The importance of input sequence set to consensus-derived proteins and their relationship to reconstructed ancestral proteins.

A protein sequence encodes its energy landscape-all the accessible conformations, energetics, and dynamics. The evolutionary relationship between sequence and landscape can be probed phylogenetically by compiling a multiple sequence alignment of homologous sequences and generating common ancestors via Ancestral Sequence Reconstruction or a consensus protein containing the most common amino acid at each position. Both ancestral and consensus proteins are often more stable than their extant homologs-questioning the differences between them and suggesting that both approaches serve as general methods to engineer thermostability. We used the Ribonuclease H family to compare these approaches and evaluate how the evolutionary relationship of the input sequences affects the properties of the resulting consensus protein. While the consensus protein derived from our full Ribonuclease H sequence alignment is structured and active, it neither shows properties of a well-folded protein nor has enhanced stability. In contrast, the consensus protein derived from a phylogenetically-restricted set of sequences is significantly more stable and cooperatively folded, suggesting that cooperativity may be encoded by different mechanisms in separate clades and lost when too many diverse clades are combined to generate a consensus protein. To explore this, we compared pairwise covariance scores using a Potts formalism as well as higher-order sequence correlations using singular value decomposition (SVD). We find the SVD coordinates of a stable consensus sequence are close to coordinates of the analogous ancestor sequence and its descendants, whereas the unstable consensus sequences are outliers in SVD space.

Unraveling paralog-specific Notch signaling through thermodynamics of ternary complex formation and transcriptional activation of chimeric receptors.

Notch signaling in humans is mediated by four paralogous receptors that share conserved architectures and possess overlapping, yet non-redundant functions. The receptors share a canonical activation pathway wherein upon extracellular ligand binding, the Notch intracellular domain (NICD) is cleaved from the membrane and translocates to the nucleus where its N-terminal RBP-j-associated molecule (RAM) region and ankyrin repeat (ANK) domain bind transcription factor CSL and recruit co-activator Mastermind-like-1 (MAML1) to activate transcription. However, different paralogs can lead to distinct outcomes. To better understand paralog-specific differences in Notch signaling, we performed a thermodynamic analysis of the Notch transcriptional activation complexes for all four Notch paralogs using isothermal titration calorimetry. Using chimeric constructs, we find that the RAM region is the primary determinant of stability of binary RAMANK:CSL complexes, and that the ANK regions are largely the determinants of MAML1 binding to pre-formed RAMANK:CSL complexes. Free energies of these binding reactions (ΔGRA and ΔGMAML) vary among the four Notch paralogs, although variations for Notch2, 3, and 4 offset in the free energy of the ternary complex (ΔGTC, where ΔGTC = ΔGRA + ΔGMAML). To probe how these affinity differences affect Notch signaling, we performed transcriptional activation assays with the paralogous and chimeric NICDs, and analyzed the results with an independent multiplicative model that quantifies contributions of the paralogous RAM, ANK, and C-terminal regions (CTR) to activation. This analysis shows that transcription activation correlates with ΔGTC, but that activation is further modified by CTR identity in a paralog-specific way.

The importance of input sequence set to consensus-derived proteins and their relationship to reconstructed ancestral proteins.

A protein sequence encodes its energy landscape - all the accessible conformations, energetics, and dynamics. The evolutionary relationship between sequence and landscape can be probed phylogenetically by compiling a multiple sequence alignment of homologous sequences and generating common ancestors via Ancestral Sequence Reconstruction or a consensus protein containing the most common amino acid at each position. Both ancestral and consensus proteins are often more stable than their extant homologs - questioning the differences and suggesting that both approaches serve as general methods to engineer thermostability. We used the Ribonuclease H family to compare these approaches and evaluate how the evolutionary relationship of the input sequences affects the properties of the resulting consensus protein. While the overall consensus protein is structured and active, it neither shows properties of a well-folded protein nor has enhanced stability. In contrast, the consensus protein derived from a phylogenetically-restricted region is significantly more stable and cooperatively folded, suggesting that cooperativity may be encoded by different mechanisms in separate clades and lost when too many diverse clades are combined to generate a consensus protein. To explore this, we compared pairwise covariance scores using a Potts formalism as well as higher-order couplings using singular value decomposition (SVD). We find the SVD coordinates of a stable consensus sequence are close to coordinates of the analogous ancestor sequence and its descendants, whereas the unstable consensus sequences are outliers in SVD space.

