Automating the search of molecular motor templates by evolutionary methods

Biological molecular motors are nanoscale devices capable of transforming chemical energy into mechanical work, which are being researched in many scientific disciplines. From a computational point of view, the characteristics and dynamics of these motors are studied at multiple time scales, ranging from very detailed and complex molecular dynamics simulations spanning a few microseconds, to extremely simple and coarse-grained theoretical models of their working cycles. However, this research is performed only in the (relatively few) instances known from molecular biology. In this work, results from elastic network analysis and behaviour-finding methods are applied to explore a subset of the configuration space of template molecular structures that are able to transform chemical energy into directed movement, for a fixed instance of working cycle. While using methods based on elastic networks limits the scope of our results, it enables the implementation of computationally lightweight methods, in a way that evolutionary search techniques can be applied to discover novel molecular motor templates. The results show that molecular motion can be attained from a variety of structural configurations, when a functional working cycle is provided. Additionally, these methods enable a new computational way to test hypotheses about molecular motors.     

Systematic analysis of stability patterns in plant primary metabolism

Metabolic networks are characterized by complex interactions and regulatory mechanisms between many individual components. These interactions determine whether a steady state is stable to perturbations. Structural kinetic modeling (SKM) is a framework to analyze the stability of metabolic steady states that allows the study of the system Jacobian without requiring detailed knowledge about individual rate equations. Stability criteria can be derived by generating a large number of structural kinetic models (SK-models) with randomly sampled parameter sets and evaluating the resulting Jacobian matrices. Until now, SKM experiments applied univariate tests to detect the network components with the largest influence on stability. In this work, we present an extended SKM approach relying on supervised machine learning to detect patterns of enzyme-metabolite interactions that act together in an orchestrated manner to ensure stability. We demonstrate its application on a detailed SK-model of the Calvin-Benson cycle and connected pathways. The identified stability patterns are highly complex reflecting that changes in dynamic properties depend on concerted interactions between several network components. In total, we find more patterns that reliably ensure stability than patterns ensuring instability. This shows that the design of this system is strongly targeted towards maintaining stability. We also investigate the effect of allosteric regulators revealing that the tendency to stability is significantly increased by including experimentally determined regulatory mechanisms that have not yet been integrated into existing kinetic models.     

Periodic coexistence of four species competing for three essential resources

We show the existence of a periodic solution in which four species coexist in competition for three essential resources in the standard model of resource competition. By assuming that species i is limited by resource i for each i near the positive equilibrium, and that the matrix of contents of resources in species is a combination of cyclic matrix and a symmetric matrix, we obtain an asymptotically stable periodic solution of three species on three resources via Hopf bifurcation. A simple bifurcation argument is then employed which allows us to add a fourth species. In principle, the argument can be continued to obtain a periodic solution adding one new species at a time so long as asymptotic stability can be assured at each step. Numerical simulations are provided to illustrate our analytical results. The results of this paper suggest that competition can generate coexistence of species in the form of periodic cycles, and that the number of coexisting species can exceed the number of resources in a constant and homogeneous environment.     

Probing the Folding-Unfolding Transition of a Thermophilic Protein,MTH1880

The folding mechanism of typical proteins has been studied widely, while our understanding of the origin of the high stability of thermophilic proteins is still elusive. Of particular interest is how an atypical thermophilic protein with a novel fold maintains its structure and stability under extreme conditions. Folding-unfolding transitions of MTH1880, a thermophilic protein from Methanobacterium thermoautotrophicum, induced by heat, urea, and GdnHCl, were investigated using spectroscopic techniques including circular dichorism, fluorescence, NMR combined with molecular dynamics (MD) simulations. Our results suggest that MTH1880 undergoes a two-state N to D transition and it is extremely stable against temperature and denaturants. The reversibility of refolding was confirmed by spectroscopic methods and size exclusion chromatography. We found that the hyper-stability of the thermophilic MTH1880 protein originates from an extensive network of both electrostatic and hydrophobic interactions coordinated by the central β-sheet. Spectroscopic measurements, in combination with computational simulations, have helped to clarify the thermodynamic and structural basis for hyper-stability of the novel thermophilic protein MTH1880.     

