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A Note on the Effects of Linear Topology Preservation in Monte Carlo Simulations of Knotted Proteins

João N. C. Especial, Antonio Rey & Patrícia F.N. Faísca
Journal PaperInternational Journal of Molecular Sciences (2022) 23, 13871


Monte Carlo simulations are a powerful technique and are widely used in different fields. When applied to complex molecular systems with long chains, such as those in synthetic polymers and proteins, they have the advantage of providing a fast and computationally efficient way to sample equilibrium ensembles and calculate thermodynamic and structural properties under desired conditions. Conformational Monte Carlo techniques employ a move set to perform the transitions in the simulation Markov chain. While accepted conformations must preserve the sequential bonding of the protein chain model and excluded volume among its units, the moves themselves may take the chain across itself. We call this a break in linear topology preservation. In this manuscript, we show, using simple protein models, that there is no difference in equilibrium properties calculated with a move set that preserves linear topology and one that does not. However, for complex structures, such as those of deeply knotted proteins, the preservation of linear topology provides correct equilibrium results but only after long relaxation. In any case, to analyze folding pathways, knotting mechanisms and folding kinetics, the preservation of linear topology may be an unavoidable requirement.

A concise introduction to thermodynamics for physicists

Patrícia Faísca
BookCRC Press (2022)


This introductory textbook provides a synthetic overview of the laws and formal aspects of thermodynamics and was designed for undergraduate students in physics, and in the physical sciences. Language and notation have been kept as simple as possible throughout the text.

While this is a self-contained text on thermodynamics (i.e. focused on macroscopic physics), emphasis is placed on the microscopic underlying model to facilitate the understanding of key concepts such as entropy, and motivate a future course on statistical physics.

This book will equip the reader with an understanding of the scope of this discipline and of its applications to a variety of physical systems.

Throughout the text readers are continuously challenged with conceptual questions that prompt reflection and facilitate the understanding of subtle issues. Each chapter ends by presenting worked problems to support and motivate self-study, in addition to a series of proposed exercises whose solutions are available as supplementary material.

Predicting stable binding modes from simulated dimers of the D76N mutant of β2-microglobulin

Nuno F.B. Oliveira, Filipe E.P. Rodrigues, João N.M. Vitorino, Patrícia F.N. Faísca & Miguel Machuqueiro
Journal Paper Computational and Structural Biotechnology Journal (2021) 19, 5160-5169


The D76N mutant of the beta-2-microgobulin protein is a biologically motivated model system to study protein aggregation. There is strong experimental evidence, supported by molecular simulations, that D76N populates a highly dynamic conformation (which we originally named I2) that exposes aggregation-prone patches as a result of the detachment of the two terminal regions. Here, we use Molecular Dynamics simulations to study the stability of an ensemble of dimers of I2 generated via protein-protein docking. MM-PBSA calculations indicate that within the ensemble of investigated dimers the major contribution to interface stabilization at physiological pH comes from hydrophobic interactions between apolar residues. Our structural analysis also reveals that the interfacial region associated with the most stable binding modes are particularly rich in residues pertaining to both the N- and C-terminus, as well residues from the BC- and DE-loops. On the other hand, the less stable interfaces are stabilized by intermolecular interactions involving residues from the CD- and EF-loops. By focusing on the most stable binding modes, we used a simple geometric rule to propagate the corresponding dimer interfaces. We found that, in the absence of any kind of structural rearrangement occurring at an early stage of the oligomerization pathway, some interfaces drive a self-limited growth process, while others can be propagated indefinitely allowing the formation of long, polymerized chains. In particular, the interfacial region of the most stable binding mode reported here falls in the class of self-limited growth.

A specific set of heterogeneous native interactions yields efficient knotting in protein folding

João N. C. Especial & Patrícia F.N. Faísca
Journal Paper J. Phys. Chem. B (2021) 125, 7359–7367


Native interactions are crucial for folding, and non-native interactions appear to be critical for efficiently knotting proteins. Therefore, it is important to understand both their roles in the folding of knotted proteins. It has been proposed that non-native interactions drive the correct order of contact formation, which is essential to avoid backtracking and efficiently self-tie. In this study we ask if non-native interactions are strictly necessary to tangle a protein, or if the correct order of contact formation can be assured by a specific set of native, but otherwise heterogeneous (i.e. having distinct energies), interactions. In order to address this problem we conducted extensive Monte Carlo simulations of lattice models of proteinlike sequences designed to fold into a pre-selected knotted conformation embedding a trefoil knot. We were able to identify a specific set of heterogeneous native interactions that drives efficient knotting, and is able to fold the protein when combined with the remaining native interactions modeled as homogeneous. This specific set of heterogeneous native interactions is strictly enough to efficiently self-tie. A distinctive feature of these native interactions is that they do not backtrack, because their energies ensure the correct order of contact formation. Furthermore, they stabilize a knotted intermediate state, which is en-route to the native structure. Our results thus show that - at least in the context of the adopted model - non-native interactions are not necessary to knot a protein. However, when they are taken into account into protein energetics it is possible to find specific, non-local non-native interactions that operate as a scaffold that assists the knotting step.

The folding space of β2-microglobulin is modulated by a single disulfide bond

Jules Morand, Ana Nunes & Patrícia F.N. Faísca
Journal Paper Phys. Biol. (2021) 18, 056001


AProtein β2-microglobulin (β2m) is classically considered the causative agent of dialysis related amyloidosis (DRA), a conformational disorder that affects patients undergoing long-term hemodialysis. The wild type form, the $\Delta N6$ structural variant, and the D76N mutant have been extensively used as model systems of $\beta 2m$ aggregation. In all of them, the native structure is stabilized by a disulfide bridge between the sulphur atoms of the cysteine residues 25 (at B strand) and 80 (at F strand), which has been considered fundamental in β2m fibrillogenesis. Here, we use extensive Discrete Molecular Dynamics simulations of a full atomistic structure-based model to explore the role of this disulfide bridge as a modulator of the folding space of β2m. In particular, by considering different models for the disulfide bridge, we explore the thermodynamics of the folding transition, and the formation of intermediate states that may have the potential to trigger the aggregation cascade. Our results show that the dissulfide bridge affects folding transition and folding thermodynamics of the considered model systems, although to different extents. In particular, when the interaction between the sulphur atoms is stabilized relative to the other intramolecular interactions, or even locked (i.e. permanently established), the WT form populates an intermediate state featuring a well preserved core, and two unstructured termini, which was previously detected only for the D76N mutant. The formation of this intermediate state may have important implications in our understanding of β2m fibrillogenesis.

The Early Phase of β2-Microglobulin Aggregation: Perspectives From Molecular Simulations

Rui J. S. Loureiro & Patrícia F.N. Faísca
ReviewFront. Mol. Biosci. (2020) 7, 578433


AProtein β2-microglobulin is the causing agent of two amyloidosis, dialysis related amyloidosis (DRA), affecting the bones and cartilages of individuals with chronic renal failure undergoing long-term hemodialysis, and a systemic amyloidosis, found in one French family, which impairs visceral organs. The protein’s small size and its biomedical significance attracted the attention of theoretical scientists, and there are now several studies addressing its aggregation mechanism in the context of molecular simulations. Here, we review the early phase of β2-microglobulin aggregation, by focusing on the identification and structural characterization of monomers with the ability to trigger aggregation, and initial small oligomers (dimers, tetramers, hexamers etc.) formed in the so-called nucleation phase. We focus our analysis on results from molecular simulations and integrate our views with those coming from in vitro experiments to provide a broader perspective of this interesting field of research. We also outline directions for future computer simulation studies.

