Transition modes in Ising networks: an approximate theory for macromolecular recognition.

For a statistical lattice, or Ising network, composed of N identical units existing in two possible states, 0 and 1, and interacting according to a given geometry, a set of values can be found for the mean free energy of the 0-->1 transition of a single unit. Each value defines a transition mode in an ensemble of nu N = 3N - 2N possible values and reflects the role played by intermediate states in shaping the energetics of the system as a whole. The distribution of transition modes has a number of intriguing properties. Some of them apply quite generally to any Ising network, regardless of its dimension, while others are specific for each interaction geometry and dimensional embedding and bear on fundamental aspects of analytical number theory. The landscape of transition modes encapsulates all of the important thermodynamic properties of the network. The free energy terms defining the partition function of the system can be derived from the modes by simple transformations. Classical mean-field expressions can be obtained from consideration of the properties of transition modes in a rather straightforward way. The results obtained in the analysis of the transition mode distributions have been used to develop an approximate treatment of the problem of macromolecular recognition. This phenomenon is modeled as a cooperative process that involves a number of recognition subsites across an interface generated by the binding of two macromolecular components. The distribution of allowed binding free energies for the system is shown to be a superposition of Gaussian terms with mean and variance determined a priori by the theory. Application to the analysis of the biologically interaction of thrombin with hirudin has provided some useful information on basic aspects of the interaction, such as the number of recognition subsites involved and the energy balance for binding and cooperative coupling among them. Our results agree quite well with information derived independently from analysis of the crystal structure of the thrombin-hirudin complex.     

A modified Ising model of Barabási–Albert network with gene-type spins

The central question of systems biology is to understand how individual components of a biological system such as genes or proteins cooperate in emerging phenotypes resulting in the evolution of diseases. As living cells are open systems in quasi-steady state type equilibrium in continuous exchange with their environment, computational techniques that have been successfully applied in statistical thermodynamics to describe phase transitions may provide new insights to the emerging behavior of biological systems. Here we systematically evaluate the translation of computational techniques from solid-state physics to network models that closely resemble biological networks and develop specific translational rules to tackle problems unique to living systems. We focus on logic models exhibiting only two states in each network node. Motivated by the apparent asymmetry between biological states where an entity exhibits boolean states i.e. is active or inactive, we present an adaptation of symmetric Ising model towards an asymmetric one fitting to living systems here referred to as the modified Ising model with gene-type spins. We analyze phase transitions by Monte Carlo simulations and propose a mean-field solution of a modified Ising model of a network type that closely resembles a real-world network, the Barabási–Albert model of scale-free networks. We show that asymmetric Ising models show similarities to symmetric Ising models with the external field and undergoes a discontinuous phase transition of the first-order and exhibits hysteresis. The simulation setup presented herein can be directly used for any biological network connectivity dataset and is also applicable for other networks that exhibit similar states of activity. The method proposed here is a general statistical method to deal with non-linear large scale models arising in the context of biological systems and is scalable to any network size.

     

Effects of conformational selectivity and of overlapping kinetically influential ionizations on the characteristics of pH-dependent enzyme kinetics. Implications of free-enzyme pKa variability in reactions of papain for its catalytic mechanism.

The effects of selection by a small molecule, when binding to a protein, of a particular conformation from an equilibrium stereopopulation on the characteristics of the pH-dependence of reaction with a reactivity probe or substrate were determined by analysis of an appropriate kinetic model. For reaction in one protonic state containing an equilibrium mixture of two conformational isomers, the pH-second-order rate constant (k) profile is of conventional sigmoidal form. The apparent pKa value is a composite of the pKa values of the two conformational states. The value of pKapp. for a given enzyme under given experimental conditions will always be the same (provided that the site-specificity assumed in the model is maintained) irrespective of whether only one conformation reacts or both react, with the same or with different rate constants. The experimentally determined pH-independent rate constant (kapp.) is an average of the reactivities of the two conformational states weighted in favour of the predominant form. The presence of an additional but unreactive conformational state also affects the value of kapp. The possibility that overlapping acid dissociations that affect the reactivity of the enzyme might provide pH-k profiles often indistinguishable in practice from simple sigmoidal dissociation curves and subject to variability in apparent pKa values was evaluated by a simulation study. If two reactive protonic states of the enzyme respond differently to changes in the structure of the substrate or site-specific reactivity probe, differences in apparent pKa values of up to approx. 1 unit can be exhibited without deviation from sigmoidal behaviour being reliably observed. Differences in apparent pKa values observed in some site-specific reactions of papain and their possible consequences for its catalytic mechanism are discussed.     