Dynamical Behaviour of Viral Cycle and Identification of Steady States

The molecular biology of viruses can be effectively described by kinetic logic as several feedback loops are implicated in all viral cycles and as viral proteins generally display several functions. We applied this method to the study of the rhabdovirus cycle.Formally, the dynamics of the model are explored on the basis of a discrete caricature (kinetic logic), with special emphasis on the role of the constitutive feedback loops to determine the essential dynamical behaviour of the viral cycle. From a biological point of view, our model accounts for several stable regimes or attractors: healthy cells, acute infection and different kinds of persistent infections, a multistationarity in good agreement with the existence of several positive feedback loops in our system.     

qPIPSA: Relating enzymatic kinetic parameters and interaction fields

Background  

The simulation of metabolic networks in quantitative systems biology requires the assignment of enzymatic kinetic parameters. Experimentally determined values are often not available and therefore computational methods to estimate these parameters are needed. It is possible to use the three-dimensional structure of an enzyme to perform simulations of a reaction and derive kinetic parameters. However, this is computationally demanding and requires detailed knowledge of the enzyme mechanism. We have therefore sought to develop a general, simple and computationally efficient procedure to relate protein structural information to enzymatic kinetic parameters that allows consistency between the kinetic and structural information to be checked and estimation of kinetic constants for structurally and mechanistically similar enzymes.     

Effects of conduction delays on the existence and stability of one to one phase locking between two pulse-coupled oscillators

Gamma oscillations can synchronize with near zero phase lag over multiple cortical regions and between hemispheres, and between two distal sites in hippocampal slices. How synchronization can take place over long distances in a stable manner is considered an open question. The phase resetting curve (PRC) keeps track of how much an input advances or delays the next spike, depending upon where in the cycle it is received. We use PRCs under the assumption of pulsatile coupling to derive existence and stability criteria for 1:1 phase-locking that arises via bidirectional pulse coupling of two limit cycle oscillators with a conduction delay of any duration for any 1:1 firing pattern. The coupling can be strong as long as the effect of one input dissipates before the next input is received. We show the form that the generic synchronous and anti-phase solutions take in a system of two identical, identically pulse-coupled oscillators with identical delays. The stability criterion has a simple form that depends only on the slopes of the PRCs at the phases at which inputs are received and on the number of cycles required to complete the delayed feedback loop. The number of cycles required to complete the delayed feedback loop depends upon both the value of the delay and the firing pattern. We successfully tested the predictions of our methods on networks of model neurons. The criteria can easily be extended to include the effect of an input on the cycle after the one in which it is received.     

Structural biology of proteins involved in nitrogen cycling

Microbial metabolic processes drive the global nitrogen cycle through sophisticated and often unique metalloenzymes that facilitate difficult redox reactions at ambient temperature and pressure. Understanding the intricacies of these biological nitrogen transformations requires a detailed knowledge that arises from the combination of a multitude of powerful analytical techniques and functional assays. Recent developments in spectroscopy and structural biology have provided new, powerful tools for addressing existing and emerging questions, which have gained urgency due to the global environmental implications of these fundamental reactions. The present review focuses on the recent contributions of the wider area of structural biology to understanding nitrogen metabolism, opening new avenues for biotechnological applications to better manage and balance the challenges of the global nitrogen cycle.     

Role of solvation barriers in protein kinetic stability

The stability of several protein systems of interest has been shown to have a kinetic basis. Besides the obvious biotechnological implications, the general interest of understanding protein kinetic stability is emphasized by the fact that some emerging molecular approaches to the inhibition of amyloidogenesis focus on the increase of the kinetic stability of protein native states. Lipases are among the most important industrial enzymes. Here, we have studied the thermal denaturation of the wild-type form, four single-mutant variants and two highly stable, multiple-mutant variants of lipase from Thermomyces lanuginosa. In all cases, thermal denaturation was irreversible, kinetically controlled and conformed to the two-state irreversible model. This result supports that the novel molecular-dynamics-focused, directed-evolution approach involved in the preparation of the highly stable variants is successful likely because it addresses kinetic stability and, in particular, because heated molecular dynamics simulations possibly identify regions of disrupted native interactions in the transition state for irreversible denaturation. Furthermore, we find very large mutation effects on activation enthalpy and entropy, which were not accompanied by similarly large changes in kinetic urea m-value. From this we are led to conclude that these mutation effects are associated to some structural feature of the transition state for the irreversible denaturation process that is not linked to large changes in solvent accessibility. Recent computational studies have suggested the existence of solvation/desolvation barriers in at least some protein folding/unfolding processes. We thus propose that a solvation barrier (arising from the asynchrony between breaking of internal contacts and water penetration) may contribute to the kinetic stability of lipase from T. lanuginosa (and, possibly, to the kinetic stability of other proteins as well).     