Knotted proteins: Tie etiquette in structural biology

Ana Nunes & Patrícia F.N. Faísca
ReviewContemporary Mathematics (AMS) (2020) 746, 155-183


A small fraction of all protein structures characterized so far are entangled. The challenge of understanding the properties of these knotted proteins, and the why and the how of their natural folding process, has been taken up in the past decade with different approaches, such as structural characterization, in vitro experiments, and simulations of protein models with varying levels of complexity. The simplest among these are the lattice Gō models, which belong to the class of structure-based models, i.e., models that are biased to the native structure by explicitly including structural data. In this review we highlight the contributions to the field made in the scope of lattice Gō models, putting them into perspective in the context of the main experimental and theoretical results and of other, more realistic, computational approaches.

Protein folding: An introduction

Cláudio Gomes & Patrícia F.N. Faísca
BookSpringerBriefs in Molecular Science. (2019), Springer Nature

The Early Phase of β2m Aggregation: An Integrative Computational Study Framed on the D76N Mutant and the ΔN6 Variant

Rui J. S. Loureiro, Diogo V. Viçosa, Miguel Machuqueiro, Eugene Shakhnovich & Patrícia F.N. Faísca
Journal PaperBiomolecules (2019) 9, 366


Human β2-microglobulin (b2m) protein is classically associated with dialysis-related amyloidosis (DRA). Recently, the single point mutant D76N was identified as the causative agent of a hereditary systemic amyloidosis affecting visceral organs. To get insight into the early stage of the β2m aggregation mechanism, we used molecular simulations to perform an in depth comparative analysis of the dimerization phase of the D76N mutant and the ΔN6 variant, a cleaved form lacking the first six N-terminal residues, which is a major component of ex vivo amyloid plaques from DRA patients. We also provide first glimpses into the tetramerization phase of D76N at physiological pH. Results from extensive protein–protein docking simulations predict an essential role of the C- and N-terminal regions (both variants), as well as of the BC-loop (ΔN6 variant), DE-loop (both variants) and EF-loop (D76N mutant) in dimerization. The terminal regions are more relevant under acidic conditions while the BC-, DE- and EF-loops gain importance at physiological pH. Our results recapitulate experimental evidence according to which Tyr10 (A-strand), Phe30 and His31 (BC-loop), Trp60 and Phe62 (DE-loop) and Arg97 (C-terminus) act as dimerization hot-spots, and further predict the occurrence of novel residues with the ability to nucleate dimerization, namely Lys-75 (EF-loop) and Trp-95 (C-terminus). We propose that D76N tetramerization is mainly driven by the self-association of dimers via the N-terminus and DE-loop, and identify Arg3 (N-terminus), Tyr10, Phe56 (D-strand) and Trp60 as potential tetramerization hot-spots.

Hydrophobic confinement modulates thermal stability and assists knotting in the folding of tangled proteins

João Especial, Ana Nunes, Antonio Rey & Patrícia F.N. Faísca
Journal PaperPhys. Chem. Chem. Phys. (2019) 21, 21, 11764-11775


There is growing support for the idea that the in vivo folding process of knotted proteins is assisted by chaperonins, but the mechanism of chaperonin assisted folding remains elusive. Here, we conduct extensive Monte Carlo simulations of lattice and off-lattice models to explore the effects of confinement and hydrophobic intermolecular interactions with the chaperonin cage in the folding and knotting processes. We find that moderate to high protein-cavity interactions (which are likely to be established in the beginning of the chaperonin working cycle) cause an energetic destabilization of the protein that overcomes the entropic stabilization driven by excluded volume, and leads to a decrease of the melting temperature relative to bulk conditions. Moreover, mild-to-moderate hydrophobic interactions with the cavity (which would be established later in the cycle) lead to a significant enhancement of knotting probability in relation to bulk conditions while simultaneously moderating the effect of steric confinement in the enhancement of thermal stability. Our results thus indicate that the chaperonin may be able to assist knotting without simultaneously thermally stabilizing potential misfolded states to a point that would hamper productive folding thus compromising its functional role.

A tale of two tails: The importance of unstructured termini in the aggregation pathway of beta-2-microglobulin

Rui J. S. Loureiro, Diogo Vila-Viçosa, Miguel Machuqueiro, Eugene Shakhnovich & Patrícia F.N. Faísca
Journal PaperProteins: Structure, Function, and Bioinformatics (2017) 85, 2045-2057


The identification of intermediate states for folding and aggregation is important from a fundamental standpoint and for the design of novel therapeutic strategies targeted at conformational disorders. Protein human β2-microglobulin (HB2m) is classically associated with dialysis-related amyloidosis, but the single point mutant D76N was recently identified as the causative agent of a hereditary systemic amyloidosis affecting visceral organs. Here, we use D76N as a model system to explore the early stage of the aggregation mechanism of HB2m by means of an integrative approach framed on molecular simulations. Discrete molecular dynamics simulations of a structured-based model predict the existence of two intermediate states populating the folding landscape. The intermediate I1 features an unstructured C-terminus, while I2, which is exclusively populated by the mutant, exhibits two unstructured termini. Docking simulations indicate that I2 is the key species for aggregation at acidic and physiological pH contributing to rationalize the higher amyloidogenic potential of D76N relative to the wild-type protein and the ΔN6 variant. The analysis carried out here recapitulates the importance of the DE-loop in HB2m self-association at a neutral pH and predicts a leading role of the C-terminus and the adjacent G-strand in the dimerization process under acidic conditions. The identification of aggregation hot‐spots is in line with experimental results that support the importance of Phe56, Asp59, Trp60, Phe62, Tyr63, and Tyr66 in HB2m amyloidogenesis. We further predict the involvement of new residues such as Lys94 and Trp95 in the aggregation process.

Steric confinement and enhanced local flexibility assist knotting in simple models of protein folding

Miguel A. Soler, Antonio Rey & Patrícia F.N. Faísca
Journal PaperPhys. Chem. Chem. Phys. (2016) 18, 26391-26403


The chaperonin complex GroEL–GroES is able to accelerate the folding process of knotted proteins considerably. However, the folding mechanism inside the chaperonin cage is elusive. Here we use a combination of lattice and off-lattice Monte Carlo simulations of simple Gō models to study the effect of physical confinement and local flexibility on the folding process of protein model systems embedding a trefoil knot in their native structure. This study predicts that steric confinement plays a specific role in the folding of knotted proteins by increasing the knotting probability for very high degrees of confinement. This effect is observed for protein MJ0366 even above the melting temperature for confinement sizes compatible with the size of the GroEL/GroES chaperonin cage. An enhanced local flexibility produces the same qualitative effects on the folding process. In particular, we observe that knotting probability increases up to 40% in the transition state of protein MJ0366 when flexibility is enhanced. This is underlined by a structural change in the transition state, which becomes devoid of helical content. No relation between the knotting mechanism and flexibility was found in the context of the off-lattice model adopted in this work.

Thermal unfolding simulations of NBD1 domain variants reveal structural motifs associated with the impaired folding of F508del-CFTR

Sílvia G. Estácio, Hugo Martiniano & Patrícia F.N. Faísca
Journal PaperMolecular Biosystems (2016) 12, 2834-2848


We employed high-temperature classical molecular dynamics (MD) simulations to investigate the unfolding process of the wild-type (WT) and F508del-NBD1 domains of CFTR protein, with and without second-site mutations. To rationalize the in vitro behavior of F508del-NBD1, namely its lower folding yield and higher aggregation propensity, we focused our analysis of the MD data on the existence of intermediate states with aggregation potential and/or stabilized by a significant number of non-native interactions (i.e. misfolded states). We find that the deletion of phenylalanine 508 is able to forcefully reshape the conformational space of the NBD1 domain to the extent that it uniquely populates intermediate states whose structural traits provide important insights into the molecular events that underlie the impaired folding of F508del-NBD1. In particular, our simulations predict the formation of a misfolded intermediate whose population is highly enhanced by deletion of residue 508. The stabilization of this intermediate is a direct consequence of the enhanced non-native coupling between various key regions of the α-helical subdomain and ATP-binding subdomain; it is singularly characterized by a set of non-native interactions within the ATP-binding subdomain and between that domain and the α-helical subdomain region. The formation of this intermediate is not blocked by second-site suppressor mutations which indicates a limited role of the latter in correcting the rather complex folding process of the CFTR protein missing residue 508.