Stability Islands and the Folding Cooperativity of a Seven-Repeat Array from Topoisomerase V.

Cooperativity is a central feature of protein folding, but the thermodynamic and structural origins of cooperativity remain poorly understood. To quantify cooperativity, we measured guanidine-induced unfolding transitions of single helix-hairpin-helix (HhH)2 repeats and tandem pairs from a seven-repeat segment of Methanopyrus kandleri Topoisomerase V (Topo V) to determine intrinsic repeat stability and interfacial free energies between repeats. Most single-repeat constructs are folded and stable; moreover, several pairs have unfolding midpoints that exceed midpoints of the single repeats they comprise, demonstrating favorable coupling between repeats. Analyzing unfolding transitions with a modified Ising model, we find a broad range of intrinsic and interfacial free energies. Surprisingly, the G repeat, which lacks density in the crystal structure of Topo V without DNA, is the most stable repeat in the array. Using nuclear magnetic resonance spectroscopy, we demonstrate that the isolated G repeat adopts a canonical (HhH)2 fold and forms an ordered interface with the F-repeat but not with the H repeat. Using parameters from our paired Ising fit, we built a partition function for the seven-repeat array. The multistate unfolding transition predicted from this partition function is in excellent agreement with the experimental unfolding transition, providing strong justification for the nearest-neighbor model. The seven-repeat partition function predicts a native state in which three independent segments ("stability islands") of interacting repeats are separated by two unstable interfaces. We confirm this segmented architecture by measuring the unfolding transition of an equimolar mixture of these three separate polypeptides. This segmented structural organization may facilitate wrapping around DNA.

Structural features of the Notch ankyrin domain-Deltex WWE2 domain heterodimer determined by NMR spectroscopy and functional implications.

The Notch signaling pathway, an important cell fate determination pathway, is modulated by the ubiquitin ligase Deltex. Here, we investigate the structural basis for Deltex-Notch interaction. We used nuclear magnetic resonance (NMR) spectroscopy to assign the backbone of the Drosophila Deltex WWE2 domain and mapped the binding site of the Notch ankyrin (ANK) domain to the N-terminal WWEA motif. Using cultured Drosophila S2R+ cells, we find that point substitutions within the ANK-binding surface of Deltex disrupt Deltex-mediated enhancement of Notch transcriptional activation and disrupt ANK binding in cells and in vitro. Likewise, ANK substitutions that disrupt Notch-Deltex heterodimer formation in vitro block disrupt Deltex-mediated stimulation of Notch transcription activation and diminish interaction with full-length Deltex in cells. Surprisingly, the Deltex-Notch intracellular domain (NICD) interaction is not disrupted by deletion of the Deltex WWE2 domain, suggesting a secondary Notch-Deltex interaction. These results show the importance of the WWEA:ANK interaction in enhancing Notch signaling.

Singular value decomposition of protein sequences as a method to visualize sequence and residue space.

Singular value decomposition (SVD) of multiple sequence alignments (MSAs) is an important and rigorous method to identify subgroups of sequences within the MSA, and to extract consensus and covariance sequence features that define the alignment and distinguish the subgroups. This information can be correlated to structure, function, stability, and taxonomy. However, the mathematics of SVD is unfamiliar to many in the field of protein science. Here, we attempt to present an intuitive yet comprehensive description of SVD analysis of MSAs. We begin by describing the underlying mathematics of SVD in a way that is both rigorous and accessible. Next, we use SVD to analyze sequences generated with a simplified model in which the extent of sequence conservation and covariance between different positions is controlled, to show how conservation and covariance produce features in the decomposed coordinate system. We then use SVD to analyze alignments of two protein families, the homeodomain and the Ras superfamilies. Both families show clear evidence of sequence clustering when projected into singular value space. We use k-means clustering to group MSA sequences into specific clusters, show how the residues that distinguish these clusters can be identified, and show how these clusters can be related to taxonomy and function. We end by providing a description a set of Python scripts that can be used for SVD analysis of MSAs, displaying results, and identifying and analyzing sequence clusters. These scripts are freely available on GitHub.

Surface residues and nonadditive interactions stabilize a consensus homeodomain protein.

