Principles underlying energetic coupling along an allosteric communication trajectory of a voltage-activated K+ channel

The simplicity of protein sequence-function relationships

How complex are the rules by which a protein's sequence determines its function? High-order epistatic interactions among residues are thought to be pervasive, suggesting an idiosyncratic and unpredictable sequence-function relationship. But many prior studies may have overestimated epistasis, because they analyzed sequence-function relationships relative to a single reference sequence-which causes measurement noise and local idiosyncrasies to snowball into high-order epistasis-or they did not fully account for global nonlinearities. Here we present a reference-free method that jointly infers specific epistatic interactions and global nonlinearity using a bird's-eye view of sequence space. This technique yields the simplest explanation of sequence-function relationships and is more robust than existing methods to measurement noise, missing data, and model misspecification. We reanalyze 20 experimental datasets and find that context-independent amino acid effects and pairwise interactions, along with a simple nonlinearity to account for limited dynamic range, explain a median of 96% of phenotypic variance and over 92% in every case. Only a tiny fraction of genotypes are strongly affected by higher-order epistasis. Sequence-function relationships are also sparse: a miniscule fraction of amino acids and interactions account for 90% of phenotypic variance. Sequence-function causality across these datasets is therefore simple, opening the way for tractable approaches to characterize proteins' genetic architecture.

The simplicity of protein sequence-function relationships

How complicated is the genetic architecture of proteins - the set of causal effects by which sequence determines function? High-order epistatic interactions among residues are thought to be pervasive, making a protein's function difficult to predict or understand from its sequence. Most studies, however, used methods that overestimate epistasis, because they analyze genetic architecture relative to a designated reference sequence - causing measurement noise and small local idiosyncrasies to propagate into pervasive high-order interactions - or have not effectively accounted for global nonlinearity in the sequence-function relationship. Here we present a new reference-free method that jointly estimates global nonlinearity and specific epistatic interactions across a protein's entire genotype-phenotype map. This method yields a maximally efficient explanation of a protein's genetic architecture and is more robust than existing methods to measurement noise, partial sampling, and model misspecification. We reanalyze 20 combinatorial mutagenesis experiments from a diverse set of proteins and find that additive and pairwise effects, along with a simple nonlinearity to account for limited dynamic range, explain a median of 96% of total variance in measured phenotypes (and >92% in every case). Only a tiny fraction of genotypes are strongly affected by third- or higher-order epistasis. Genetic architecture is also sparse: the number of terms required to explain the vast majority of variance is smaller than the number of genotypes by many orders of magnitude. The sequence-function relationship in most proteins is therefore far simpler than previously thought, opening the way for new and tractable approaches to characterize it.

Molecular rearrangements in S6 during slow inactivation in Shaker-IR potassium channels

Voltage-gated K+ channels have distinct gates that regulate ion flux: the activation gate (A-gate) formed by the bundle crossing of the S6 transmembrane helices and the slow inactivation gate in the selectivity filter. These two gates are bidirectionally coupled. If coupling involves the rearrangement of the S6 transmembrane segment, then we predict state-dependent changes in the accessibility of S6 residues from the water-filled cavity of the channel with gating. To test this, we engineered cysteines, one at a time, at S6 positions A471, L472, and P473 in a T449A Shaker-IR background and determined the accessibility of these cysteines to cysteine-modifying reagents MTSET and MTSEA applied to the cytosolic surface of inside-out patches. We found that neither reagent modified either of the cysteines in the closed or the open state of the channels. On the contrary, A471C and P473C, but not L472C, were modified by MTSEA, but not by MTSET, if applied to inactivated channels with open A-gate (OI state). Our results, combined with earlier studies reporting reduced accessibility of residues I470C and V474C in the inactivated state, strongly suggest that the coupling between the A-gate and the slow inactivation gate is mediated by rearrangements in the S6 segment. The S6 rearrangements are consistent with a rigid rod-like rotation of S6 around its longitudinal axis upon inactivation. S6 rotation and changes in its environment are concomitant events in slow inactivation of Shaker KV channels.