Knotted proteins: A tangled tale of structural biology

Patrícia F.N. Faísca
ReviewComputational and Structural Biology Journal (2015) 13, 459-468


Knotted proteins have their native structures arranged in the form of an open knot. In the last ten years researchers have been making significant efforts to reveal their folding mechanism and understand which functional advantage(s) knots convey to their carriers. Molecular simulations have been playing a fundamental role in this endeavor, and early computational predictions about the knotting mechanism have just been confirmed in wet lab experiments. Here we review a collection of simulation results that allow outlining the current status of the field of knotted proteins, and discuss directions for future research.

How determinant is N-terminal to C-terminal coupling for protein folding?

Heinrich Krobath, Antonio Rey & Patrícia F.N. Faísca
Journal PaperPhys. Chem. Chem. Phys. (2015) 17, 3512-3524


This work investigates the role of N- to C- termini coupling in the folding transition of small, single domain proteins via extensive Monte Carlo simulations of both lattice and off-lattice models. The reported results provide compelling evidence that the existence of native interactions between the terminal regions of the polypeptide chain (i.e. termini coupling) is a major determinant of the height of the free energy barrier that separates the folded from the denatured state in a two-state folding transition, therefore being a critical modulator of protein folding rates and thermodynamic cooperativity. We further report that termini interactions are able to substantially modify the kinetic behavior dictated by the full set of native interactions. Indeed, a native structure of high contact order with “switched-off” termini-interactions actually folds faster than its circular permutant of lowest CO.

Calcium binding to gatekeeper residues flanking aggregation-prone segments underlies non-fibrillar amyloid traits in superoxide dismutase 1 (SOD1)

Sílvia G. Estácio, Sónia S. Leal, Joana S. Cristovão, Patrícia F.N. Faísca & Cláudio M. Gomes
Journal PaperBBA - Proteins and Proteomics (2015) 1854, 118-126


Calcium deregulation is a central feature among neurodegenerative diseases, including amyotrophic lateral sclerosis (ALS). Calcium accumulates in the spinal and brain stem motor neurons of ALS patients triggering multiple pathophysiological processes which have been recently shown to include direct effects on the aggregation cascade of superoxide dismutase 1 (SOD1). SOD1 is a Cu/Zn enzyme whose demetallated form is implicated in ALS protein deposits, contributing to toxic gain of function phenotypes. Here we undertake a combined experimental and computational study aimed at establishing the molecular details underlying the regulatory effects of Ca2 + over SOD1 aggregation potential. Isothermal titration calorimetry indicates entropy driven low affinity association of Ca2 + ions to apo SOD1, at pH 7.5 and 37 °C. Molecular dynamics simulations denote a noticeable loss of native structure upon Ca2 + association that is especially prominent at the zinc-binding and electrostatic loops, whose decoupling is known to expose the central SOD1 β-barrel triggering aggregation. Structural mapping of the preferential apo SOD1 Ca2 + binding locations reveals that among the most frequent ligands for Ca2 + are negatively-charged gatekeeper residues located in boundary positions with respect to segments highly prone to edge-to-edge aggregation. Calcium interactions thus diminish gatekeeping roles of these residues, by shielding repulsive interactions via stacking between aggregating β-sheets, partly blocking fibril formation and promoting amyloidogenic oligomers such as those found in ALS inclusions. Interestingly, many fALS mutations occur at these positions, disclosing how Ca2 + interactions recreate effects similar to those of genetic defects, a finding with relevance to understand sporadic ALS pathomechanisms.

Effects of knot type in the folding of topologically complex lattice proteins

M.A. Soler, A. Nunes & P.F.N. Faísca
Journal PaperJ. Chem. Phys. (2014) 141, 025101


The folding properties of a protein whose native structure contains a 52 knot are investigated by means of extensive Monte Carlo simulations of a simple lattice model and compared with those of a 31 knot. A 52 knot embedded in the native structure enhances the kinetic stability of the carrier lattice protein in a way that is clearly more pronounced than in the case of the 31 knot. However, this happens at the expense of a severe loss in folding efficiency, an observation that is consistent with the relative abundance of 31 and 52 knots in the Protein Data Bank. The folding mechanism of the 52 knot shares with that of the 31 knot the occurrence of a threading movement of the chain terminus that lays closer to the knotted core. However, co-concomitant knotting and folding in the 52 knot occurs with negligible probability, in sharp contrast to what is observed for the 31 knot. The study of several single point mutations highlights the importance in the folding of knotted proteins of the so-called structural mutations (i.e., energetic perturbations of native interactions between residues that are critical for knotting but not for folding). On the other hand, the present study predicts that mutations that perturb the folding transition state may significantly enhance the kinetic stability of knotted proteins provided they involve residues located within the knotted core.

A Simulated Intermediate State for Folding and Aggregation Provides Insights into ΔN6 β2-Microglobulin Amyloidogenic Behavior

S.G. Estácio, H. Krobath, D. Vila-Viçosa, M. Machuqueiro, E.I. Shakhnovich & P.F.N. Faísca
Journal PaperPLoS Computational Biology (2014) 10, e1003606


A major component of ex vivo amyloid plaques of patients with dialysis-related amyloidosis (DRA) is a cleaved variant of β2-microglobulin (ΔN6) lacking the first six N-terminal residues. Here we perform a computational study on ΔN6, which provides clues to understand the amyloidogenicity of the full-length β2-microglobulin. Contrary to the wild-type form, ΔN6 is able to efficiently nucleate fibrillogenesis in vitro at physiological pH. This behavior is enhanced by a mild acidification of the medium such as that occurring in the synovial fluid of DRA patients. Results reported in this work, based on molecular simulations, indicate that deletion of the N-terminal hexapeptide triggers the formation of an intermediate state for folding and aggregation with an unstructured strand A and a native-like core. Strand A plays a pivotal role in aggregation by acting as a sticky hook in dimer assembly. This study further predicts that the detachment of strand A from the core is maximized at pH 6.2 resulting into higher aggregation efficiency. The structural mapping of the dimerization interface suggests that Tyr10, His13, Phe30 and His84 are hot-spot residues in ΔN6 amyloidogenesis.

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Effects of knots on protein folding properties

M.A. Soler & P.F.N. Faísca
Journal PaperPLoS One (2013) 8, e74755


This work explores the impact of knots, knot depth and motif of the threading terminus in protein folding properties (kinetics, thermodynamics and mechanism) via extensive Monte Carlo simulations of lattice models. A knotted backbone has no effect on protein thermodynamic stability but it may affect key aspects of folding kinetics. In this regard, we found clear evidence for a functional advantage of knots: knots enhance kinetic stability because a knotted protein unfolds at a distinctively slower rate than its unknotted counterpart. However, an increase in knot deepness does not necessarily lead to more effective changes in folding properties. In this regard, a terminus with a non-trivial conformation (e.g. hairpin) can have a more dramatic effect in enhancing kinetic stability than knot depth. Nevertheless, our results suggest that the probability of the denatured ensemble to keep knotted is higher for proteins with deeper knots, indicating that knot depth plays a role in determining the topology of the denatured state. Refolding simulations starting from denatured knotted conformations show that not every knot is able to nucleate folding and further indicate that the formation of the knotting loop is a key event in the folding of knotted trefoils. They also show that there are specific native contacts within the knotted core that are crucial to keep a native knotting loop in denatured conformations which otherwise have no detectable structure. The study of the knotting mechanism reveals that the threading of the knotting loop generally occurs towards late folding in conformations that exhibit a significant degree of structural consolidation.