Modulating repeat protein stability: the effect of individual helix stability on the collective behavior of the ensemble

Repeat proteins are tandem arrays of a small structural motif, in which tertiary structure is stabilized by interactions within a repeat and between neighboring repeats. Several studies have shown that this modular structure is manifest in modular thermodynamic properties. Specifically, the global stability of a repeat protein can be described by simple linear models, considering only two parameters: the stability of the individual repeated units (H) and the coupling interaction between the units (J). If the repeat units are identical, single values of H and J, together with the number of repeated units, is sufficient to completely describe the thermodynamic behavior of any protein within a series. In this work, we demonstrate how the global stability of a repeat protein can be changed, in a predictable fashion, by modifying only the H parameter. Taking a previously characterized series of consensus tetratricopeptide repeats (TPR) (CTPRa) proteins, we introduced mutations into the basic repeating unit, such that the stability of the individual repeat unit was increased, but its interaction with neighboring units was unchanged. In other words, we increased H but kept J constant. We demonstrated that the denaturation curves for a series of such repeat proteins can be fit and additional curves can be predicted by the one-dimensional Ising model in which only H has changed from the original fit for the CTPRa series. Our results show that we can significantly increase the stability of a repeat protein by rationally increasing the stability of the units (H), whereas the interaction between repeats (J) remains unchanged.     

A discrete fully recurrent network of max product units for associative memory and classification

This paper defines the truncated normalized max product operation for the transformation of states of a network and provides a method for solving a set of equations based on this operation. The operation serves as the transformation for the set of fully connected units in a recurrent network that otherwise might consist of linear threshold units. Component values of the state vector and outputs of the units take on the values in the set [0, 0.1,..., 0.9, 1]. The result is a much larger state space given a particular number of units and size of connection matrix than for a network based on threshold units. Since the operation defined here can form the basis of transformations in a recurrent network with a finite number of states, fixed points or cycles are possible and the network based on this operation for transformations can be used as an associative memory or pattern classifier with fixed points taking on the role of prototypes. Discrete fully recurrent networks have proven themselves to be very useful as associative memories and as classifiers. However they are often based on units that have binary states. The effect of this is that the data to be processed consisting of vectors in R(n) have to be converted to vectors in [0, 1]m with m much larger than n since binary encoding based on positional notation is not feasible. This implies a large increase in the number of components. The effect can be lessened by allowing more states for each unit in our network. The network proposed demonstrates those properties that are desirable in an associative memory very well as the simulations show.     

Neurohypophyseal hormone-responsive renal adenylate cyclase. IV. A random-hit matrix model for coupline in a hormone-sensitive adenylate cyclase system

A "random-hit" matrix model is proposed to account for the dynamic and steady state relationship between occupation of bovine renal medullary membrane receptors by [Lys8]vasopressin (LVP) and neurohypophyseal hormones (NHH) and the associated activation of membrane-bound adenylate cyclase. The model was developed by systematic introduction of specific rules concerning receptor coupling into a general structural model which consists of two square matrices of identical size, one composed of homogeneous R ("receptor") units, the second of homogeneous C ("cyclase") units. R units are either occupied (RO) or unoccupied (RU); C units are either active (CA) or inactive (CI). Hormone molecules are envisioned to "collide" with R units randomly; collision with RU leads to "binding", and occupation is maintained for a characteristic mean occupancy time, TO. In this structure, each R unit has an "interaction field" which consists of the "twin" unit in the "C" matrix, and the 4 nearest neighbor C units surrounding the twin. Occupation of an R unit leads to activation of all CI units in the interaction field of that R; CA units in the interaction field are refractory. Thus binding at a given R may "recruit" a variable number of inactive neighboring C units (5, 4, 3, 2, 1, or 0). The model requires that there be individual coupling delays between the moment of binding at a given R and subsequent activation of CI units (mean coupling delay (Td) approximately 10% To). Activation of C units persists as long as the "parent" R is occupied and is maintained for an additional short time interval (Tp) after RO reverts to RU, corresponding to hormone dissociation from receptor. The model accounts for the following previously demonstrated relations between LVP occupation of receptors and adenylate cyclase activation in bovine renal medullary membranes: 1) the shape of the nonlinear steady state relation between normalized (percentage maximal) receptor occupation (O) and cyclase activation (A), uniformly observed in different membrane preparations: 2) variable hormone concentration-dependent trajectories of approach to the final steady state A:O value (A:Oss) which may be either monophasic or biphasic; 3) the loss of intrinsic adenylate cyclase activity observed in bovine membranes for a series of NHH analogs with progressively diminishing affinity for receptors. The model represents an explicit theory of coupling where a successive series of temporal events are quantitatively related to each other and privide major constraints to any interpretation of the molecular organization of receptors and adenylate cyclase units in membranes. The model excludes a number of mechanistic proposals and suggests a new hypothesis for membrane coupling with features which may be generally applicable to other hormone-sensitive adenylate cyclase systems.     