High-throughput thermal denaturation of tryptophanyl-tRNA synthetase combinatorial mutants reveals high-order energetic coupling determinants of conformational stability

Landscape descriptions provide a framework for identifying functionally significant dynamic linkages in proteins but cannot supply details. Rate measurements of combinatorial mutations can implicate dynamic linkages in catalysis. A major difficulty is filtering dynamic linkages from the vastly more numerous static interactions that stabilize domain folding. The Geobacillus stearothermophilus (TrpRS) D1 switch is such a dynamic packing motif; it links domain movement to catalysis and specificity. We describe Thermofluor and far UV circular dichroism melting curves for all 16 D1 switch variants to determine their higher-order impact on unliganded TrpRS stability. A prominent transition at intermediate temperatures in TrpRS thermal denaturation is molten globule formation. Combinatorial analysis of thermal melting transcends the protein landscape in four significant respects: (i) bioinformatic methods identify dynamic linkages from coordinates of multiple conformational states. (ii) Relative mutant melting temperatures, δTM, are proportional to free energy changes. (iii) Structural analysis of thermal melting implicates unexpected coupling between the D1 switch packing and regions of high local frustration. Those segments develop molten globular characteristics at the point of greatest complementarity to the chemical transition state and are the first TrpRS structures to melt. (iv) Residue F37 stabilizes both native and molten globular states; its higher-order interactions modify the relative intrinsic impacts of mutations to other D1 switch residues from those estimated for single point mutants. The D1 switch is a central component of an escapement mechanism essential to free energy transduction. These conclusions begin to relate the escapement mechanism to differential TrpRS conformational stabilities.

The nonconducting W434F mutant adopts upon membrane depolarization an inactivated-like state that differs from wild-type Shaker-IR potassium channels

Voltage-gated K⁺ (Kv) channels mediate the flow of K⁺ across the cell membrane by regulating the conductive state of their activation gate (AG). Several Kv channels display slow C-type inactivation, a process whereby their selectivity filter (SF) becomes less or nonconductive. It has been proposed that, in the fast inactivation-removed Shaker-IR channel, the W434F mutation epitomizes the C-type inactivated state because it functionally accelerates this process. By introducing another pore mutation that prevents AG closure, P475D, we found a way to record ionic currents of the Shaker-IR-W434F-P475D mutant at hyperpolarized membrane potentials as the W434F-mutant SF recovers from its inactivated state. This W434F conductive state lost its high K⁺ over Na⁺ selectivity, and even NMDG⁺ can permeate, features not observed in a wild-type SF. This indicates that, at least during recovery from inactivation, the W434F-mutant SF transitions to a widened and noncationic specific conformation.

Leveraging intrinsic flexibility to engineer enhanced enzyme catalytic activity

Dynamic motions of enzymes occurring on a broad range of timescales play a pivotal role in all steps of the reaction pathway, including substrate binding, catalysis, and product release. However, it is unknown whether structural information related to conformational flexibility can be exploited for the directed evolution of enzymes with higher catalytic activity. Here, we show that mutagenesis of residues exclusively located at flexible regions distal to the active site of Homo sapiens kynureninase (HsKYNase) resulted in the isolation of a variant (BF-HsKYNase) in which the rate of the chemical step toward kynurenine was increased by 45-fold. Mechanistic pre–steady-state kinetic analysis of the wild type and the evolved enzyme shed light on the underlying effects of distal mutations (>10 Å from the active site) on the rate-limiting step of the catalytic cycle. Hydrogen-deuterium exchange coupled to mass spectrometry and molecular dynamics simulations revealed that the amino acid substitutions in BF-HsKYNase allosterically affect the flexibility of the pyridoxal-5′-phosphate (PLP) binding pocket, thereby impacting the rate of chemistry, presumably by altering the conformational ensemble and sampling states more favorable to the catalyzed reaction.

Novel insights into the allosteric gating mechanism of MthK channel

Allostery is a fundamental element during channel gating in response to an appropriate stimulus by which events occurring at one site are transmitted to distal sites to regulate activity. To address how binding of the first Ca²⁺ ion at one of the eight chemically identical subunits facilitates the other Ca²⁺-binding events in MthK, a Ca²⁺-gated K⁺ channel containing a conserved ligand-binding RCK domain, we analysed a large collection of MthK structures and performed the corresponding thermodynamic and electrophysiological measurements. These structural and functional studies led us to conclude that the conformations of the Ca²⁺-binding sites alternate between two quaternary states and exhibit significant differences in Ca²⁺ affinity. We further propose an allosteric model of the MthK-gating mechanism by which a cascade of structural events connect the initial Ca²⁺-binding to the final changes of the ring structure that open the ion-conduction pore. This mechanical model reveals the exquisite design that achieves the allosteric gating and could be of general relevance for the action of other ligand-gated ion channels containing the RCK domain.