Assessing the effect of loop mutations in the folding space of beta2-microglobulin with Molecular Dynamics simulations

S.G. Estácio, E.I. Shakhnovich & P.F.N. Faísca
Journal PaperInt. J. Mol. Sci. (2013) 14, 17256-17278


We use molecular dynamics simulations of a full atomistic Gō model to explore the impact of selected DE-loop mutations (D59P and W60C) on the folding space of protein human β2-microglobulin (Hβ2m), the causing agent of dialysis-related amyloidosis, a conformational disorder characterized by the deposition of insoluble amyloid fibrils in the osteoarticular system. Our simulations replicate the effect of mutations on the thermal stability that is observed in experiments in vitro. Furthermore, they predict the population of a partially folded state, with 60% of native internal free energy, which is akin to a molten globule. In the intermediate state, the solvent accessible surface area increases up to 40 times relative to the native state in 38% of the hydrophobic core residues, indicating that the identified species has aggregation potential. The intermediate state preserves the disulfide bond established between residue Cys25 and residue Cys80, which helps maintain the integrity of the core region, and is characterized by having two unstructured termini. The movements of the termini dominate the essential modes of the intermediate state, and exhibit the largest displacements in the D59P mutant, which is the most aggregation prone variant. PROPKA predictions of pKa suggest that the population of the intermediate state may be enhanced at acidic pH explaining the larger amyloidogenic potential observed in vitro at low pH for the WT protein and mutant forms.

Structural and energetic determinants of co-translational folding

Heinrich Krobath, Eugene Shakhnovich & Patricia F. N. Faísca
Journal PaperJ. Chem. Phys. (2013) 138, 215101


We performed extensive lattice Monte Carlo simulations of ribosome-bound stalled nascent chains (RNCs) to explore the relative roles of native topology and non-native interactions in co-translational folding of small proteins. We found that the formation of a substantial part of the native structure generally occurs towards the end of protein synthesis. However, multi-domain structures, which are rich in local interactions, are able to develop gradually during chain elongation, while those with proximate chain termini require full protein synthesis to fold. A detailed assessment of the conformational ensembles populated by RNCs with different lengths reveals that the directionality of protein synthesis has a fine-tuning effect on the probability to populate low-energy conformations. In particular, if the participation of non-native interactions in folding energetics is mild, the formation of native-like conformations is majorly determined by the properties of the contact map around the tethering terminus. Likewise, a pair of RNCs differing by only 1-2 residues can populate structurally well-resolved low energy conformations with significantly different probabilities. An interesting structural feature of these low-energy conformations is that, irrespective of native structure, their non-native interactions are always long-ranged and marginally stabilizing. A comparison between the conformational spectra of RNCs and chain fragments folding freely in the bulk reveals drastic changes amongst the two set-ups depending on the native structure. Furthermore, they also show that the ribosome may enhance (up to 20%) the population of low energy conformations for chains folding to native structures dominated by local interactions. In contrast, a RNC folding to a non-local topology is forced to remain largely unstructured but can attain low energy conformations in bulk.

Interplay between native topology and non-native interactions in the folding of tethered proteins

Heinrich Krobath & Patricia F. N. Faísca
Journal PaperPhys. Biol. (2013) 10, 016002


e assessed the interplay of native topology and non-native interactions on surface-tethered protein folding via extensive Monte Carlo simulations of a simple lattice model. In particular, we investigated the thermodynamics and kinetics of protein-like sequences enclosing different amounts of non-native interactions to protein energetics, and which were designed to fold to distinct native topologies. Our results show that the high-contact order (CO) structure renders a folding transition that is robust to (external) steric constraints and non-native interactions. On the other hand, the folding process of the simple low-CO topology can be easily hampered by the presence of a nearby chemically inert plane. In this case, if non-native interactions are highly conspicuous during folding they can actually drive chain collapse into a very native-like trapped state, which impedes the formation of the native structure. The analysis of folding kinetics reveals that the empirical correlation between folding rate and CO may not apply to surface-tethered protein folding. Indeed, results reported here show that depending on the native environment of the tethered chain terminus the folding rate of a low-CO topology can become so drastically small that the high-CO topology actually folds faster under the same conditions. We predict that complex topologies are more likely to conserve their bulk folding mechanism upon surface tethering.

How difficult is it to fold a knotted protein? In silico insights from surface-tethered folding experiments

M.A. Soler & P.F.N. Faísca
Journal PaperPLoS One(2012) 7, e52343


We explore the effect of surface tethering on the folding process of a lattice protein that contains a trefoil knot in its native structure via Monte Carlo simulations. We show that the outcome of the tethering experiment depends critically on which terminus is used to link the protein to a chemically inert plane. In particular, if surface tethering occurs at the bead that is closer to the knotted core the folding rate becomes exceedingly slow and the protein is not able to find the native structure in all the attempted folding trajectories. Such low folding efficiency is also apparent from the analysis of the probability of knot formation, pknot, as a function of nativeness. Indeed, pknot increases abruptly from ~0 to ~1 only when the protein has more than 80% of its native contacts formed, showing that a highly compact conformation must undergo substantial structural re-arrangement in order to get effectively knotted. When the protein is surface tethered by the bead that is placed more far away from the knotted core pknot is higher than in the other folding setups (including folding in the bulk), especially if conformations are highly native-like. These results show that the mobility of the terminus closest to the knotted core is critical for successful folding of trefoil proteins, which, in turn, highlights the importance of a knotting mechanism that is based on a threading movement of this terminus through a knotting loop. The results reported here predict that if this movement is blocked, knotting occurs via an alternative mechanism, the so-called spindle mechanism, which is prone to misfolding. Our simulations show that in the three considered folding setups the formation of the knot is typically a late event in the folding process. We discuss the implications of our findings for co-translational folding of knotted trefoils.

Robustness of atomistic Go models in predicting native-like folding intermediates

S. G. Estácio, C.S. Fernandes, H. Krobath, P.F.N. Faísca & E.I. Shakhnovich
Journal PaperJ. Chem. Phys. (2012) 137, 085102


Gō models are exceedingly popular tools in computer simulations of protein folding. These models are native-centric, i.e., they are directly constructed from the protein's native structure. Therefore, it is important to understand up to which extent the atomistic details of the native structure dictate the folding behavior exhibited by Gō models. Here we address this challenge by performing exhaustive discrete molecular dynamics simulations of a Gō potential combined with a full atomistic protein representation. In particular, we investigate the robustness of this particular type of Gō models in predicting the existence of intermediate states in protein folding. We focus on the N47G mutational form of the Spc-SH3 folding domain (x-ray structure) and compare its folding pathway with that of alternative native structures produced in silico. Our methodological strategy comprises equilibrium folding simulations, structural clustering, and principal component analysis.