Metastable equilibrium with random local fluctuations: Simulations of dynamic receptor pattern generation in a fluid mosaic membrane

The generation of receptors in the animal cell's membrane was simulated by a model consisting of units in four possible states within a hexagonal area (playboard) ofn units of a triangular network. The state of each unit was determined by the previous state or itself and of its six nearest neighbours, as regulated by a set of transition rules, which kept the mean relative frequency (m.r.f.) of each state constant. The transition rules were applied to the system exactlyn times, regardedless whether this involved selection of a unit on 0, 1, 2 or more occasions (programme random selection with repeat; RS-R). Comparison to previous results obtained by other ways of application of the rules has shown that the RS-R programme accounted for the highest m.r.f. of quiet (Q) units and Q clusters (sub-patterns), and also for the longest survival of Q configurations through several generations. Functioning of the model under the RS-R programme simulates an integrated system in metastable equilibrium with random local fluctuations, such as the cytoplasmic membrane is imagined to be in standardized environmental conditions. The formation-persistence-disintegration cycle of the sub-patterns is believed to simulate the dynamic generation of transitory receptor configurations in the cell membrane.     

How cytochrome c folds, and why: submolecular foldon units and their stepwise sequential stabilization

Native state hydrogen exchange experiments have shown that the cytochrome c (Cyt c) protein consists of five cooperative folding-unfolding units, called foldons. These are named, in the order of increasing unfolding free energy, the nested-Yellow, Red, Yellow, Green, and Blue foldons. Previous results suggest that these units unfold in a stepwise sequential way so that each higher energy partially unfolded form includes all of the previously unfolded lower free energy units. If this is so, then selectively destabilizing any given foldon should equally destabilize each subsequent unfolding step above it in the unfolding ladder but leave the lower ones before it unaffected. To perform this test, we introduced the mutation Glu62Gly, which deletes a salt link in the Yellow unit and destabilizes the protein by 0.8 kcal/mol. Native state hydrogen exchange and other experiments show that the stability of the Yellow unit and the states above it in the free energy ladder are destabilized by about the same amount while the lower lying states are unaffected. These results help to confirm the sequential stepwise nature of the Cyt c unfolding pathway and therefore a similar refolding pathway. The steps in the pathway are dictated by the concerted folding-unfolding property of the individual unit foldons; the order of steps is determined by the sequential stabilization of progressively added foldons in the native context. Much related information for Cyt c strongly conforms with this mechanism. Its generality is supported by available information for other proteins.     

Model for a DNA-mediated synaptic complex suggested by crystal packing of gamma delta resolvase subunits.

The packing arrangement of the 12 subunits of intact gamma delta resolvase in the unit cell of a hexagonal crystal form suggests a model for site-specific recombination that involves a DNA-mediated synaptic intermediate. The crystal structure has been determined by molecular replacement and partially refined at 2.8/3.5 A resolution. Although the small DNA-binding domain is disordered in these crystals, packing considerations show that only a small region of space in the crystal could accommodate a domain of its size. A family of related models for a synaptic complex between two DNA duplexes and 12 monomers that are arranged as situated in the crystal is consistent with the known topology of the complex and the distances between the three resolvase dimer-binding sites per DNA; further, these models place the two DNA recombination sites in contact with each other between two resolvase dimers, implying that strand exchange is accomplished through direct DNA-DNA interaction. A major role postulated, then, for the resolvase protein assembly is to stabilize a res DNA structure that is close to the topological transition state of the reaction.     

An advanced version of the dynamic receptor pattern generation model: The flux model

In the recently described simple model of dynamic receptor pattern generation we used a two-dimensional hexagonal area of a regular triangular network, formed by a statistically constant distribution of unit electrostatic charges in a dynamic equilibrium. A set of 16 transition rules was applied to all units simultaneously; the next state of each unit depended only on the previous state of its six nearest neighbours, and the transition of the total pattern into the new one occurred in a single jump. Hence we designated the initial simple model as jump model. In this paper we describe an advanced version of the model, in which simplified rules are applied to one unit after the other in a sequential order, from left to right, starting with the top row of units. In the advanced version the state of a unit depends not only on that of its six nearest neighbours, but also on the state of all units preceding in sequence the one actually considered. This results in flux-like transitions. We therefore designated the advanced version as the flux model. It is shown that the flux model represents a closer approximation of physical and biological realities than the original jump model.     