Time delays in age-structured populations

A combination of analytical and computational techniques is employed to investigate age-structured populations in which the life cycle consists of two sequential demographic phases. Individuals within each phase have identical demographic rates that are functions of population size, but these rates may differ between phases. A model consisting of a system of delay ordinary differential equations is derived, and existence and stability of equilibria are discussed. Analysis reveals how equilibrium abundances depend on all demographic variables and, in particular, on the lengths of the demographic phases.     

Differential Modulation of Functional Dynamics and Allosteric Interactions in the Hsp90-Cochaperone Complexes with p23 and Aha1: A Computational Study

Allosteric interactions of the molecular chaperone Hsp90 with a large cohort of cochaperones and client proteins allow for molecular communication and event coupling in signal transduction networks. The integration of cochaperones into the Hsp90 system is driven by the regulatory mechanisms that modulate the progression of the ATPase cycle and control the recruitment of the Hsp90 clientele. In this work, we report the results of computational modeling of allosteric regulation in the Hsp90 complexes with the cochaperones p23 and Aha1. By integrating protein docking, biophysical simulations, modeling of allosteric communications, protein structure network analysis and the energy landscape theory we have investigated dynamics and stability of the Hsp90-p23 and Hsp90-Aha1 interactions in direct comparison with the extensive body of structural and functional experiments. The results have revealed that functional dynamics and allosteric interactions of Hsp90 can be selectively modulated by these cochaperones via specific targeting of the regulatory hinge regions that could restrict collective motions and stabilize specific chaperone conformations. The protein structure network parameters have quantified the effects of cochaperones on conformational stability of the Hsp90 complexes and identified dynamically stable communities of residues that can contribute to the strengthening of allosteric interactions. According to our results, p23-mediated changes in the Hsp90 interactions may provide “molecular brakes” that could slow down an efficient transmission of the inter-domain allosteric signals, consistent with the functional role of p23 in partially inhibiting the ATPase cycle. Unlike p23, Aha1-mediated acceleration of the Hsp90-ATPase cycle may be achieved via modulation of the equilibrium motions that facilitate allosteric changes favoring a closed dimerized form of Hsp90. The results of our study have shown that Aha1 and p23 can modulate the Hsp90-ATPase activity and direct the chaperone cycle by exerting the precise control over structural stability, global movements and allosteric communications in Hsp90.     

On the analysis of futile cycles in metabolism

So-called futile cycles in cellular metabolism consist of paired opposing reactions that, if simultaneously operant, act only to degrade free energy of ATP to heat. Previous considerations of the behavior of such substrate cycles have indicated their possible usefulness in regulating flux along metabolic pathways, but such analyses have treated the cycles in isolation, i.e. without taking into account the effects of enzymatic inputs to and outputs from the cycle. We here develop models of three typical substrate cycles that include enzymatic inputs to and outputs from the cycle and allow the enzymes of the cycles per se to be subject to a variety of allosteric modulations. The non-linear equations which describe these models were solved by an iterative procedure for sets of parameter values of metabolic interest. The results, when analyzed using appropriate definitions of regulatory sensitivity and energetic futility, demonstrate that the effects of the enzymes leading into and out of the cycle may cause profound changes in the operation of the substrate cycle and therefore may not be ignored. We find that the structural differences among the three cycles considered here result in corresponding functional differences. Our results suggest that (1) the fructose-6-P/fructose-1,6-di-P cycle acts effectively to gate bidirectional flux, but doesn't appreciably enhance regulation of unidirectional flux, (2) the glucose/glucose-6-P cycle is well suited to perform a homeostatic function and to adjust the set points for these two metabolites, and (3) the cycle at the pyruvate crossroads functions largely as a complex switch box that directs metabolic flow towards gluconeogenesis or glycolysis not only in response to inputs of or requirements for oxaloacetate, pyruvate, and phosphoenolpyruvate, but also in response to the combined action of allosteric modulators on the individual enzymes of this substrate cycle.     