Identification of a conserved aggregation-prone intermediate state in the folding pathways of Spc-SH3 amyloidogenic variants

Heinrich Krobath, Silvia G. Estácio, Patricia F. N. Faísca & E.I. Shakhnovich
Journal PaperJ. Mol. Biol. (2012) 422, 705-722


We compared the folding pathways of selected mutational variants of the α-spectrin SH3 domain (Spc-SH3) by using a continuum model that combines a full atomistic protein representation with the Gō potential. Experimental data show that the N47G mutant shows very little tendency to aggregate while the N47A and triple mutant D48G(2Y) are both amyloidogenic, with the latter being clearly more aggregation prone. We identified a strikingly similar native-like folding intermediate across the three mutants, in which strand β1 is totally unstructured and more than half of the major hydrophobic core residues are highly solvent exposed. Results from extensive docking simulations show that the ability of the intermediates to dimerize is largely driven by strand β1 and is consistent with the in vitro aggregation behavior reported for the corresponding mutants. They further suggest that residues 44 and 53, which are key players in the nucleation–condensation mechanism of folding, are also important triggers of the aggregation process.

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Why do protein folding rates correlate with metrics of native topology?

Patricia F. N. Faísca, Rui D.M. Travasso, Andrea Parisi & Antonio Rey
Journal PaperPLoS One (2012) 7, e35599


For almost 15 years, the experimental correlation between protein folding rates and the contact order parameter has been under scrutiny. Here, we use a simple simulation model combined with a native-centric interaction potential to investigate the physical roots of this empirical observation. We simulate a large set of circular permutants, thus eliminating dependencies of the folding rate on other protein properties (e.g. stability). We show that the rate-contact order correlation is a consequence of the fact that, in high contact order structures, the contact order of the transition state ensemble closely mirrors the contact order of the native state. This happens because, in these structures, the native topology is represented in the transition state through the formation of a network of tertiary interactions that are distinctively long-ranged.

Non-native interactions play an effective role in protein folding dynamics

Patricia F. N. Faísca, Ana Nunes, Rui D.M. Travasso & E.I. Shakhnovich
Journal PaperProtein Sci. (2010) 19, 2196-2209


Systematic Monte Carlo simulations of simple lattice models show that the final stage of protein folding is an ordered process where native contacts get locked (i.e., the residues come into contact and remain in contact for the duration of the folding process) in a well‐defined order. The detailed study of the folding dynamics of protein‐like sequences designed as to exhibit different contact energy distributions, as well as different degrees of sequence optimization (i.e., participation of non‐native interactions in the folding process), reveals significant differences in the corresponding locking scenarios—the collection of native contacts and their average locking times, which are largely ascribable to the dynamics of non-native contacts. Furthermore, strong evidence for a positive role played by non-native contacts at an early folding stage was also found. Interestingly, for topologically simple target structures, a positive interplay between native and non‐native contacts is observed also toward the end of the folding process, suggesting that non‐native contacts may indeed affect the overall folding process. For target models exhibiting clear two-state kinetics, the relation between the nucleation mechanism of folding and the locking scenario is investigated. Our results suggest that the stabilization of the folding transition state can be achieved through the establishment of a very small network of native contacts that are the first to lock during the folding process.

See also

Editor's Highlight

The protein folding transition state: Insights from kinetics and thermodynamics

Rui D. M. Travasso, Patricia F. N. Faísca & Antonio Rey
Journal PaperJ. Chem. Physics. (2010) 133, 125102 & Virtual Journal of Biological Physics Research (2010) 20(7), October-1
Copyright (2010) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.


We perform extensive lattice Monte Carlo simulations of protein folding to construct and compare the equilibrium and the kinetic transition state ensembles of a model protein that folds to the native state with two-state kinetics. The kinetic definition of the transition state is based on the folding probability analysis method, and therefore on the selection of conformations with 0.4<Pfold<0.6, while for the equilibrium characterization we consider conformations for which the evaluated values of several reaction coordinates correspond to the maximum of the free energy measured as a function of those reaction coordinates. Our results reveal a high degree of structural similarity between the ensembles determined by the two methods. However, the folding probability distribution of the conformations belonging to our definition of the equilibrium transition state (0.2<Pfold<0.8) is broader than that displayed by the kinetic transition state.

Folding of knotted proteins: Insights from lattice simulations

Patricia F. N. Faísca, Rui D. M. Travasso, Tiago Charters, Ana Nunes & Marek Cieplak
Journal PaperPhysical Biology (2010) 7, 016009
Copyright (2010) IOP Publishing Ltd.


We carry out systematic Monte Carlo simulations of Gō lattice proteins to investigate and compare the folding processes of two model proteins whose native structures differ from each other due to the presence of a trefoil knot located near the terminus of one of the protein chains. We show that the folding time of the knotted fold is larger than that of the unknotted protein and that this difference in folding time is particularly striking in the temperature region below the optimal folding temperature. Both proteins display similar folding transition temperatures, which is indicative of similar thermal stabilities. By using the folding probability reaction coordinate as an estimator of folding progression we have found out that the formation of the knot is mainly a late folding event in our shallow knot system.

The nucleation mechanism of protein folding: a survey of computer simulation studies

The nucleation mechanism of protein folding: a survey of computer simulation studies
ReviewJ. Phys. Cond. Matt. (2009) 21, 373102
Copyright (2009) IOP Publishing Ltd.


The nucleation mechanism of protein folding, originally proposed by Baldwin in the early 1970s, was firstly observed by Shakhnovich and co-workers two decades later in the context of Monte Carlo simulations of a simple lattice model. At about the same time the extensive use of φ-value analysis provided the first experimental evidence that the folding of Chymotrypsin-inhibitor 2, a small single-domain protein, which folds with two-state kinetics, is also driven by a nucleation mechanism. Since then, the nucleation mechanism is generally considered the most common form of folding mechanism amongst two-state proteins. However, recent experimental data has put forward the idea that this may not necessarily be so, since the accuracy of the experimentally determined φ values, which are used to identify the critical (i.e. nucleating) residues, is typically poor. Here, we provide a survey of in silico results on the nucleation mechanism, ranging from simple lattice Monte Carlo to more sophisticated off-lattice molecular dynamics simulations, and discuss them in light of experimental data.

On the relation between conformational plasticity and native geometry

P. F. N. Faísca & C. M. Gomes
Journal PaperBiophysical Chemistry (2008) 138, 99-106
Copyright (2008) Bentham Science Publishers. All rights reserved.


In protein folding the term plasticity refers to the number of alternative folding pathways encountered in response to free energy perturbations such as those induced by mutation. Here we explore the relation between folding plasticity and a gross, generic feature of the native geometry, namely, the relative number of local and non-local native contacts. The results from our study, which is based on Monte Carlo simulations of simple lattice proteins, show that folding to a structure that is rich in local contacts is considerably more plastic than folding to a native geometry characterized by having a very large number of long-range contacts (i.e., contacts between amino acids that are separated by more than 12 units of backbone distance). The smaller folding plasticity of native geometries is probably a direct consequence of their higher folding cooperativity that renders the folding reaction more robust against single- and multiple-point mutations.

Identifying critical residues in protein folding: Insights from phi-value and Pfold analysis

P.F.N. Faísca, R.D.M. Travasso, R.C. Ball & E.I. Shakhnovich
Journal PaperJ. Chem. Physics (2008) 129, 095108 & Virtual Journal of Biological Physics Research. (2008) 16(6), September-15
Copyright (2008) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.