Despite the widely reported success of consensus design in producing highly stabilized proteins, little is known about the physical mechanisms underlying this stabilization. Here, we explore the potential sources of stabilization by performing a systematic analysis of the 29 substitutions that we previously found to collectively stabilize a consensus homeodomain compared with an extant homeodomain. By separately introducing groups of consensus substitutions that alter or preserve charge state, occur at varying degrees of residue burial, and occur at positions of varying degrees of conservation, we determine the extent to which these three features contribute to the consensus stability enhancement. Surprisingly, we find that the largest total contribution to stability comes from consensus substitutions on the protein surface and that the largest per substitution contributions come from substitutions that maintain charge state. This finding suggests that, although consensus proteins are often enriched in charged residues, consensus stabilization does not result primarily from interactions involving charged residues. Although consensus substitutions at strongly conserved positions also contribute disproportionately to stabilization, significant stabilization is also contributed from substitutions at weakly conserved positions. Furthermore, we find that identical consensus substitutions show larger stabilizing effects when introduced into the consensus background than when introduced into an extant homeodomain, indicating that synergistic, stabilizing interactions among the consensus residues contribute to consensus stability enhancement of the homeodomain. By measuring DNA binding affinity for the same set of variants, we find that, although consensus design of the homeodomain increases both affinity and folding stability, it does so using a largely nonoverlapping set of substitutions.

Analysis of Tandem Repeat Protein Folding Using Nearest-Neighbor Models.

Cooperativity is a hallmark of protein folding, but the thermodynamic origins of cooperativity are difficult to quantify. Tandem repeat proteins provide a unique experimental system to quantify cooperativity due to their internal symmetry and their tolerance of deletion, extension, and in some cases fragmentation into single repeats. Analysis of repeat proteins of different lengths with nearest-neighbor Ising models provides values for repeat folding ([Formula: see text]) and inter-repeat coupling (ΔGi-1,i). In this article, we review the architecture of repeat proteins and classify them in terms of ΔGi and ΔGi-1,i; this classification scheme groups repeat proteins according to their degree of cooperativity. We then present various statistical thermodynamic models, based on the 1D-Ising model, for analysis of different classes of repeat proteins. We use these models to analyze data for highly and moderately cooperative and noncooperative repeat proteins and relate their fitted parameters to overall structural features.

A collection of programs for one-dimensional Ising analysis of linear repeat proteins with point substitutions.

A collection of programs is presented to analyze the thermodynamics of folding of linear repeat proteins using a 1D Ising model to determine intrinsic folding and interfacial coupling free energies. Expressions for folding transitions are generated for a series of constructs with different repeat numbers and are globally fitted to transitions for these constructs. These programs are designed to analyze Ising parameters for capped homopolymeric consensus repeat constructs as well as heteropolymeric constructs that contain point substitutions, providing a rigorous framework for analysis of the effects of mutation on intrinsic and directional (i.e., N- vs. C-terminal) interfacial coupling free-energies. A bootstrap analysis is provided to estimate parameter uncertainty as well as correlations among fitted parameters. Rigorous statistical analysis is essential for interpreting fits using the complex models required for Ising analysis of repeat proteins, especially heteropolymeric repeat proteins. Programs described here are available at https://github.com/barricklab-at-jhu/Ising_programs.

The use of consensus sequence information to engineer stability and activity in proteins.

The goal of protein design is to create proteins that are stable, soluble, and active. Here we focus on one approach to protein design in which sequence information is used to create a "consensus" sequence. Such consensus sequences comprise the most common residue at each position in a multiple sequence alignment (MSA). After describing some general ideas that relate MSA and consensus sequences and presenting a statistical thermodynamic framework that relates consensus and non-consensus sequences to stability, we detail the process of designing a consensus sequence and survey reports of consensus design and characterization from the literature. Many of these consensus proteins retain native biological activities including ligand binding and enzyme activity. Remarkably, in most cases the consensus protein shows significantly higher stability than extant versions of the protein, as measured by thermal or chemical denaturation, consistent with the statistical thermodynamic model. To understand this stability increase, we compare various features of consensus sequences with the extant MSA sequences from which they were derived. Consensus sequences show enrichment in charged residues (most notably glutamate and lysine) and depletion of uncharged polar residues (glutamine, serine, and asparagine). Surprisingly, a survey of stability changes resulting from point substitutions show little correlation with residue frequencies at the corresponding positions within the MSA, suggesting that the high stability of consensus proteins may result from interactions among residue pairs or higher-order clusters. Whatever the source, the large number of reported successes demonstrates that consensus design is a viable route to generating active and in many cases highly stabilized proteins.

A Second Backbone: The Contribution of a Buried Asparagine Ladder to the Global and Local Stability of a Leucine-Rich Repeat Protein.

