Differential Scanning Calorimetry (DSC): a tool to study the thermal behavior of lipid bilayers and liposomal stability

Thermodynamical techniques are applied for determining the thermal stress of medicinal compounds of the excipients as well as their interactions during the formulation process. The physicochemical properties and the stability of the medicinal products could be measured as a function of temperature or time using thermal analysis. Differential Scanning Calorimetry (DSC) is a suitable thermal analysis technique for determining the purity, the polymorphic forms and the melting point of a sample in the Pharmaceutical Industry. It is also considered as a tool to study the thermal behavior of lipid bilayers and of lipidic drug delivery systems, like liposomes by measuring thermodynamic parameters (i.e. DeltaH and Tm), which affect the stability of the liposomal suspension under given storage conditions.     

Differential Scanning Calorimetry (DSC): A Tool to Study the Thermal Behavior of Lipid Bilayers and Liposomal Stability

Thermodynamical techniques are applied for determining the thermal stress of medicinal compounds of the excipients as well as their interactions during the formulation process.

The physicochemical properties and the stability of the medicinal products could be measured as a function of temperature or time using thermal analysis.

Differential Scanning Calorimetry (DSC) is a suitable thermal analysis technique for determining the purity, the polymorphic forms and the melting point of a sample in the Pharmaceutical Industry. It is also considered as a tool to study the thermal behavior of lipid bilayers and of lipidic drug delivery systems, like liposomes by measuring thermodynamic parameters (i.e. ΔH and Tm), which affect the stability of the liposomal suspension under given storage conditions.     

Metabolic systems cost-benefit analysis for interpreting network structure and regulation

MOTIVATION: Interpretation of bioinformatics data in terms of cellular function is a major challenge facing systems biology. This question is complicated by robust metabolic networks filled with structural features like parallel pathways and isozymes. Under conditions of nutrient sufficiency, metabolic networks are well known to be regulated for thermodynamic efficiency however; efficient biochemical pathways are anabolically expensive to construct. While parameters like thermodynamic efficiency have been extensively studied, a systems-based analysis of anabolic proteome synthesis 'costs' and the cellular function implications of these costs has not been reported. RESULTS: A cost-benefit analysis of an in silico Escherichia coli network revealed the relationship between metabolic pathway proteome synthesis requirements, DNA-coding sequence length, thermodynamic efficiency and substrate affinity. The results highlight basic metabolic network design principles. Pathway proteome synthesis requirements appear to have shaped biochemical network structure and regulation. Under conditions of nutrient scarcity and other general stresses, E. coli expresses pathways with relatively inexpensive proteome synthesis requirements instead of more efficient but also anabolically more expensive pathways. This evolutionary strategy provides a cellular function-based explanation for common network motifs like isozymes and parallel pathways and possibly explains 'overflow' metabolisms observed during nutrient scarcity. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Stoichiometric analysis of self-maintaining metabolisms

This paper presents an extension of stoichiometric analysis in systems where the catalytic compounds (enzymes) are also intermediates of the metabolic network (dual property), so they are produced and degraded by the reaction network itself. To take this property into account, we introduce the definition of enzyme-maintaining mode, a set of reactions that produces its own catalyst and can operate at stationary state. Moreover, an enzyme-maintaining mode is defined as elementary with respect to a given reaction if the removal of any of the remaining reactions causes the cessation of any steady state flux through this reference reaction. These concepts are applied to determine the network structure of a simple self-maintaining system.     

Networks as constrained thermodynamic systems

We show how a network of interconnections between nodes can be constructed to have a specified distribution of nodal degrees. This is achieved by treating the network as a thermodynamic system subject to constraints and then rewiring the system to maintain the constraints while increasing the entropy. The general construction is given and illustrated by the simple example of an exponential network. By considering the constraints as a cost function analogous to an internal energy, we obtain a characterisation of the correspondence between the intensive and extensive variables of the network. Applied to networks in living organisms, this approach may lead to macroscopic variables useful in characterising living systems.     