We apply a simulational proxy of the phi-value analysis and perform extensive mutagenesis experiments to identify the nucleating residues in the folding "reactions" of two small lattice Go polymers with different native geometries. Our findings show that for the more complex native fold (i.e., the one that is rich in nonlocal, long-range bonds), mutation of the residues that form the folding nucleus leads to a considerably larger increase in the folding time than the corresponding mutations in the geometry that is predominantly local. These results are compared to data obtained from an accurate analysis based on the reaction coordinate folding probability Pfold and on structural clustering methods. Our study reveals a complex picture of the transition state ensemble. For both protein models, the transition state ensemble is rather heterogeneous and splits up into structurally different populations. For the more complex geometry the identified subpopulations are actually structurally disjoint. For the less complex native geometry we found a broad transition state with microscopic heterogeneity. These findings suggest that the existence of multiple transition state structures may be linked to the geometric complexity of the native fold. For both geometries, the identification of the folding nucleus via the Pfold analysis agrees with the identification of the folding nucleus carried out with the phi-value analysis. For the most complex geometry, however, the applied methodologies give more consistent results than for the more local geometry. The study of the transition state structure reveals that the nucleus residues are not necessarily fully native in the transition state. Indeed, it is only for the more complex geometry that two of the five critical residues show a considerably high probability of having all its native bonds formed in the transition state. Therefore, one concludes that, in general, the phi-value correlates with the acceleration/deceleration of folding induced by mutation, rather than with the degree of nativeness of the transition state, and that the "traditional" interpretation of phi-values may provide a more realistic picture of the structure of the transition state only for more complex native geometries.

Pathways to folding, nucleation events and native geometry

Rui D.M. Travasso, Margarida M. Telo da Gama & Patrícia F.N. Faísca
Journal PaperJ. Chem. Physics (2007) 127, 145106 & Virtual Journal of Biological Physics Research. (2007) 14(8), October-15
Copyright (2007) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.


We perform extensive Monte Carlo simulations of a lattice model and the Gō potential [N. Gō and H. Taketomi, Proc. Natl. Acad. Sci. U.S.A. 75, 559563 (1978)] to investigate the existence of folding pathways at the level of contact cluster formation for two native structures with markedly different geometries. Our analysis of folding pathways revealed a common underlying folding mechanism, based on nucleation phenomena, for both protein models. However, folding to the more complex geometry (i.e., that with more nonlocal contacts) is driven by a folding nucleus whose geometric traits more closely resemble those of the native fold. For this geometry folding is clearly a more cooperative process.

Conformational states and protein stability in a proteomic perspective

Vesna Prosinecki, Patrícia F.N. Faísca & Cláudio M. Gomes
ReviewCurrent Proteomics (2007) 4, 44-52
Copyright (2008) Elsevier B.V. All rights reserved.


Protein structure and stability rely on the interplay of a large number of weak molecular interactions working in concert to assure a stable and unique native fold. Throughout evolution, different strategies have been devised to modulate protein conformational stability and enhance function and survival of proteins even under adverse conditions. The increasing number of characterized genomes and proteomes, especially those from thermophiles, provides a unique resource to study protein conformations at a wider scale. An integrated proteome-level perspective of protein conformational states in different cellular contexts is likely to contribute to a better understanding of functioning and control of biological systems. This review will address recent proteomic approaches, which allow screening and profiling proteins according to particular conformational features. We will discuss emerging methodologies that allow screening proteomes for unstructured or conformationally altered proteins, and novel approaches that profile and identify proteins within complete proteomes on the basis of their differential resistances to temperature, chemicals, or proteolysis. In particular, the profiling of proteins from thermophiles according to their thermostability will be highlighted as these studies may contribute to elicit general strategies accounting for protein stability and thermostable cellular processes.

Nucleation phenomena in protein folding: The modulating role of protein sequence

Rui D.M. Travasso, Patrícia F.N. Faísca & Margarida M. Telo da Gama
Journal PaperJ. Phys.: Cond. Matt. (2007) 19, 285212
Copyright (2007) IOP Publishing Ltd


For the vast majority of naturally occurring, small, single-domain proteins, folding is often described as a two-state process that lacks detectable intermediates. This observation has often been rationalized on the basis of a nucleation mechanism for protein folding whose basic premise is the idea that, after completion of a specific set of contacts forming the so-called folding nucleus, the native state is achieved promptly. Here we propose a methodology to identify folding nuclei in small lattice polymers and apply it to the study of protein molecules with a chain length of N = 48. To investigate the extent to which protein topology is a robust determinant of the nucleation mechanism, we compare the nucleation scenario of a native-centric model with that of a sequence-specific model sharing the same native fold. To evaluate the impact of the sequence's finer details in the nucleation mechanism, we consider the folding of two non-homologous sequences. We conclude that, in a sequence-specific model, the folding nucleus is, to some extent, formed by the most stable contacts in the protein and that the less stable linkages in the folding nucleus are solely determined by the fold's topology. We have also found that, independently of the protein sequence, the folding nucleus performs the same 'topological' function. This unifying feature of the nucleation mechanism results from the residues forming the folding nucleus being distributed along the protein chain in a similar and well-defined manner that is determined by the fold's topological features.

Shaping protein folding dynamics with native state's geometry

P.F.N. Faísca
Book ChapterSoft Condensed Matter: New Research (2007) K.L. Dillon (Ed.), Nova Science Publishers

Cooperativity and the origins of rapid, single-exponential kinetics in protein folding

P.F.N. Faísca & K.W. Plaxco
Journal PaperProtein Sci. (2006) 15, 1608-1618
Copyright (2006) The Protein Society.


The folding of naturally occurring, single-domain proteins is usually well described as a simple, single-exponential process lacking significant trapped states. Here we further explore the hypothesis that the smooth energy landscape this implies, and the rapid kinetics it engenders, arises due to the extraordinary thermodynamic cooperativity of protein folding. Studying Miyazawa-Jernigan lattice polymers, we find that, even under conditions where the folding energy landscape is relatively optimized (designed sequences folding at their temperature of maximum folding rate), the folding of protein-like heteropolymers is accelerated when their thermodynamic cooperativity is enhanced by enhancing the nonadditivity of their energy potentials. At lower temperatures, where kinetic traps presumably play a more significant role in defining folding rates, we observe still greater cooperativity-induced acceleration. Consistent with these observations, we find that the folding kinetics of our computational models more closely approximates single‐exponential behavior as their cooperativity approaches optimal levels. These observations suggest that the rapid folding of naturally occurring proteins is, in part, a consequence of their remarkably cooperative folding.

Folding of small proteins: A matter of geometry?

P.F.N. Faísca & M.M. Telo da Gama
ReviewMolec. Phys. (2005) 103, 2903-2910


We review some of our recent results obtained within the scope of simple lattice models and Monte Carlo simulations that illustrate the role of native geometry in the folding kinetics of two state folders.

The Go model revisited: Native structure and the geometric coupling between local and long-range contacts

P.F.N. Faísca, M.M. Telo da Gama & A. Nunes
Journal PaperProteins: Structure, Function and Bioinformatics. (2005) 60, 712-722
This is a preprint of an article accepted for publication in Proteins: Structure, Function and Bioinformatics. Copyright © (1999-2005) John Wiley & Sons. All rights reserved.


Monte Carlo simulations show that long-range interactions play a major role in determining the folding rates of 48-mer three-dimensional lattice polymers modeled by the Gō potential. For three target structures with different native geometries we found a sharp increase in the folding time when the relative contribution of the long-range interactions to the native state's energy is decreased from ~50% towards zero. However, the dispersion of the simulated folding times is strongly dependent on native geometry and Gō polymers folding to one of the target structures exhibits folding times spanning three orders of magnitude. We have also found that, depending on the target geometry, a strong geometric coupling may exist between local and long-range contacts, which means that, when this coupling exists, the formation of long-range contacts is forced by the previous formation of local contacts. The absence of a strong geometric coupling results in a kinetics that is more sensitive to the interaction energy parameters; in this case, the formation of local contacts is not capable of promoting the establishment of long‐range ones when the latter are strongly penalized energetically and this results in longer folding times.

Native geometry and the dynamics of protein folding

P.F.N. Faisca & M.M. Telo da Gama
Journal PaperBiophysical Chemistry (2005) 115, 169-175
Copyright (2005) Elsevier B.V. All rights reserved.