A distinct mechanism of C-type inactivation in the Kv-like KcsA mutant E71V

C-type inactivation is of great physiological importance in voltage-activated K⁺ channels (Kv), but its structural basis remains unresolved. Knowledge about C-type inactivation has been largely deduced from the bacterial K⁺ channel KcsA, whose selectivity filter constricts under inactivating conditions. However, the filter is highly sensitive to its molecular environment, which is different in Kv channels than in KcsA. In particular, a glutamic acid residue at position 71 along the pore helix in KcsA is substituted by a valine conserved in most Kv channels, suggesting that this side chain is a molecular determinant of function. Here, a combination of X-ray crystallography, solid-state NMR and MD simulations of the E71V KcsA mutant is undertaken to explore inactivation in this Kv-like construct. X-ray and ssNMR data show that the filter of the Kv-like mutant does not constrict under inactivating conditions. Rather, the filter adopts a conformation that is slightly narrowed and rigidified. On the other hand, MD simulations indicate that the constricted conformation can nonetheless be stably established in the mutant channel. Together, these findings suggest that the Kv-like KcsA mutant may be associated with different modes of C-type inactivation, showing that distinct filter environments entail distinct C-type inactivation mechanisms.

Computational study of non-conductive selectivity filter conformations and C-type inactivation in a voltage-dependent potassium channel

C-type inactivation is a time-dependent process of great physiological significance that is observed in a large class of K+ channels. Experimental and computational studies of the pH-activated KcsA channel show that the functional C-type inactivated state, for this channel, is associated with a structural constriction of the selectivity filter at the level of the central glycine residue in the signature sequence, TTV(G)YGD. The structural constriction is allosterically promoted by the wide opening of the intracellular activation gate. However, whether this is a universal mechanism for C-type inactivation has not been established with certainty because similar constricted structures have not been observed for other K+ channels. Seeking to ascertain the general plausibility of the constricted filter conformation, molecular dynamics simulations of a homology model of the pore domain of the voltage-gated potassium channel Shaker were performed. Simulations performed with an open intracellular gate spontaneously resulted in a stable constricted-like filter conformation, providing a plausible nonconductive state responsible for C-type inactivation in the Shaker channel. While there are broad similarities with the constricted structure of KcsA, the hypothetical constricted-like conformation of Shaker also displays some subtle differences. Interestingly, those are recapitulated by the Shaker-like E71V KcsA mutant, suggesting that the residue at this position along the pore helix plays a pivotal role in determining the C-type inactivation behavior. Free energy landscape calculations show that the conductive-to-constricted transition in Shaker is allosterically controlled by the degree of opening of the intracellular activation gate, as observed with the KcsA channel. The behavior of the classic inactivating W434F Shaker mutant is also characterized from a 10-μs MD simulation, revealing that the selectivity filter spontaneously adopts a nonconductive conformation that is constricted at the level of the second glycine in the signature sequence, TTVGY(G)D.

The activation gate controls steady-state inactivation and recovery from inactivation in Shaker

Despite major advances in the structure determination of ion channels, the sequence of molecular rearrangements at negative membrane potentials in voltage-gated potassium channels of the Shaker family remains unknown. Four major composite gating states are documented during the gating process: closed (C), open (O), open-inactivated (OI), and closed-inactivated (CI). Although many steps in the gating cycle have been clarified experimentally, the development of steady-state inactivation at negative membrane potentials and mandatory gating transitions for recovery from inactivation have not been elucidated. In this study, we exploit the biophysical properties of Shaker-IR mutants T449A/V474C and T449A/V476C to evaluate the status of the activation and inactivation gates during steady-state inactivation and upon locking the channel open with intracellular Cd²⁺. We conclude that at negative membrane potentials, the gating scheme of Shaker channels can be refined in two aspects. First, the most likely pathway for the development of steady-state inactivation is C→O→OI⇌CI. Second, the OI→CI transition is a prerequisite for recovery from inactivation. These findings are in accordance with the widely accepted view that tight coupling is present between the activation and C-type inactivation gates in Shaker and underscore the role of steady-state inactivation and recovery from inactivation as determinants of excitability.

