/[drug_{outside DPPC}] was 1:0, 1:0.2, 1:1, or 1:2.5. Incorporation of the drugs into liposomes caused the T_m to shift to a higher temperature and the δH_m and δT_1/2 values to decrease. The 2A_max and the order parameter (S), obtained from the EPR spectra, indicated that the fluidity of the liposomal membrane was affected by the type of drug and by the concentration used; GN and TOB decreased the fluidity and disturbed chain packing at mole ratios of [drug_{inside DPPC}]/[drug_{outside DPPC}] ranging from 1:0 to 1:0.2, while AMI increased the fluidity and disrupted chain packing at an osmotic gradient of 1:2.5. In conclusion, the molecular organization and thermotropic properties of the multilamellar DPPC vesicles were dependent on the osmotic gradient and structure of the aminoglycoside.     

Mathematical model of the immune response]

A model of immune reaction is suggested, ahich takes into account the delay in the development of an immune response. The model depending on parameters values describes: an asymptotic decrease of antigene quantity, approach of its quantity towards constant value, periodic course of the illness, unlimited growth of the antigene quantity. It is shown that the course of the reaction essentially depends on the duration of delay. Parameters regions corresponding to different regimes are determined.     

Mathematical model of children mortality

A mathematical model of infantile mortality is proposed. The model is based on the probability principle of organism-environment interactions assuming that the organism is able to remember the diseases encountered previously and resist them. The adequacy of the model was assessed using the demographic database for two countries. The dynamics of the model parameters during the last century is presented.