Ab initio prediction of thermodynamically feasible reaction directions from biochemical network stoichiometry

Analysis of the stoichiometric structure of metabolic networks provides insights into the relationships between structure, function, and regulation of metabolic systems. Based on knowledge of only reaction stoichiometry, certain aspects of network functionality and robustness can be predicted. Current theories focus on breaking a metabolic network down into non-decomposable pathways able to operate in steady state. The physics underlying these theories is based on mass balance and the laws of thermodynamics. However, due to the inherent nonlinearity of the thermodynamic constraints on metabolic fluxes, computational analysis of large-scale biochemical systems can be expensive. In this study, it is shown how the feasible reaction directions may be determined by either computing the allowable ranges under the mass-balance and thermodynamic constraints or by analyzing the stoichiometric structure of the network. The computed reaction directions translate into a set of linear constraints necessary for thermodynamic feasibility. This set of necessary linear constraints is shown to be sufficient to guarantee feasibility in certain cases, thus translating the nonlinear thermodynamic constraints to linear. We show that for a reaction network of 44 internal reactions representing energy metabolism, the computed linear inequality constraints represent necessary and sufficient conditions for thermodynamic feasibility.     

Prospects for advancing the understanding of complex biochemical systems

The application of mathematical theories to understanding the behaviour of complex biochemical systems is reviewed. Key aspects of behaviour are identified as the flux through particular pathways in a steady state, the nature and stability of dynamical states, and the thermodynamic properties of systems. The first of these is dealt primarily in theories of metabolic control, and metabolic control analysis (MCA) is an important example. The valid application of this theory is limited to steady-state systems, and the cases where the essential features of control can be derived from calibration experiments which perturb the state of the system by a sufficiently small amount from its operating point. In practice, time-dependent systems exist, it is not always possible to know a priori whether applied perturbations are sufficiently small, and important features of control may lie farther from the operating point than the application of the theory permits. The nature and stability of dynamical and thermodynamical states is beyond the scope of MCA. To understand the significance of these limitations fully, and to address the dynamical and thermodynamical properties, more complete theories are required. Non-linear systems theory offers the possibility of studying important questions regarding control of steady and dynamical states. It can also link to thermodynamic properties of the system including the energetic efficiency of particular pathways. However, its application requires a more detailed characterisation of the system under study. This extra detail may be an essential feature of the study of non-equilibrium states in general, and non-ideal pathways in particular. Progress requires considerably more widespread integration of theoretical and experimental approaches than currently exists.     

On the Chemical Nature and Origin of Teleonomy

The physico-chemical characterization of a teleonomic event and the nature of the physico-chemical process by which teleonomic systems could emerge from non-teleonomic systems are addressed in this paper. It is proposed that teleonomic events are those whose primary directive is discerned to be non-thermodynamic, while regular (non-teleonomic) events are those whose primary directive is the traditional thermodynamic one. For the archetypal teleonomic event, cell multiplication, the non-thermodynamic directive can be identified as being a kinetic directive. It is concluded, therefore, that the process of emergence, whereby non-teleonomic replicating chemical systems were transformed into teleonomic ones, involved a switch in the primacy of thermodynamic and kinetic directives. It is proposed that the step where that transformation took place was the one in which some pre-metabolic replicating system acquired an energy-gathering capability, thereby becoming metabolic. Such a transformation was itself kinetically directed given that metabolic replicators tend to be kinetically more stable than non-metabolic ones. The analysis builds on our previous work that considers living systems to be a kinetic state of matteras opposed to the traditional thermodynamic states that dominate the inanimate world     

The Glansdorff-Prigogine thermodynamic stability criterion in the light of Lyapunov's theory.