Allosteric conformational ensembles have unlimited capacity for integrating information

Integration of binding information by macromolecular entities is fundamental to cellular functionality. Recent work has shown that such integration cannot be explained by pairwise cooperativities, in which binding is modulated by binding at another site. Higher-order cooperativities (HOCs), in which binding is collectively modulated by multiple other binding events, appear to be necessary but an appropriate mechanism has been lacking. We show here that HOCs arise through allostery, in which effective cooperativity emerges indirectly from an ensemble of dynamically interchanging conformations. Conformational ensembles play important roles in many cellular processes but their integrative capabilities remain poorly understood. We show that sufficiently complex ensembles can implement any form of information integration achievable without energy expenditure, including all patterns of HOCs. Our results provide a rigorous biophysical foundation for analysing the integration of binding information through allostery. We discuss the implications for eukaryotic gene regulation, where complex conformational dynamics accompanies widespread information integration.

Roadmap on biology in time varying environments

Biological organisms experience constantly changing environments, from sudden changes in physiology brought about by feeding, to the regular rising and setting of the Sun, to ecological changes over evolutionary timescales. Living organisms have evolved to thrive in this changing world but the general principles by which organisms shape and are shaped by time varying environments remain elusive. Our understanding is particularly poor in the intermediate regime with no separation of timescales, where the environment changes on the same timescale as the physiological or evolutionary response. Experiments to systematically characterize the response to dynamic environments are challenging since such environments are inherently high dimensional. This roadmap deals with the unique role played by time varying environments in biological phenomena across scales, from physiology to evolution, seeking to emphasize the commonalities and the challenges faced in this emerging area of research.

Mechanism of C-type inactivation in the hERG potassium channel

The fast C-type inactivation displayed by the voltage-activated potassium channel hERG plays a critical role in the repolarization of cardiac cells, and malfunction caused by nonspecific binding of drugs or naturally occurring missense mutations affecting inactivation can lead to pathologies. Because of its impact on human health, understanding the molecular mechanism of C-type inactivation in hERG represents an advance of paramount importance. Here, long-time scale molecular dynamics simulations, free energy landscape calculations, and electrophysiological experiments are combined to address the structural and functional impacts of several disease-associated mutations. Results suggest that C-type inactivation in hERG is associated with an asymmetrical constricted-like conformation of the selectivity filter, identifying F627 side-chain rotation and the hydrogen bond between Y616 and N629 as key determinants. Comparison of hERG with other K⁺ channels suggests that C-type inactivation depends on the degree of opening of the intracellular gate via the filter-gate allosteric coupling.

The Selectivity Filter Is Involved in the U-Type Inactivation Process of Kv2.1 and Kv3.1 Channels

Voltage-gated potassium (Kv) channels display several types of inactivation processes, including N-, C-, and U-types. C-type inactivation is attributed to a nonconductive conformation of the selectivity filter (SF). It has been proposed that the activation gate and the channel's SF are allosterically coupled because the conformational changes of the former affect the structure of the latter and vice versa. The second threonine of the SF signature sequence (e.g., TTVGYG) has been proven to be essential for this allosteric coupling. To further study the role of the SF in U-type inactivation, we substituted the second threonine of the TTVGYG sequence by an alanine in the hKv2.1 and hKv3.1 channels, which are known to display U-type inactivation. Both hKv2.1-T377A and hKv3.1-T400A yielded channels that were resistant to inactivation, and as a result, they displayed noninactivating currents upon channel opening; i.e., hKv2.1-T377A and hKv3.1-T400A remained fully conductive upon prolonged moderate depolarizations, whereas in wild-type hKv2.1 and hKv3.1, the current amplitude typically reduces because of U-type inactivation. Interestingly, increasing the extracellular K⁺ concentration increased the macroscopic current amplitude of both hKv2.1-T377A and hKv3.1-T400A, which is similar to the response of the homologous T to A mutation in Shaker and hKv1.5 channels that display C-type inactivation. Our data support an important role for the second threonine of the SF signature sequence in the U-type inactivation gating of hKv2.1 and hKv3.1.

Molecular mechanism of a potassium channel gating through activation gate-selectivity filter coupling

Potassium channels are presumed to have two allosterically coupled gates, the activation gate and the selectivity filter gate, that control channel opening, closing, and inactivation. However, the molecular mechanism of how these gates regulate K+ ion flow through the channel remains poorly understood. An activation process, occurring at the selectivity filter, has been recently proposed for several potassium channels. Here, we use X-ray crystallography and extensive molecular dynamics simulations, to study ion permeation through a potassium channel MthK, for various opening levels of both gates. We find that the channel conductance is controlled at the selectivity filter, whose conformation depends on the activation gate. The crosstalk between the gates is mediated through a collective motion of channel helices, involving hydrophobic contacts between an isoleucine and a conserved threonine in the selectivity filter. We propose a gating model of selectivity filter-activated potassium channels, including pharmacologically relevant two-pore domain (K2P) and big potassium (BK) channels.