Correlation of structural stability with functional remodeling of high-density lipoproteins: the importance of being disordered

High-density lipoproteins (HDLs) are protein-lipid assemblies that remove excess cell cholesterol and prevent atherosclerosis. HDLs are stabilized by kinetic barriers that decelerate protein dissociation and lipoprotein fusion. We propose that similar barriers modulate metabolic remodeling of plasma HDLs; hence, changes in particle composition that destabilize HDLs and accelerate their denaturation may accelerate their metabolic remodeling. To test this notion, we correlate existing reports on HDL-mediated cell cholesterol efflux and esterification, which are obligatory early steps in cholesterol removal, with our kinetic studies of HDL stability. The results support our hypothesis and show that factors accelerating cholesterol efflux and esterification in model discoidal lipoproteins (including reduced protein size, reduced fatty acyl chain length, and/or increased level of cis unsaturation) destabilize lipoproteins and accelerate their fusion and apolipoprotein dissociation. Oxidation studies of plasma spherical HDLs show a similar trend: mild oxidation by Cu(2+) or OCl(-) accelerates cell cholesterol efflux, protein dissociation, and HDL fusion, while extensive oxidation inhibits these reactions. Consequently, moderate destabilization may be beneficial for HDL functions by facilitating insertion of cholesterol and lipophilic enzymes, promoting dissociation of lipid-poor apolipoproteins, which are primary acceptors of cell cholesterol, and thereby accelerating HDL metabolism. Therefore, HDL stability must be delicately balanced to maintain the structural integrity of the lipoprotein assembly and ensure structural specificity necessary for interactions of HDL with its metabolic partners, while facilitating rapid HDL remodeling and turnover at key junctures of cholesterol transport. The inverse correlation between HDL stability and remodeling illustrates the functional importance of structural disorder in macromolecular assemblies stabilized by kinetic barriers.     

Folding and Hydrodynamics of a DNA i-Motif from the c-MYC Promoter Determined by Fluorescent Cytidine Analogs

The four-stranded i-motif (iM) conformation of cytosine-rich DNA has importance to a wide variety of biochemical systems that range from their use in nanomaterials to potential roles in oncogene regulation. The iM structure is formed at slightly acidic pH, where hemiprotonation of cytosine results in a stable C-C⁺ basepair. Here, we performed fundamental studies to examine iM formation from a C-rich strand from the promoter of the human c-MYC gene. We used a number of biophysical techniques to characterize both the hydrodynamic properties and folding kinetics of a folded iM. Our hydrodynamic studies using fluorescence anisotropy decay and analytical ultracentrifugation show that the iM structure has a compact size in solution and displays the rigidity of a double strand. By studying the rates of circular dichroism spectral changes and quenching of fluorescent cytidine analogs, we also established a mechanism for the folding of a random coil oligo into the iM. In the course of determining this folding pathway, we established that the fluorescent dC analogs tC° and PdC can be used to monitor individual residues of an iM structure and to determine the pK_a of an iM. We established that the C-C⁺ hydrogen bonding of certain bases initiates the folding of the iM structure. We also showed that substitutions in the loop regions of iMs give a distinctly different kinetic signature during folding compared with bases that are intercalated. Our data reveal that the iM passes through a distinct intermediate form between the unfolded and folded forms. Taken together, our results lay the foundation for using fluorescent dC analogs to follow structural changes during iM formation. Our technique may also be useful for examining folding and structural changes in more complex iMs.     

Folding and Hydrodynamics of a DNA i-Motif from the c-MYC Promoter Determined by Fluorescent Cytidine Analogs

The four-stranded i-motif (iM) conformation of cytosine-rich DNA has importance to a wide variety of biochemical systems that range from their use in nanomaterials to potential roles in oncogene regulation. The iM structure is formed at slightly acidic pH, where hemiprotonation of cytosine results in a stable C-C⁺ basepair. Here, we performed fundamental studies to examine iM formation from a C-rich strand from the promoter of the human c-MYC gene. We used a number of biophysical techniques to characterize both the hydrodynamic properties and folding kinetics of a folded iM. Our hydrodynamic studies using fluorescence anisotropy decay and analytical ultracentrifugation show that the iM structure has a compact size in solution and displays the rigidity of a double strand. By studying the rates of circular dichroism spectral changes and quenching of fluorescent cytidine analogs, we also established a mechanism for the folding of a random coil oligo into the iM. In the course of determining this folding pathway, we established that the fluorescent dC analogs tC° and PdC can be used to monitor individual residues of an iM structure and to determine the pK_a of an iM. We established that the C-C⁺ hydrogen bonding of certain bases initiates the folding of the iM structure. We also showed that substitutions in the loop regions of iMs give a distinctly different kinetic signature during folding compared with bases that are intercalated. Our data reveal that the iM passes through a distinct intermediate form between the unfolded and folded forms. Taken together, our results lay the foundation for using fluorescent dC analogs to follow structural changes during iM formation. Our technique may also be useful for examining folding and structural changes in more complex iMs.     