The significance of thermodynamic coupling in chemical reactions—which recently has been questioned on thermodynamic grounds—is examined from the point of view of kinetics. It is shown that considerations of stoichiometry lead to a meaningful definition of velocity for elementary and certain elementary-complex reactions, whereas the non-equilibrium thermodynamic definition of reaction velocity is ambiguous in multireaction systems. Based on rate laws which include the effects of nonideality, it is proven that elementary-type reactions are not coupled thermodynamically and concluded that thermodynamic coupling has no kinetic significance. A discussion is given to show that this result is compatible with coupling in both biochemical systems and oscillating reactions.     

A scalable algorithm to explore the Gibbs energy landscape of genome-scale metabolic networks

The integration of various types of genomic data into predictive models of biological networks is one of the main challenges currently faced by computational biology. Constraint-based models in particular play a key role in the attempt to obtain a quantitative understanding of cellular metabolism at genome scale. In essence, their goal is to frame the metabolic capabilities of an organism based on minimal assumptions that describe the steady states of the underlying reaction network via suitable stoichiometric constraints, specifically mass balance and energy balance (i.e. thermodynamic feasibility). The implementation of these requirements to generate viable configurations of reaction fluxes and/or to test given flux profiles for thermodynamic feasibility can however prove to be computationally intensive. We propose here a fast and scalable stoichiometry-based method to explore the Gibbs energy landscape of a biochemical network at steady state. The method is applied to the problem of reconstructing the Gibbs energy landscape underlying metabolic activity in the human red blood cell, and to that of identifying and removing thermodynamically infeasible reaction cycles in the Escherichia coli metabolic network (iAF1260). In the former case, we produce consistent predictions for chemical potentials (or log-concentrations) of intracellular metabolites; in the latter, we identify a restricted set of loops (23 in total) in the periplasmic and cytoplasmic core as the origin of thermodynamic infeasibility in a large sample (10(6)) of flux configurations generated randomly and compatibly with the prior information available on reaction reversibility.     

Analysis of protein self-association under conditions of the thermodynamic non-ideality

Analysis of protein-protein interactions in highly concentrated solutions requires a consideration of the non-ideality in such solutions which is expressed by the virial coefficients. Different equations are presented to estimate effects of the thermodynamic non-ideality on the macromolecular interaction of self-associating proteins in sedimentation equilibrium experiments. Usually the influence of thermodynamic non-ideal behavior are described by concentration power series. The convergence of such power series is limited at high solute concentration. When expressing the thermodynamic non-ideality by an activity power series this disadvantage can be minimized. The developed centrifuge equations are the basis for a global analysis to estimate equilibrium constants and the corresponding thermodynamic activities of the reactants. Based on fit analysis of synthetic concentration profiles it was established that marked deviations from the expected association constants are observed for proteins with strong association forces between solute molecules. Considerable differences were also observed in weakly interacting systems. This was due to the excluded volume of the protein which is similar in magnitude to the binding constant. For interactions with moderate affinities values extremely close to the true binding values were obtained, as confirmed by experimental results with concanavalin A.     

Thermodynamics of Random Reaction Networks

Reaction networks are useful for analyzing reaction systems occurring in chemistry, systems biology, or Earth system science. Despite the importance of thermodynamic disequilibrium for many of those systems, the general thermodynamic properties of reaction networks are poorly understood. To circumvent the problem of sparse thermodynamic data, we generate artificial reaction networks and investigate their non-equilibrium steady state for various boundary fluxes. We generate linear and nonlinear networks using four different complex network models (Erdős-Rényi, Barabási-Albert, Watts-Strogatz, Pan-Sinha) and compare their topological properties with real reaction networks. For similar boundary conditions the steady state flow through the linear networks is about one order of magnitude higher than the flow through comparable nonlinear networks. In all networks, the flow decreases with the distance between the inflow and outflow boundary species, with Watts-Strogatz networks showing a significantly smaller slope compared to the three other network types. The distribution of entropy production of the individual reactions inside the network follows a power law in the intermediate region with an exponent of circa −1.5 for linear and −1.66 for nonlinear networks. An elevated entropy production rate is found in reactions associated with weakly connected species. This effect is stronger in nonlinear networks than in the linear ones. Increasing the flow through the nonlinear networks also increases the number of cycles and leads to a narrower distribution of chemical potentials. We conclude that the relation between distribution of dissipation, network topology and strength of disequilibrium is nontrivial and can be studied systematically by artificial reaction networks.     