The dynamics of K+ channel gates as a biological transistor

Potassium channels are pore-forming membrane proteins that open and close in response to changes in a chemical or electrical potential, thereby regulating the flow of potassium ions across biological membranes. Two regions of the same channels are acting in tandem and enable ion flow through the channel pore. I refer to this coupled action as a "gate linker". To closely examine the role of the gate linker in the channel function, I mutated the amino acids in the cDNA of this region, and used from knowen mutaion, either alone or together with the amino acids of adjacent regions. I have emphasized the importance of the linker between these two gates - mutations in this region may cause conformational changes that play a fundamental role in mediating the coupling between the voltage sensor, activation gate and selectivity filter elements of Kv channels. I observe that free energy considerations show the significance of the coupling between the activation and inactivation gates. Moreover, a symmetry between the coupling and sensor spring strength leads to the destruction of ion conductivity. I present a thermodynamic framework for the possible study of multiple channel blocks. The arising physical perspective of the gating process gives rise to new research avenues of the coupling mode of potassium channels and may assist in explaining the centrality of the "gate linker" to the channel function.

Inactivation in the potassium channel KcsA

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C-type inactivation in potassium channels is a nearly universal regulatory mechanism.

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A major hypothesis states that C-type inactivation involves ion loss at the selectivity filter as an allosteric response to activation.

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NMR is used to probe protein conformational changes in response to pH and [K⁺], demonstrating that H⁺ and K⁺ binding are allosterically coupled in KcsA.

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The lipids are integrated parts of potassium channels in terms of structure, energetics and function.

Inactivation, the slow cessation of transmission after activation, is a general feature of potassium channels. It is essential for their function, and malfunctions in inactivation leads to numerous pathologies. The detailed mechanism for the C-type inactivation, distinct from the N-type inactivation, remains an active area of investigation. Crystallography, computational simulations, and NMR have greatly enriched our understanding of the process. Here we review the major hypotheses regarding C-type inactivation, particularly focusing on the key role played by NMR studies of the prokaryotic potassium channel KcsA, which serves as a good model for voltage gated mammalian channels.

Double-mutant cycles: new directions and applications

Double-mutant cycle (DMC) analysis is a powerful approach for detecting and quantifying the energetics of both direct and long-range interactions in proteins and other chemical systems. It can also be used to unravel higher-order interactions (e.g. three-body effects) that lead to cooperativity in protein folding and function. In this review, we describe new applications of DMC analysis based on advances in native mass spectrometry and high-throughput methods such as next generation sequencing and protein complementation assays. These developments have facilitated carrying out high-throughput DMC analysis, which can be used to characterize increasingly higher-order interactions and very large interaction networks in proteins. Such studies have provided insights into the extent of cooperativity (epistasis) in protein structures. High-throughput DMC studies have also been used to validate correlated mutation analysis and can provide restraints for protein docking.

Identifying coupled clusters of allostery participants through chemical shift perturbations

Allosteric couplings underlie many cellular signaling processes and provide an exciting avenue for development of new diagnostics and therapeutics. A general method for identifying important residues in allosteric mechanisms would be very useful, but remains elusive due to the complexity of long-range phenomena. Here, we introduce an NMR method to identify residues involved in allosteric coupling between two ligand-binding sites in a protein, which we call chemical shift detection of allostery participants (CAP). Networks of functional groups responding to each ligand are defined through correlated NMR perturbations. In this process, we also identify allostery participants, groups that respond to both binding events and likely play a role in the coupling between the binding sites. Such residues exhibit multiple functional states with distinct NMR chemical shifts, depending on binding status at both binding sites. Such a strategy was applied to the prototypical ion channel KcsA. We had previously shown that the potassium affinity at the extracellular selectivity filter is strongly dependent on proton binding at the intracellular pH sensor. Here, we analyzed proton and potassium binding networks and identified groups that depend on both proton and potassium binding (allostery participants). These groups are viewed as candidates for transmitting information between functional units. The vital role of one such identified amino acid was validated through site-specific mutagenesis, electrophysiology functional studies, and NMR-detected thermodynamic analysis of allosteric coupling. This strategy for identifying allostery participants is likely to have applications for many other systems.