Parallel ß-sheet-containing repeat proteins often display a structural motif in which conserved asparagines form a continuous ladder buried within the hydrophobic core. In such "asparagine ladders", the asparagine side-chain amides form a repetitive pattern of hydrogen bonds with neighboring main-chain NH and CO groups. Although asparagine ladders have been thought to be important for stability, there is little experimental evidence to support such speculation. Here we test the contribution of a minimal asparagine ladder from the leucine-rich repeat protein pp32 to stability and investigate lattice rigidity and hydrogen bond character using solution nuclear magnetic resonance (NMR) spectroscopy. Point substitutions of the two ladder asparagines of pp32 are strongly destabilizing and decrease the cooperativity of unfolding. The chemical shifts of the ladder side-chain HZ protons are shifted significantly downfield in the NMR spectrum and have low temperature coefficients, indicative of strong hydrogen bonding. In contrast, the HE protons are shifted upfield and have temperature coefficients close to zero, suggesting an asymmetry in hydrogen bond strength along the ladder. Ladder NH2 groups have weak 1H-15N cross-peak intensities; 1H-15N nuclear Overhauser effect and 15N CPMG experiments show this to be the result of high rigidity. Hydrogen exchange measurements demonstrate that the ladder NH2 groups exchange very slowly, with rates approaching the global exchange limit. Overall, these results show that the asparagine side chains are held in a very rigid, nondynamic structure, making a significant contribution to the overall stability. In this regard, buried asparagine ladders can be considered "second backbones" within the cores of their elongated ß-sheet host proteins.

Consensus sequence design as a general strategy to create hyperstable, biologically active proteins.

Consensus sequence design offers a promising strategy for designing proteins of high stability while retaining biological activity since it draws upon an evolutionary history in which residues important for both stability and function are likely to be conserved. Although there have been several reports of successful consensus design of individual targets, it is unclear from these anecdotal studies how often this approach succeeds and how often it fails. Here, we attempt to assess generality by designing consensus sequences for a set of six protein families with a range of chain lengths, structures, and activities. We characterize the resulting consensus proteins for stability, structure, and biological activities in an unbiased way. We find that all six consensus proteins adopt cooperatively folded structures in solution. Strikingly, four of six of these consensus proteins show increased thermodynamic stability over naturally occurring homologs. Each consensus protein tested for function maintained at least partial biological activity. Although peptide binding affinity by a consensus-designed SH3 is rather low, Km values for consensus enzymes are similar to values from extant homologs. Although consensus enzymes are slower than extant homologs at low temperature, they are faster than some thermophilic enzymes at high temperature. An analysis of sequence properties shows consensus proteins to be enriched in charged residues, and rarified in uncharged polar residues. Sequence differences between consensus and extant homologs are predominantly located at weakly conserved surface residues, highlighting the importance of these residues in the success of the consensus strategy.

Functional instability allows access to DNA in longer transcription Activator-Like effector (TALE) arrays.

Transcription activator-like effectors (TALEs) bind DNA through an array of tandem 34-residue repeats. How TALE repeat domains wrap around DNA, often extending more than 1.5 helical turns, without using external energy is not well understood. Here, we examine the kinetics of DNA binding of TALE arrays with varying numbers of identical repeats. Single molecule fluorescence analysis and deterministic modeling reveal conformational heterogeneity in both the free- and DNA-bound TALE arrays. Our findings, combined with previously identified partly folded states, indicate a TALE instability that is functionally important for DNA binding. For TALEs forming less than one superhelical turn around DNA, partly folded states inhibit DNA binding. In contrast, for TALEs forming more than one turn, partly folded states facilitate DNA binding, demonstrating a mode of 'functional instability' that facilitates macromolecular assembly. Increasing repeat number slows down interconversion between the various DNA-free and DNA-bound states.

The consequences of cavity creation on the folding landscape of a repeat protein depend upon context.

The effect of introducing internal cavities on protein native structure and global stability has been well documented, but the consequences of these packing defects on folding free-energy landscapes have received less attention. We investigated the effects of cavity creation on the folding landscape of the leucine-rich repeat protein pp32 by high-pressure (HP) and urea-dependent NMR and high-pressure small-angle X-ray scattering (HPSAXS). Despite a modest global energetic perturbation, cavity creation in the N-terminal capping motif (N-cap) resulted in very strong deviation from two-state unfolding behavior. In contrast, introduction of a cavity in the most stable, C-terminal half of pp32 led to highly concerted unfolding, presumably because the decrease in stability by the mutations attenuated the N- to C-terminal stability gradient present in WT pp32. Interestingly, enlarging the central cavity of the protein led to the population under pressure of a distinct intermediate in which the N-cap and repeats 1-4 were nearly completely unfolded, while the fifth repeat and the C-terminal capping motif remained fully folded. Thus, despite modest effects on global stability, introducing internal cavities can have starkly distinct repercussions on the conformational landscape of a protein, depending on their structural and energetic context.