In this paper, we investigate the role of native geometry on the kinetics of protein folding based on simple lattice models and Monte Carlo simulations. Results obtained within the scope of the Miyazawa-Jernigan indicate the existence of two dynamical folding regimes depending on the protein chain length. For chains larger than 80 amino acids, the folding performance is sensitive to the native state's conformation. Smaller chains, with less than 80 amino acids, fold via two-state kinetics and exhibit a significant correlation between the contact order parameter and the logarithmic folding times. In particular, chains with N=48 amino acids were found to belong to two broad classes of folding, characterized by different cooperativity, depending on the contact order parameter. Preliminary results based on the Gō model show that the effect of long-range contact interaction strength in the folding kinetics is largely dependent on the native state's geometry.

Folding and form: Insights from lattice simulations

P.F.N. Faísca, M.M. Telo da Gama & R.C. Ball
Journal PaperPhys. Rev. E (2004) 69, 051917 & Virtual Journal of Biological Physics Research (2004) 7(11), June-1
Copyright (2004) The American Physical Society.


Monte Carlo simulations of a Miyazawa-Jernigan lattice-polymer model indicate that, depending on the native structure’s geometry, the model exhibits two broad classes of folding mechanisms for two-state folders. Folding to native structures of low contact order is driven by backbone distance and is characterized by a progressive accumulation of structure towards the native fold. By contrast, folding to high contact order targets is dominated by intermediate stage contacts not present in the native fold, yielding a more cooperative folding process.

Protein folding kinetics: Insights from lattice simulations

P.F.N. Faísca, M.M. Telo da Gama & R.C. Ball
Journal PaperProceedings of the International School of Physics Enrico Fermi, Course CLV, 'The Physics of Complex Systems (New advances and perspectives)'. (2004) 155, 515-520, F. Mallamace (Ed.) & H.E. Stanley(Ed.), IOS press


The identification of intermediate states for folding and aggregation is important from a fundamental standpoint and for the design of novel therapeutic strategies targeted at conformational disorders. Protein human β2-microglobulin (HB2m) is classically associated with dialysis-related amyloidosis, but the single point mutant D76N was recently identified as the causative agent of a hereditary systemic amyloidosis affecting visceral organs. Here, we use D76N as a model system to explore the early stage of the aggregation mechanism of HB2m by means of an integrative approach framed on molecular simulations. Discrete molecular dynamics simulations of a structured-based model predict the existence of two intermediate states populating the folding landscape. The intermediate I1 features an unstructured C-terminus, while I2, which is exclusively populated by the mutant, exhibits two unstructured termini. Docking simulations indicate that I2 is the key species for aggregation at acidic and physiological pH contributing to rationalize the higher amyloidogenic potential of D76N relative to the wild-type protein and the ΔN6 variant. The analysis carried out here recapitulates the importance of the DE-loop in HB2m self-association at a neutral pH and predicts a leading role of the C-terminus and the adjacent G-strand in the dimerization process under acidic conditions. The identification of aggregation hot-spots is in line with experimental results that support the importance of Phe56, Asp59, Trp60, Phe62, Tyr63, and Tyr66 in HB2m amyloidogenesis. We further predict the involvement of new residues such as Lys94 and Trp95 in the aggregation process.

Melnikov method for parabolic orbits

J. Casasayas, P. Faísca & A. Nunes
Journal PaperNonlinear Differential Equations and Applications (2003) 10, 119-131


The present work completes the study of the conditions under which Melnikov method can be used when the unperturbed system has a parabolic periodic orbit with a homoclinic loop, by considering the case of orbits whose associated Poicaré map has linear part equal to the identity. The result is that the conditions for the persistence under perturbation of the invariant manifolds also ensure the convergence of the Melnikov integral and hence the applicability of the method.

Topological complexity, contact order and protein folding rates

P.F.N. Faísca & R.C. Ball
Journal PaperJ. Chem. Physics (2002) 11, 8587-8592 & Virtual Journal of Biological Physics Research. (2002) 4(9), November-1
Copyright (2002) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.


Monte Carlo simulations of protein folding show the emergence of a strong correlation between the relative contact order parameter, CO, and the folding time, t, of two-state folding proteins for longer chains with number of amino acids N≥54, and higher contact order, CO<0.17. The correlation is particularly strong for N=80 corresponding to slow and more complex folding kinetics. These results are qualitatively compatible with experimental data where a general trend towards increasing t with CO is indeed observed in a set of proteins with chain length ranging from 41 to 154 amino acids.

Thermodynamic control and dynamical regimes in protein folding

P.F.N. Faísca & R.C. Ball
Journal PaperJ. Chem. Physics (2002) 116, 7231-7238 & Virtual Journal of Biological Physics Research. (2002) 3(8), April-15
Copyright (2002) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.


Monte Carlo simulations of a simple lattice model of protein folding show two distinct regimes depending on the chain length. The first regime well describes the folding of small protein sequences and its kinetic counterpart appears to be single exponential in nature, while the second regime is typical of sequences longer than 80 amino acids and the folding performance achievable is sensitive to target conformation. The extent to which stability, as measured by the energy of a sequence in the target, is an essential requirement and affects the folding dynamics of protein molecules in the first regime is investigated. The folding dynamics of sequences whose design stage was restricted to a certain fraction of randomly selected amino acids shows that while some degree of stability is a necessary and sufficient condition for successful folding, designing sequences that provide the lowest energy in the target seems to be a superfluous constraint. By studying the dynamics of under annealed but otherwise freely designed sequences we explore the relation between stability and kinetic accessibility. We find that there is no one-to-one correspondence between having low energy and folding quickly to the target, as only a small fraction of the most stable sequences were also found to fold relatively quickly.

Protein folding physics: in virtuo experiments

P.F.N. Faísca
ThesisPh.D. dissertation. University of Warwick (June 2002)

Interview with Mike Kosterlitz

Patrícia F.N. Faísca e Rui D.M. Travasso
InterviewEurophysics News (2019) 50, (3), 12-14


In the summer of 2018, Professor Michael Kosterlitz visited Portugal as a plenary speaker of the FÍSICA2018 conference organised by the Portuguese Physical Society (SPF) and by the University of Beira Interior. FÍSICA 2018 comprised two meetings: the 28th Iberian Meeting for Physics Teaching, and the 21st National Conference of Physics, a biannual event that brings together researchers from all areas of Physics working in Portugal.

Entrevista com Mike Kosterlitz [PT]

Patrícia F.N. Faísca e Rui D.M. Travasso
InterviewGazeta de Física (2018) 41, (Fasc. 3/4), 24-29


O Professor Michael Kosterlitz esteve recentemente em Portugal a convite da Sociedade Portuguesa de Física (SPF) para participar na conferência FÍSICA2018 que teve lugar na Universidade da Beira Interior entre 29 de agosto e 1 de setembro. A FÍSICA2018, organizada pela SPF e pela Universidade da Beira Interior, consistiu na junção de dois encontros: a 21ª Conferência Nacional de Física, e o 28º Encontro Ibérico para o Ensino da Física. Deste modo, a FÍSICA2018 foi um encontro frutífero entre investigadores, professores (desde o ensino secundário ao ensino superior) e alunos, interessados na partilha de experiências e no debate do estado da arte da investigação em Física. A palestra plenária do Professor Michael Kosterlitz intitulada “Topological defects and phase transitions – Vortices and dislocations (A random walk through physics to a Nobel Prize)” teve lugar no âmbito da 21a Conferência Nacional de Física, um evento bianual que congrega investigadores que desenvolvem a sua investigação em Portugal em todas as áreas da Física com o objetivo de apresentarem os seus resultados mais recentes à comunidade.