Optical characterization of intermediates in the water-splitting enzyme system of photosynthesis — possible states and configurations of manganese and water

Absorption changes coupled with the individual transitions S₀–S₃ and redox reactions in the water-splitting enzyme system S of photosynthesis have been measured. The principal difficulties of measuring the very small absorption changes in the ultraviolet coupled with those reactions have been reduced drastically through the use of a highly purified Photosystem II complex isolated from the Cyanobacterium synechococcus. The general problem caused by the mixing of the S states during a train of flashes and the falsification through the overlap with absorption changes of Q_B (binary oscillations) have been treated as follows. (1) The binary oscillations were bypassed through the use of silicomolybdate and high concentrations of DCBQ, respectively, as external electron acceptor. (2) Stable absorption changes of the mixed S-state transitions have been deconvoluted through fitting procedures to get the changes of the individual transitions of S₁ → S₂ → S₃ → S₀ → S₁. (3) Kinetically resolved absorption changes of the S-states in the 100-μs range gave independent information on the individual transitions. (4) Stable absorption changes of the S₀ → S₁ transitions in the forefront were induced after shifting the S states through low concentrations of NH₂OH two units backwards. Analysis of the resulting sequence S_x → S₀ → S₁ → S₂ → S₃ → S₀, beginning with an NH₂OH depending pre-state, S_x, and followed by an S₀ → S₁ transition not mixed with the opposite S₃ → S₀ transition, increased the conclusiveness considerably. It results that the ultraviolet spectrum of the S₀ → S₁ transition is different from the spectra of the S₁ → S₂ and S₂ → S₃ transition. Possible states of manganese, water and surplus charges responsible for these spectra are presented.     

Simultaneous on/off regulation of transgenes located on a mammalian chromosome with Cre-expressing adenovirus and a mutant loxP

The site-specific recombinase Cre has often been used for on/off regulation of expression of transgenes introduced into the mammalian chromosome. However, this method is only applicable to the regulation of a single gene and cannot be used to simultaneously regulate two genes, because site-specific recombination occurs from the target loxP sequence of one regulating unit to the loxP sequence of any other unit and would eventually disrupt the structure of both regulating units. We previously reported a mutant loxP sequence with a two base substitution called loxP V (previously called loxP 2272), with which wild-type loxP cannot recombine but with which the identical mutant loxP recombines efficiently. In the present study we isolated cell lines bearing two regulating units on a chromosome containing a pair of wild-type loxP sequences or mutant loxP V sequences. After infection with Cre-expressing recombinant adenovirus AxCANCre, expression of a gene in each regulating unit was simultaneously turned on and off. Southern analyses showed that both regulating units were processed simultaneously and independently, even after infection with a limited amount of AxCANCre. The results showed that simultaneous regulation of gene expression on a mammalian chromosome mediated by Cre can be achieved by using mutant loxP V and wild-type loxP. This method may be a useful approach for conditional transgenic/knockout animals and investigation of gene function involving two genes simultaneously. Another possible application is for preparation of a new packaging cell line of viral vectors through simultaneous production of toxic viral genes.     

Structures and Antitumor Activities of the Polysaccharides Isolated from Fruiting Body and the Growing Culture of Mycelium of Ganoderma lucidum

Several β-D-glucans, appertaining to the same molecular species but having different degrees of branching, were isolated from water and alkali extracts of the fruiting body of Ganoderma lucidum (Reishi). The purified glucans that were mostly water-insoluble had a backbone of (1 →3)-linked D-glucose residues, attached mainly with single D-glucosyl units at 0-6 and also with a few short (l→4)-linked glucosyl units at 0-2 positions. However, their degrees of branching appeared to differ in the range of d.b. 1/3 ~ 1/23, depending on the extracted glucan fractions. In addition to the ^-glucans, the fruiting body contained water-soluble heteropolysaccharides, comprising D-glucose, D-galactose, D-mannose, L-(or D)-arabinose, D-xylose, and L-fucose.