The Role of Proton Transport in Gating Current in a Voltage Gated Ion Channel, as Shown by Quantum Calculations

Over two-thirds of a century ago, Hodgkin and Huxley proposed the existence of voltage gated ion channels (VGICs) to carry Na⁺ and K⁺ ions across the cell membrane to create the nerve impulse, in response to depolarization of the membrane. The channels have multiple physiological roles, and play a central role in a wide variety of diseases when they malfunction. The first channel structure was found by MacKinnon and coworkers in 1998. Subsequently, the structure of a number of VGICs was determined in the open (ion conducting) state. This type of channel consists of four voltage sensing domains (VSDs), each formed from four transmembrane (TM) segments, plus a pore domain through which ions move. Understanding the gating mechanism (how the channel opens and closes) requires structures. One TM segment (S4) has an arginine in every third position, with one such segment per domain. It is usually assumed that these arginines are all ionized, and in the resting state are held toward the intracellular side of the membrane by voltage across the membrane. They are assumed to move outward (extracellular direction) when released by depolarization of this voltage, producing a capacitive gating current and opening the channel. We suggest alternate interpretations of the evidence that led to these models. Measured gating current is the total charge displacement of all atoms in the VSD; we propose that the prime, but not sole, contributor is proton motion, not displacement of the charges on the arginines of S4. It is known that the VSD can conduct protons. Quantum calculations on the K_v1.2 potassium channel VSD show how; the key is the amphoteric nature of the arginine side chain, which allows it to transfer a proton. This appears to be the first time the arginine side chain has had its amphoteric character considered. We have calculated one such proton transfer in detail: this proton starts from a tyrosine that can ionize, transferring to the NE of the third arginine on S4; that arginine’s NH then transfers a proton to a glutamate. The backbone remains static. A mutation predicted to affect the proton transfer has been qualitatively confirmed experimentally, from the change in the gating current-voltage curve. The total charge displacement in going from a normal closed potential of −70 mV across the membrane to 0 mV (open), is calculated to be approximately consistent with measured values, although the error limits on the calculation require caution in interpretation.

Rapid constriction of the selectivity filter underlies C-type inactivation in the KcsA potassium channel

C-type inactivation in K⁺ channels is thought to be a result of constriction of the selectivity filter. By using MD simulations, Li et al. show that rapid constriction occurs within 1–2 s when the intracellular activation gate is fully open, but not when the gate is closed or partially open.

C-type inactivation is a time-dependent process observed in many K⁺ channels whereby prolonged activation by an external stimulus leads to a reduction in ionic conduction. While C-type inactivation is thought to be a result of a constriction of the selectivity filter, the local dynamics of the process remain elusive. Here, we use molecular dynamics (MD) simulations of the KcsA channel to elucidate the nature of kinetically delayed activation/inactivation gating coupling. Microsecond-scale MD simulations based on the truncated form of the KcsA channel (C-terminal domain deleted) provide a first glimpse of the onset of C-type inactivation. We observe over multiple trajectories that the selectivity filter consistently undergoes a spontaneous and rapid (within 1–2 µs) transition to a constricted conformation when the intracellular activation gate is fully open, but remains in the conductive conformation when the activation gate is closed or partially open. Multidimensional umbrella sampling potential of mean force calculations and nonequilibrium voltage-driven simulations further confirm these observations. Electrophysiological measurements show that the truncated form of the KcsA channel inactivates faster and greater than full-length KcsA, which is consistent with truncated KcsA opening to a greater degree because of the absence of the C-terminal domain restraint. Together, these results imply that the observed kinetics underlying activation/inactivation gating reflect a rapid conductive-to-constricted transition of the selectivity filter that is allosterically controlled by the slow opening of the intracellular gate.

Inverted allosteric coupling between activation and inactivation gates in K+ channels

The selectivity filter and the activation gate in potassium channels are functionally and structurally coupled. An allosteric coupling underlies C-type inactivation coupled to activation gating in this ion-channel family (i.e., opening of the activation gate triggers the collapse of the channel's selectivity filter). We have identified the second Threonine residue within the TTVGYGD signature sequence of K⁺ channels as a crucial residue for this allosteric communication. A Threonine to Alanine substitution at this position was studied in three representative members of the K⁺-channel family. Interestingly, all of the mutant channels exhibited lack of C-type inactivation gating and an inversion of their allosteric coupling (i.e., closing of the activation gate collapses the channel's selectivity filter). A state-dependent crystallographic study of KcsA-T75A proves that, on activation, the selectivity filter transitions from a nonconductive and deep C-type inactivated conformation to a conductive one. Finally, we provide a crystallographic demonstration that closed-state inactivation can be achieved by the structural collapse of the channel's selectivity filter.