Extreme stability in de novo-designed repeat arrays is determined by unusually stable short-range interactions.

Designed helical repeats (DHRs) are modular helix-loop-helix-loop protein structures that are tandemly repeated to form a superhelical array. Structures combining tandem DHRs demonstrate a wide range of molecular geometries, many of which are not observed in nature. Understanding cooperativity of DHR proteins provides insight into the molecular origins of Rosetta-based protein design hyperstability and facilitates comparison of energy distributions in artificial and naturally occurring protein folds. Here, we use a nearest-neighbor Ising model to quantify the intrinsic and interfacial free energies of four different DHRs. We measure the folding free energies of constructs with varying numbers of internal and terminal capping repeats for four different DHR folds, using guanidine-HCl and glycerol as destabilizing and solubilizing cosolvents. One-dimensional Ising analysis of these series reveals that, although interrepeat coupling energies are within the range seen for naturally occurring repeat proteins, the individual repeats of DHR proteins are intrinsically stable. This favorable intrinsic stability, which has not been observed for naturally occurring repeat proteins, adds to stabilizing interfaces, resulting in extraordinarily high stability. Stable repeats also impart a downhill shape to the energy landscape for DHR folding. These intrinsic stability differences suggest that part of the success of Rosetta-based design results from capturing favorable local interactions.

High-Pressure NMR and SAXS Reveals How Capping Modulates Folding Cooperativity of the pp32 Leucine-rich Repeat Protein.

Many repeat proteins contain capping motifs, which serve to shield the hydrophobic core from solvent and maintain structural integrity. While the role of capping motifs in enhancing the stability and structural integrity of repeat proteins is well documented, their contribution to folding cooperativity is not. Here we examined the role of capping motifs in defining the folding cooperativity of the leucine-rich repeat protein, pp32, by monitoring the pressure- and urea-induced unfolding of an N-terminal capping motif (N-cap) deletion mutant, pp32-∆N-cap, and a C-terminal capping motif destabilization mutant pp32-Y131F/D146L, using residue-specific NMR and small-angle X-ray scattering. Destabilization of the C-terminal capping motif resulted in higher cooperativity for the unfolding transition compared to wild-type pp32, as these mutations render the stability of the C-terminus similar to that of the rest of the protein. In contrast, deletion of the N-cap led to strong deviation from two-state unfolding. In both urea- and pressure-induced unfolding, residues in repeats 1-3 of pp32-ΔN-cap lost their native structure first, while the C-terminal half was more stable. The residue-specific free energy changes in all regions of pp32-ΔN-cap were larger in urea compared to high pressure, indicating a less cooperative destabilization by pressure. Moreover, in contrast to complete structural disruption of pp32-ΔN-cap at high urea concentration, its pressure unfolded state remained compact. The contrasting effects of the capping motifs on folding cooperativity arise from the differential local stabilities of pp32, whereas the contrasting effects of pressure and urea on the pp32-ΔN-cap variant arise from their distinct mechanisms of action.

Control of transcriptional activity by design of charge patterning in the intrinsically disordered RAM region of the Notch receptor.

Intrinsically disordered regions (IDRs) play important roles in proteins that regulate gene expression. A prominent example is the intracellular domain of the Notch receptor (NICD), which regulates the transcription of Notch-responsive genes. The NICD sequence includes an intrinsically disordered RAM region and a conserved ankyrin (ANK) domain. The 111-residue RAM region mediates bivalent interactions of NICD with the transcription factor CSL. Although the sequence of RAM is poorly conserved, the linear patterning of oppositely charged residues shows minimal variation. The conformational properties of polyampholytic IDRs are governed as much by linear charge patterning as by overall charge content. Here, we used sequence design to assess how changing the charge patterning within RAM affects its conformational properties, the affinity of NICD to CSL, and Notch transcriptional activity. Increased segregation of oppositely charged residues leads to linear decreases in the global dimensions of RAM and decreases the affinity of a construct including a C-terminal ANK domain (RAMANK) for CSL. Increasing charge segregation from WT RAM sharply decreases transcriptional activation for all permutants. Activation also decreases for some, but not all, permutants with low charge segregation, although there is considerable variation. Our results suggest that the RAM linker is more than a passive tether, contributing local and/or long-range sequence features that modulate interactions within NICD and with downstream components of the Notch pathway. We propose that sequence features within IDRs have evolved to ensure an optimal balance of sequence-encoded conformational properties, interaction strengths, and cellular activities.