A simple chemical example of hierarchical thermodynamic interactions: the protonation equilibria of inorganic polyprotic acids

A general method for formulating complex thermodynamic systems in terms of hierarchical interactions has been developed, and has been applied in a previous analysis to hemoglobin oxygen binding data. Polyprotic acids can be considered a simple chemical model of thermodynamic interaction between ligand binding events. To further illustrate the hierarchical interaction approach it is applied to the analysis of the thermodynamic interactions between proton binding events in inorganic polyprotic acids. pK values for arsenate, carbonate, chromate, phosphate, phosphite, selenite, sulfide and sulfite were recast into hierarchical interaction terms. The intrinsic K(d,h) for protonation ranged from 8.8 x 10(-13) (M) for phosphate to 1.3 x 10(-6) (M) for chromate. Pairwise interactions (K(d,hh)) between protonation events ranged from 1.3 x 10(4) for phosphite to 9.4 x 10(5) for carbonate. Third order interactions (K(d,hhh)) were 0.91 and 0.51 for arsenate and phosphate, respectively, values relatively close to the no interaction value of 1. A principle feature of systems described by hierarchical interactions is that higher order interactions, representing more complex interactions, are less likely to be significant than lower order interactions, and this is further illustrated by these observations from polyprotic acids. The set of significant hierarchical interaction values can be used to predict values for as yet unobserved events, and projected pK values are made for all the polyprotic acids included in this study. Finally, application of this method to the protonation equilibria of water demonstrates a profound pairwise interaction between protonation events (K(d,hh) = 1.3 x 10(17)), which is attributed to oxygen's small size and lack of polarizability.     

Equivalent multi-tissue and thermodynamic decompression algorithms

Multi-tissue and thermodynamic decompression algorithms are described and a computational equivalence is established between the two approaches. Eigenvalues and weighted eigenfunctions of the Fick-Fourier equation effectively define response functions from which Haldane half-lives can be extracted from arbitrary exposures, operationally bridging the two approaches. Decompression criteria for the algorithms are also described and coupled. Comparisons of similarities and differences of approaches are given from both theoretical and applied viewpoints. A seven-parameter set, spanning both models, forms the basis of analysis. We find that representative thermodynamic parameters in a perfusion-diffusion model effectively recover Haldane half-lives in a bootstrap and that critical parameters overlap, though ranges differ in the two cases.     

Reducing intrinsic biochemical noise in cells and its thermodynamic limit

In living cells, the specificity of biomolecular recognition can be amplified and the noise from non-specific interactions can be reduced at the expense of cellular free energy. This is the seminal idea in the Hopfield-Ninio theory of kinetic proofreading: The specificity is increased via cyclic network kinetics without altering molecular structures and equilibrium affinites. We show a thermodynamic limit of the specificity amplification with a given amount of available free energy. For a normal cell under physiological condition with sustained phosphorylation potential, this gives a factor of 10(10) as the upper bound in specificity amplification. We also study an optimal kinetic network design that is capable of approaching the thermodynamic limit.     

Determination of the upper and lower limits of the mechanistic stoichiometry of incompletely coupled fluxes. Stoichiometry of incompletely coupled reactions