A tale of two cycles – distinguishing quasi-cycles and limit cycles in finite predator–prey populations

Periodic predator – prey dynamics in constant environments are usually taken as indicative of deterministic limit cycles. It is known, however, that demographic stochasticity in finite populations can also give rise to regular population cycles, even when the corresponding deterministic models predict a stable equilibrium. Specifically, such quasi-cycles are expected in stochastic versions of deterministic models exhibiting equilibrium dynamics with weakly damped oscillations. The existence of quasi-cycles substantially expands the scope for natural patterns of periodic population oscillations caused by ecological interactions, thereby complicating the conclusive interpretation of such patterns. Here we show how to distinguish between quasi-cycles and noisy limit cycles based on observing changing population sizes in predator – prey populations. We start by confirming that both types of cycle can occur in the individual-based version of a widely used class of deterministic predator – prey model. We then show that it is feasible and straightforward to accurately distinguish between the two types of cycle through the combined analysis of autocorrelations and marginal distributions of population sizes. Finally, by confronting these results with real ecological time series, we demonstrate that by using our methods even short and imperfect time series allow quasi-cycles and limit cycles to be distinguished reliably.     

Operating regimes of signaling cycles: statics, dynamics, and noise filtering

A ubiquitous building block of signaling pathways is a cycle of covalent modification (e.g., phosphorylation and dephosphorylation in MAPK cascades). Our paper explores the kind of information processing and filtering that can be accomplished by this simple biochemical circuit. Signaling cycles are particularly known for exhibiting a highly sigmoidal (ultrasensitive) input–output characteristic in a certain steady-state regime. Here, we systematically study the cycle's steady-state behavior and its response to time-varying stimuli. We demonstrate that the cycle can actually operate in four different regimes, each with its specific input–output characteristics. These results are obtained using the total quasi–steady-state approximation, which is more generally valid than the typically used Michaelis-Menten approximation for enzymatic reactions. We invoke experimental data that suggest the possibility of signaling cycles operating in one of the new regimes. We then consider the cycle's dynamic behavior, which has so far been relatively neglected. We demonstrate that the intrinsic architecture of the cycles makes them act—in all four regimes—as tunable low-pass filters, filtering out high-frequency fluctuations or noise in signals and environmental cues. Moreover, the cutoff frequency can be adjusted by the cell. Numerical simulations show that our analytical results hold well even for noise of large amplitude. We suggest that noise filtering and tunability make signaling cycles versatile components of more elaborate cell-signaling pathways.     

Selection and the Evolution of Genetic Life Cycles

The evolution of haploid and diploid phases of the life cycle is investigated theoretically, using a model where the relative length of haploid and diploid phases is under genetic control. The model assumes that selection occurs in both phases and that fitness in each phase is a function of the time spent in that phase. The equilibrium and stability conditions that allow for all-haploid, all-diploid, or polyphasic life cycles are considered for general survivorship functions. Types of stable life cycles possible depend on the form of the viability selection. If mortality rates are constant, either haploidy or diploidy is the only stable life cycle possible. Departures from constant mortality can give qualitatively different results. For example, when survivorship in each phase is a linear, decreasing function of the time spent in the phase, stable haploid, diploid or polyphasic life cycles are possible. The addition of genetic variation at a coevolving viability locus does not qualitatively affect the outcome with respect to the maintenance of polyphasic cycles but can lead to situations where more than one life cycle is concurrently stable. These results show that trade-offs between the advantages of being diploid and of being haploid may help explain the patterns of life cycles found in nature and that the type of selection may be critical to determining the results.     

Use of structure based design to increase selectivity of pyridyl-cinnoline phosphodiesterase 10A (PDE10A) inhibitors against phosphodiesterase 3 (PDE3)

We report our successful effort to increase the PDE3 selectivity of PDE10A inhibitor pyridyl cinnoline 1 using a combination of computational modeling and structural–activity relationship investigations. An analysis of the PDE3 catalytic domain compared to the co-crystal structure of cinnoline analog 1 in PDE10A revealed two areas of structural differences in the active sites and suggested areas on the scaffold that could be modified to exploit those unique structural features. Once SAR established the cinnoline as the optimal scaffold, modifications on the methoxy groups of the cinnoline and the methyl group on the pyridine led to the discovery of compounds 33 and 36. Both compounds achieved significant improvement in selectivity against PDE3 while maintaining their PDE10A inhibitory activity and in vivo metabolic stability comparable to 1.