A branched (1 →3)-β-D-glucan was also isolated from the culture filtrate of G. lucidum grown in a glucose-yeast extract medium. The extracellular β-D-glucan was less soluble in water after purification, but soluble in dilute alkali. This glucan has essentially the same structure as that of hot-water extracted polysaccharide from the fruiting body. The repeating unit of the glucan contains a backbone chain of (1 →3)-linked D-glucose residues, five out of sixteen D-glucose residues being substituted at 0-6 positions with single D-glucosyl units and one D-glucose residue at 0-2 positions probably with a cellobiose unit.

The hot-water extractable fruiting body glucan and the extracellular glucan of the culture of growing mycelium showed relatively high growth-inhibition activities against Sarcoma 180 solid tumor in mice, when administered by. successive intraperitoneal injections. When the moderately branched glucans were modified to D-glucan-polyols by periodate oxidation and borohydride reduction, they exhibited higher antitumor activities, confirming the previous conclusion that the attachment of polyol groups to the (1 →3)-lmked backbone significantly enhances its host-mediated antitumor effect.     

An X-ray study of the condensed and separated states of sciatic nerve myelin

Low-angle X-ray diffraction patterns of peripheral nerve myelin after modification by either rehydration in various solutions or by chemical treatment have been recorded. These X-ray patterns and the previously reported modified nerve myelin patterns demonstrate that nerve myelin has at least five different states: the normal state, condensed state I and II and separated state I and II. There are two membranes per unit cell in the normal state and in states II whereas there is one membrane per unit cell in states I. Under certain conditions normal nerve can go reversibly into either of states II. With continued treatment the nerve myelin structure moves irreversibly from state II to state I and, once in state I, the nerve myelin layers cannot return to the normal state. Our results demonstrate that there is a reversible transformation between condensed state I and separated state I. Fourier profiles of nerve myelin in the normal state, condensed state I and separated state I are presented.     

Temporal coding: the relevance of classical activity, its relation to pattern frequency bands, and a remark on recoding of excitatory drive into phase shifts

We consider an oscillatory network model that is obtained as complex-valued generalization of the classical Cohen-Grossberg-Hopfield (CGH) model. Apart from a synchronizing mechanism, a stronger and/or more coherent input to a unit in the network implies a higher phase velocity of this unit. This constitutes the desynchronizing mechanism, referred to as acceleration. The units' activity of the classical model translates into the amplitudes of the phase model oscillators. This allows to associate classical and temporal coding with amplitude and phase dynamics, respectively. We discuss how the two dynamics act together to achieve the unambiguous pattern recognition that avoids the superposition problem. With respect to coherence, dominating patterns may take coherent states also if only a subset of its units is on-state. The competition for coherence, introduced by acceleration, realizes a kind of feature counting that identifies the dominating pattern as the pattern with the most on-state units. This dominating but possibly only partially active pattern may take a coherent state with a frequency level that is related to the number of on-state units. We also speculate on neurophysiological findings, related to observed phase differences between optimally and suboptimally activated neurons, that may indicate the presence of acceleration.     

A population dynamics analysis of the interaction between adaptive regulatory T cells and antigen presenting cells

Background

Regulatory T cells are central actors in the maintenance of tolerance of self-antigens or allergens and in the regulation of the intensity of the immune response during infections by pathogens. An understanding of the network of the interaction between regulatory T cells, antigen presenting cells and effector T cells is starting to emerge. Dynamical systems analysis can help to understand the dynamical properties of an interaction network and can shed light on the different tasks that can be accomplished by a network.

Methodology and Principal Findings

We used a mathematical model to describe a interaction network of adaptive regulatory T cells, in which mature precursor T cells may differentiate into either adaptive regulatory T cells or effector T cells, depending on the activation state of the cell by which the antigen was presented. Using an equilibrium analysis of the mathematical model we show that, for some parameters, the network has two stable equilibrium states: one in which effector T cells are strongly regulated by regulatory T cells and another in which effector T cells are not regulated because the regulatory T cell population is vanishingly small. We then simulate different types of perturbations, such as the introduction of an antigen into a virgin system, and look at the state into which the system falls. We find that whether or not the interaction network switches from the regulated (tolerant) state to the unregulated state depends on the strength of the antigenic stimulus and the state from which the network has been perturbed.

Conclusion/Significance

Our findings suggest that the interaction network studied in this paper plays an essential part in generating and maintaining tolerance against allergens and self-antigens.     