Gating interaction maps reveal a noncanonical electromechanical coupling mode in the Shaker K+ channel

Membrane potential regulates the activity of voltage-dependent ion channels via specialized voltage-sensing modules but the mechanisms involved in coupling voltage-sensor movement to pore opening remain unclear due to lack of resting state structures and robust methods to identify allosteric pathways. Here, using a newly developed interaction energy analysis, we probe the interfaces of the voltage-sensing and pore modules in the drosophila Shaker K⁺ channel. Our measurements reveal unexpectedly strong equilibrium gating interactions between contacts at the S4 and S5 helices in addition to those between S6 and S4–S5 linker. Network analysis of MD trajectories shows that the voltage-sensor and pore motions are linked by two distinct pathways- canonical one through the S4–S5 linker and a hitherto unknown pathway akin to rack and pinion coupling involving S4 and S5 helices. Our findings highlight the central role of the S5 helix in electromechanical transduction in the VGIC superfamily.

Solution structure of extracellular loop of human β4 subunit of BK channel and its biological implication on ChTX sensitivity

Large-conductance Ca²⁺- and voltage-dependent K⁺ (BK) channels display diverse biological functions while their pore-forming α subunit is coded by a single Slo1 gene. The variety of BK channels is correlated with the effects of BKα coexpression with auxiliary β (β1-β4) subunits, as well as newly defined γ subunits. Charybdotoxin (ChTX) blocks BK channel through physically occluding the K⁺-conduction pore. Human brain enriched β4 subunit (hβ4) alters the conductance-voltage curve, slows activation and deactivation time courses of BK channels. Its extracellular loop (hβ4-loop) specifically impedes ChTX to bind BK channel pore. However, the structure of β4 subunit's extracellular loop and the molecular mechanism for gating kinetics, toxin sensitivity of BK channels regulated by β4 are still unclear. To address them, here, we first identified four disulfide bonds in hβ4-loop by mass spectroscopy and NMR techniques. Then we determined its three-dimensional solution structure, performed NMR titration and electrophysiological analysis, and found that residue Asn123 of β4 subunit regulated the gating and pharmacological characteristics of BK channel. Finally, by constructing structure models of BKα/β4 and thermodynamic double-mutant cycle analysis, we proposed that BKα subunit might interact with β4 subunit through the conserved residue Glu264(BKα) coupling with residue Asn123(β4).

Probing the Effects of Gating on the Ion Occupancy of the K+ Channel Selectivity Filter Using Two-Dimensional Infrared Spectroscopy

The interplay between the intracellular gate and the selectivity filter underlies the structural basis for gating in potassium ion channels. Using a combination of protein semisynthesis, two-dimensional infrared (2D IR) spectroscopy, and molecular dynamics (MD) simulations, we probe the ion occupancy at the S1 binding site in the constricted state of the selectivity filter of the KcsA channel when the intracellular gate is open and closed. The 2D IR spectra resolve two features, whose relative intensities depend on the state of the intracellular gate. By matching the experiment to calculated 2D IR spectra of structures predicted by MD simulations, we identify the two features as corresponding to states with S1 occupied or unoccupied by K⁺. We learn that S1 is >70% occupied when the intracellular gate is closed and <15% occupied when the gate is open. Comparison of MD trajectories show that opening of the intracellular gate causes a structural change in the selectivity filter, which leads to a change in the ion occupancy. This work reveals the complexity of the conformational landscape of the K⁺ channel selectivity filter and its dependence on the state of the intracellular gate.

Combining multi-mutant and modular thermodynamic cycles to measure energetic coupling networks in enzyme catalysis

We measured and cross-validated the energetics of networks in Bacillus stearothermophilus Tryptophanyl-tRNA synthetase (TrpRS) using both multi-mutant and modular thermodynamic cycles. Multi-dimensional combinatorial mutagenesis showed that four side chains from this "molecular switch" move coordinately with the active-site Mg2+ ion as the active site preorganizes to stabilize the transition state for amino acid activation. A modular thermodynamic cycle consisting of full-length TrpRS, its Urzyme, and the Urzyme plus each of the two domains deleted in the Urzyme gives similar energetics. These dynamic linkages, although unlikely to stabilize the transition-state directly, consign the active-site preorganization to domain motion, assuring coupled vectorial behavior.