Creating a Homeodomain with High Stability and DNA Binding Affinity by Sequence Averaging.

There is considerable interest in generating proteins with both high stability and high activity for biomedical and industrial purposes. One approach that has been used successfully to increase the stability of linear repeat proteins is consensus design. It is unclear the extent over which the consensus design approach can be used to produce folded and hyperstable proteins, and importantly, whether such stabilized proteins would retain function. Here we extend the consensus strategy to design a globular protein. We show that a consensus-designed homeodomain (HD) sequence adopts a cooperatively folded homeodomain structure. The unfolding free energy of the consensus-HD is 5 kcal·mol-1 higher than that of the naturally occurring engrailed-HD from Drosophila melanogaster. Remarkably, the consensus-HD binds the engrailed-HD cognate DNA in a similar mode as the engrailed-HD with approximately 100-fold higher affinity. 15N relaxation studies show a decrease in ps-ns backbone dynamics in the free state of consensus-HD, suggesting that increased affinity is not a result of increased plasticity. In addition to demonstrating the potential for consensus design of globular proteins with increased stability, these results demonstrate that greatly stabilized proteins can bind cognate substrates with increased affinities, showing that high stability is compatible with function.

High-Resolution Mapping of a Repeat Protein Folding Free Energy Landscape.

A complete description of the pathways and mechanisms of protein folding requires a detailed structural and energetic characterization of the conformational ensemble along the entire folding reaction coordinate. Simulations can provide this level of insight for small proteins. In contrast, with the exception of hydrogen exchange, which does not monitor folding directly, experimental studies of protein folding have not yielded such structural and energetic detail. NMR can provide residue specific atomic level structural information, but its implementation in protein folding studies using chemical or temperature perturbation is problematic. Here we present a highly detailed structural and energetic map of the entire folding landscape of the leucine-rich repeat protein, pp32 (Anp32), obtained by combining pressure-dependent site-specific 1H-15N HSQC data with coarse-grained molecular dynamics simulations. The results obtained using this equilibrium approach demonstrate that the main barrier to folding of pp32 is quite broad and lies near the unfolded state, with structure apparent only in the C-terminal region. Significant deviation from two-state unfolding under pressure reveals an intermediate on the folded side of the main barrier in which the N-terminal region is disordered. A nonlinear temperature dependence of the population of this intermediate suggests a large heat capacity change associated with its formation. The combination of pressure, which favors the population of folding intermediates relative to chemical denaturants; NMR, which allows their observation; and constrained structure-based simulations yield unparalleled insight into protein folding mechanisms.

Broken TALEs: Transcription Activator-like Effectors Populate Partly Folded States.

Transcription activator-like effector proteins (TALEs) contain large numbers of repeats that bind double-stranded DNA, wrapping around DNA to form a continuous superhelix. Since unbound TALEs retain superhelical structure, it seems likely that DNA binding requires a significant structural distortion or partial unfolding. In this study, we use nearest-neighbor "Ising" analysis of consensus TALE (cTALE) repeat unfolding to quantify intrinsic folding free energies, coupling energies between repeats, and the free energy distribution of partly unfolded states, and to determine how those energies depend on the sequence that determines DNA-specificity (called the "RVD"). We find a moderate level of cooperativity for both the HD and NS RVD sequences (stabilizing interfaces combined with unstable repeats), as has been seen in other linear repeat proteins. Surprisingly, RVD sequence identity influences both the overall stability and the balance of intrinsic repeat stability and interfacial coupling energy. Using parameters from the Ising analysis, we have analyzed the distribution of partly folded states as a function of cTALE length and RVD sequence. We find partly unfolded states where one or more repeats are unfolded to be energetically accessible. Mixing repeats with different RVD sequences increases the population of partially folded states. Local folding free energies plateau for central repeats, suggesting that TALEs access partially folded states where a single internal repeat is unfolded while adjacent repeats remain folded. This breakage should allow TALEs to access superhelically-broken states, and may facilitate DNA binding.