Radiation oncology in Mexico: Current status according to Mexico’s Radiation Oncology Certification Board

AimDescribe the results of the first national census of radiotherapy in Mexico in order to make a situational diagnosis of radiotherapy availability, offer more accurate information to radiation oncologists, and promote an adequate scientific based investment for the country.BackgroundAccording to the Organisation for Economic Co-operation and Development (OECD), the density of radiotherapy (RT) machines per million habitants in Mexico is approximately 1.7−1.8. Other international organizations such as DIRAC-IAEA report 1.15 per million habitants. National organizations collect data indirectly and previous surveys had a low accrual rate (32.5%). Therefore, a precise census is required.Material and methodsThe Mexican Radiation Oncology Certification Board (CMRO for its acronym in Spanish) conducted a nationwide census from January through November 2019. Gathered information was combined with CMRO database for sociodemographic information and human resources.ResultsThe study included 103 RT centers [95.1% answered the survey], with a median of 2 centers by state (ranging from 0 in Tlaxcala to 20 in Mexico City) and with a report of only 1 center in 11 states (34.4%). Fifty-six (54.3%) of the centers are public. Fourteen centers (13.6%) have residency-training programs. The total number of RT machines is 162 [141 clinical and linear accelerators (87%) and 21 radionuclide units (13%)] with a median of 3 machines by state (0 in Tlaxcala to 46 in Mexico City) and with ≤3 machines in 18 states (56.25%). The overall calculated density of RT machines per million habitants is 1.32, varying from 0 in Tlaxcala to 5.16 in Mexico City. The density of linear and clinical accelerators per million population is 1.19. The total number of brachytherapy units is 66, with a median of 1 center with brachytherapy unit per state and 29 states with ≤3 centers with a brachytherapy unit (90.6%). Thirty-seven brachytherapy units (56.1%) have automated afterload high-dose rate. The overall rate of brachytherapy units per million inhabitants is 0.55, varying from 0 in 5 states (15.6%), 0.1-0.49 in 8 states (25%), 0.5–0.99 in 13 states (40.6%), 1–1.49 in 5 states (15.6%) and 1.5–1.99 in Mexico City (3.1%). The Mexican CMRO has 368 radiation oncologists certified (99 women and 269 men), of whom only 346 remain as an active part of Mexico's workforce.ConclusionsThis is the first time the CMRO conducts a national census for a radiotherapy diagnostic situation in Mexico. The country currently holds a density of clinical and linear accelerators of 1.19 per million habitants. Brachytherapy density is 0.55 devices per million habitants, and 57% of radiotherapy centers have brachytherapy units.     

Unsupervised learning and temporal context to recall complex robot trajectories

An unsupervised neural network is proposed to learn and recall complex robot trajectories. Two cases are considered: (i) A single trajectory in which a particular arm configuration (state) may occur more than once, and (ii) trajectories sharing states with each other. Ambiguities occur in both cases during recall of such trajectories. The proposed model consists of two groups of synaptic weights trained by competitive and Hebbian learning laws. They are responsible for encoding spatial and temporal features of the input sequences, respectively. Three mechanisms allow the network to deal with repeated or shared states: local and global context units, neurons disabled from learning, and redundancy. The network reproduces the current and the next state of the learned sequences and is able to resolve ambiguities. The model was simulated over various sets of robot trajectories in order to evaluate learning and recall, trajectory sampling effects and robustness.     

Effects of serine-to-cysteine mutations on beta-lactamase folding

B. licheniformis exo-small β-lactamase (ESBL) has two nonsequential domains and a complex architecture. We replaced ESBL serine residues 126 and 265 with cysteine to probe the conformation of buried regions in each domain. Spectroscopic, hydrodynamic, and chemical methods revealed that the mutations do not alter the native fold but distinctly change stability (S-126C > wild-type > S-126/265C > S-265C ESBL) and the features of partially folded states. The observed wild-type ESBL equilibrium intermediate has decreased fluorescence but full secondary structure. S-126C ESBL intermediate has the fluorescence of the unfolded state, no thiol reactivity, and partial secondary structure. S-265C and S-126/265C ESBL populate intermediate states unfolded by fluorescence and thiol reactivity but with full secondary structure. Mass analysis of S-126/265C ESBL in the partially folded state proved that both thiol groups become exposed simultaneously. None of the intermediates is compatible with sequential domain unfolding. Molecular dynamics simulation suggests that the stabilizing effect of the S-126C substitution is due to optimization of van der Waals interactions and packing. On the other hand, destabilization induced by the S-265C mutation results from alteration of the hydrogen-bond network. The results illustrate the large impact that seemingly conservative serine-to-cysteine changes can have on the energy landscape of proteins.