Entrevista com Claude Cohen-Tannoudji [PT]

P.F.N. Faísca
InterviewGazeta de Física (2007) 30, (Fasc. 2), 25-29


Claude Cohen-Tannoudji nasceu em Constantine, na Argélia Francesa. Em 1953 foi para Paris onde, em 1962, fez o doutoramento na École Normale Supérieure sob a orientação dos Professores Kastler e Brossel. Entre 1964 e 1972 foi professor na Universidade de Paris e é, desde 1973, professor no Collège de France. Fez toda a sua carreira de investigação no Laboratório Kastler-Brossel onde dirige o grupo de átomos frios.
Entre muitas distinções, recebeu o prémio Ampère da Académie des Sciences, a Thomas Young Medal and Prize do Institute of Physics, o Lilienfeld Prize da American Physical Society, o Charles Townes Award da Optical Society of America e o Quantum Electronics Prize da European Physical Society.
É membro da Académie des Sciences e “Foreign Associate” da United States National Academy of Sciences e da American Academy of Arts and Sciences.
É autor de vários livros entre os quais se destaca Mécanique Quantique, escrito em co-autoria com Bernard Diu e Franck Laloë. Em 1997, partilhou o prémio Nobel da Física com William D. Phillips e Steven Chu, pela manipulação e arrefecimento dos átomos, com a luz produzida por lasers.
Cohen-Tannoudji esteve em Lisboa, em Setembro de 2006, a convite do Centro de Física Teórica e Computacional da Universidade de Lisboa, onde proferiu uma palestra intitulada “Ultracold Atoms and molecules: Achievments and Perspectives”. Foi nessa ocasião que falei com ele.

An interview with Harold Kroto

P.F.N. Faísca & S. Estácio
InterviewEurophysics News (2007) 38 (Number 1), 28-31


In the winter of 2005 Professor Kroto visited Lisbon where he gave a public lecture “2010 a NanoSpace Odyssey” that closed a series of colloquia running in parallel with the exhibition “In Light of Einstein: 1905-2005” hosted by the Gulbenkian Foundation. This event, designed and developed under the leadership of Ana Maria Eiró and Carlos Matos Ferreira, involved the participation of a team of scientists from the University of Lisbon and from the Technical University of Lisbon. During the visit Prof Kroto was interviewed by Patricia Faísca of the Centro de Física Teórica e Computacional da Universidade de Lisboa and by Silvia Estácio of the Grupo de Física Matemática da Universidade de Lisboa. The interview that follows belowwas originally published in ‘Gazeta de Física’ which is the Bulletin of the Portuguese Physical Society.

Entrevista a Harold Kroto [PT]

P.F.N. Faísca e S. Estácio
InterviewGazeta de Física (2006) 29(Fasc. 3), 46-50


Harold Kroto, Prémio Nobel da Química em 1996, esteve recentemente em Portugal, tendo encerradoo ciclo de colóquios associado à exposição "à luz de Einstein" com a palestra "2010: a nanospace odyssey". A Gazeta aproveitou a sua estadia para o entrevistar sobre a sua carreira científica. Recorde-se que Harold Kroto, da Universidade de Sussex, em Inglaterra, integrou a equipa de investigadores que em 1985 descobriram a molécula de C60.

An interview with Anthony Leggett

P.F.N. Faísca & P. Patrício
InterviewEurophysics News (2006) 37(Number 2), 30-32


In the summer of 2005 Professor Leggett visited the University of Lisbon where he gave a seminar and public lecture. The visit was organised by the Centro de Fisica Teorica e Computacional following the ‘tradition’ of inviting a renowned physicist to close the academic year’s activities.His predecessors were Professor Eric Cornell (2003) and Professor Pierre Gilles de Gennes(2004), recipients of the Nobel Prize for Physics in 2001 and 1991, respectively.
During the visit Professor Leggett was interviewed by Patrícia Faísca of the Centro de Física Teorica e Computacional da Universidade de Lisboa and by Pedro Patrício of the Centro de Fisica Teorica e Computacional da Universidade de Lisboa e Instituto Superior de Engenharia de Lisboa.

Entrevista a Anthony Leggett [PT]

P.F.N. Faísca e P. Patrício
InterviewGazeta de Física (2005) 28(Fasc. 3), 18-22


Anthony J. Leggett é professor de Física na Universidade de Illinois (Estados Unidos da América), onde está desde 1983. É mundialmente conhecido como especialista de física teórica das baixas temperaturas e, pelo seu trabalho pioneiro sobre a superfluidez, recebeu o Prémio Nobel da Física de 2003.
Tivemos oportunidade de o entrevistar durante uma visita recente a Portugal, a convite do Centro de Física Teórica e Computacional da Universidade de Lisboa. Anthony Leggett apresentou em Lisboa duas palestras: "Testing the limits of quantum mechanics: motivation, state of play, prospects" e "Introduction to high energy low temperature physics".

Entrevista a Pierre-Gilles de Gennes

P.F.N. Faísca e P. Patrício
InterviewGazeta de Física (2004) 27(Fasc. 3), 12-19


Pierre-Gilles de Gennes nasceu em Paris. Estudou Física na École Normale de Paris e doutorou-se em 1957; trabalhou no Centre de Energie Atomique (CEA), em Saclay, com A. Aragam e J. Friedel e na Universidade da Califórnia, Berkeley, com C. Kittel. Neste período desenvolveu trabalhos sobre dispersão de neutrões e magnetismo.
Depois do serviço militar na Marinha Francesa, voltou à investigação no CNRS, em Orsay, onde formou um grupo de supercondutores; em 1971 tornou-se Professor no Collège de France.A partir de 1968, a sua investigação centrou-se na matéria mole, nomeadamente cristais líquidos.Trabalhou em problemas de física de polímeros, dinâmica de molhagem e física-química da adesão.
Entre os prémios que recebeu contam-se o Prémio Nobel da Física em 1991, o prémio Wolf (Wolf Foundation, Israel) e os prémios Holweck (das Sociedades Inglesa e Francesa de Física) e Ampère (Academia das Ciências, França).
De Gennes esteve em Lisboa, em Junho deste ano, a convite do Centro de Física Teórica e Computacional da Universidade de Lisboa, onde proferiu duas palestras intituladas "The hard life of inventors" e "How living cells find their prey: chemotactism". Foi nessa ocasião que falámos com ele.

O mistério da forma das proteínas

P.F.N. Faísca
Public awareness of scienceGazeta de Física. (2006) 29(Fasc. 3), 34-39


Chama-se folding de proteínas ao processo espontâneo a partir do qual uma cadeia linear de aminoácidos adquire uma estrutura tridimensional biologicamente activa. A compreensão deste fenómeno, considerada por muitos um dos problemas mais importantes da ciência actual, terá um grande impacto não só ao nível da saúde e do bem-estar humanos como também ao nível da ciência fundamental, na aprendizagem e aquisição de novas leis e conceitos da física dos sistemas complexos. Tendo surgido no contexto da biologia molecular, este problema é hoje claramente interdisciplinar, necessitando de ferramentas de várias áreas do conhecimento, e para o qual o contributo da física tem sido determinante. O objectivo deste artigo e mostrar como a utilização de metodologias da física, incluindo o recurso à simulação computacional de modelos simples, permitiu criar uma estrutura conceptual (a chamada “paisagem de energia”) sobre a qual uma sinergia exemplar entre a teoria e a experiência tem gerado avanços muito significativos.

O mistério da forma das proteínas

P.F.N. Faísca
Public awareness of scienceO Código secreto: À descoberta dos padrões da natureza (2017) pp. 301-326, Gradiva

Folding de proteínas: da biologia para a física na rota da complexidade

P.F.N. Faísca
Public awareness of scienceAnuário da revista Fórum Estudante (ano III), pp. 58-59 (2005)