A rationale is formulated for the design of experiments to determine the upper and lower limits of the mechanistic stoichiometry of any two incompletely coupled fluxes J1 and J2. Incomplete coupling results when there is a branch at some point in the sequence of reactions or processes coupling the two fluxes. The upper limit of the mechanistic stoichiometry is given by the minimum value of dJ2/dJ1 obtained when the fluxes are systematically varied by changes in steps after the branch point. The lower limit is given by the maximum value of dJ2/dJ1 obtained when the fluxes are varied by changes in steps prior to the branch point. The rationale for determining these limits is developed from both a simple kinetic model and from a linear nonequilibrium thermodynamic treatment of coupled fluxes, using the mechanistic approach [Westerhoff, H. V. & van Dam, K. (1979) Curr. Top. Bioenerg. 9, 1-62]. The phenomenological stoichiometry, the flux ratio at level flow and the affinity ratio at static head of incompletely coupled fluxes are defined in terms of mechanistic conductances and their relationship to the mechanistic stoichiometry is discussed. From the rationale developed, experimental approaches to determine the mechanistic stoichiometry of mitochondrial oxidative phosphorylation are outlined. The principles employed do not require knowledge of the pathway or the rate of transmembrane leaks or slippage and may also be applied to analysis of the stoichiometry of other incompletely coupled systems, including vectorial H+/O and K+/O translocation coupled to mitochondrial electron transport.     

The principle of flux minimization and its application to estimate stationary fluxes in metabolic networks.

Cellular functions are ultimately linked to metabolic fluxes brought about by thousands of chemical reactions and transport processes. The synthesis of the underlying enzymes and membrane transporters causes the cell a certain 'effort' of energy and external resources. Considering that those cells should have had a selection advantage during natural evolution that enabled them to fulfil vital functions (such as growth, defence against toxic compounds, repair of DNA alterations, etc.) with minimal effort, one may postulate the principle of flux minimization, as follows: given the available external substrates and given a set of functionally important 'target' fluxes required to accomplish a specific pattern of cellular functions, the stationary metabolic fluxes have to become a minimum. To convert this principle into a mathematical method enabling the prediction of stationary metabolic fluxes, the total flux in the network is measured by a weighted linear combination of all individual fluxes whereby the thermodynamic equilibrium constants are used as weighting factors, i.e. the more the thermodynamic equilibrium lies on the right-hand side of the reaction, the larger the weighting factor for the backward reaction. A linear programming technique is applied to minimize the total flux at fixed values of the target fluxes and under the constraint of flux balance (= steady-state conditions) with respect to all metabolites. The theoretical concept is applied to two metabolic schemes: the energy and redox metabolism of erythrocytes, and the central metabolism of Methylobacterium extorquens AM1. The flux rates predicted by the flux-minimization method exhibit significant correlations with flux rates obtained by either kinetic modelling or direct experimental determination. Larger deviations occur for segments of the network composed of redundant branches where the flux-minimization method always attributes the total flux to the thermodynamically most favourable branch. Nevertheless, compared with existing methods of structural modelling, the principle of flux minimization appears to be a promising theoretical approach to assess stationary flux rates in metabolic systems in cases where a detailed kinetic model is not yet available.     

Quantitative Assessment of Thermodynamic Constraints on the Solution Space of Genome-Scale Metabolic Models

Constraint-based methods provide powerful computational techniques to allow understanding and prediction of cellular behavior. These methods rely on physiochemical constraints to eliminate infeasible behaviors from the space of available behaviors. One such constraint is thermodynamic feasibility, the requirement that intracellular flux distributions obey the laws of thermodynamics. The past decade has seen several constraint-based methods that interpret this constraint in different ways, including those that are limited to small networks, rely on predefined reaction directions, and/or neglect the relationship between reaction free energies and metabolite concentrations. In this work, we utilize one such approach, thermodynamics-based metabolic flux analysis (TMFA), to make genome-scale, quantitative predictions about metabolite concentrations and reaction free energies in the absence of prior knowledge of reaction directions, while accounting for uncertainties in thermodynamic estimates. We applied TMFA to a genome-scale network reconstruction of Escherichia coli and examined the effect of thermodynamic constraints on the flux space. We also assessed the predictive performance of TMFA against gene essentiality and quantitative metabolomics data, under both aerobic and anaerobic, and optimal and suboptimal growth conditions. Based on these results, we propose that TMFA is a useful tool for validating phenotypes and generating hypotheses, and that additional types of data and constraints can improve predictions of metabolite concentrations.