High-Dimensional Mutant and Modular Thermodynamic Cycles, Molecular Switching, and Free Energy Transduction

Understanding how distinct parts of proteins produce coordinated behavior has driven and continues to drive advances in protein science and enzymology. However, despite consensus about the conceptual basis for allostery, the idiosyncratic nature of allosteric mechanisms resists general approaches. Computational methods can identify conformational transition states from structural changes, revealing common switching mechanisms that impose multistate behavior. Thermodynamic cycles use factorial perturbations to measure coupling energies between side chains in molecular switches that mediate shear during domain motion. Such cycles have now been complemented by modular cycles that measure energetic coupling between separable domains. For one model system, energetic coupling between domains has been shown to be quantitatively equivalent to that between dynamic side chains. Linkages between domain motion, switching residues, and catalysis make nucleoside triphosphate hydrolysis conditional on domain movement, confirming an essential yet neglected aspect of free energy transduction and suggesting the potential generality of these studies.

Hysteresis of KcsA potassium channel's activation- deactivation gating is caused by structural changes at the channel's selectivity filter

Mode-shift or hysteresis has been reported in ion channels. Voltage-shift for gating currents is well documented for voltage-gated cation channels (VGCC), and it is considered a voltage-sensing domain's (VSD) intrinsic property. However, uncoupling the Shaker K⁺ channel's pore domain (PD) from the VSD prevented the mode-shift of the gating currents. Consequently, it was proposed that an open-state stabilization of the PD imposes a mechanical load on the VSD, which causes its mode-shift. Furthermore, the mode-shift displayed by hyperpolarization-gated cation channels is likely caused by structural changes at the channel's PD similar to those underlying C-type inactivation. To demonstrate that the PD of VGCC undergoes hysteresis, it is imperative to study its gating process in the absence of the VSD. A back-door strategy is to use KcsA (a K⁺ channel from the bacteria Streptomyces lividans) as a surrogate because it lacks a VSD and exhibits an activation coupled to C-type inactivation. By directly measuring KcsA's activation gate opening and closing in conditions that promote or halt C-type inactivation, we have found (i) that KcsA undergoes mode-shift of gating when having K⁺ as the permeant ion; (ii) that Cs⁺ or Rb⁺, known to halt C-inactivation, prevented mode-shift of gating; and (iii) that, in the total absence of C-type inactivation, KcsA's mode-shift was prevented. Finally, our results demonstrate that an allosteric communication causes KcsA's activation gate to "remember" the conformation of the selectivity filter, and hence KcsA requires a different amount of energy for opening than for closing.

Computational approaches to investigating allostery

Allosteric regulation plays a key role in many biological processes, such as signal transduction, transcriptional regulation, and many more. It is rooted in fundamental thermodynamic and dynamic properties of macromolecular systems that are still poorly understood and are moreover modulated by the cellular context. Here we review the computational approaches used in the investigation of allosteric processes in protein systems. We outline how the models of allostery have evolved from their initial formulation in the sixties to the current views, which more fully account for the roles of the thermodynamic and dynamic properties of the system. We then describe the major classes of computational approaches employed to elucidate the mechanisms of allostery, the insights they have provided, as well as their limitations. We complement this analysis by highlighting the role of computational approaches in promising practical applications, such as the engineering of regulatory modules and identifying allosteric binding sites.

Equilibrium fluctuation relations for voltage coupling in membrane proteins

A general theoretical framework is developed to account for the effects of an external potential on the energetics of membrane proteins. The framework is based on the free energy relation between two (forward/backward) probability densities, which was recently generalized to non-equilibrium processes, culminating in the work-fluctuation theorem. Starting from the probability densities of the conformational states along the "voltage coupling" reaction coordinate, we investigate several interconnected free energy relations between these two conformational states, considering voltage activation of ion channels. The free energy difference between the two conformational states at zero (depolarization) membrane potential (i.e., known as the chemical component of free energy change in ion channels) is shown to be equivalent to the free energy difference between the two "equilibrium" (resting and activated) conformational states along the one-dimensional voltage couplin reaction coordinate. Furthermore, the requirement that the application of linear response approximation to the free energy functionals of voltage coupling should satisfy the general free energy relations, yields a novel closed-form expression for the gating charge in terms of other basic properties of ion channels. This connection is familiar in statistical mechanics, known as the equilibrium fluctuation-response relation. The theory is illustrated by considering the coupling of a unit charge to the external voltage in the two sites near the surface of membrane, representing the activated and resting states. This is done using a coarse-graining (CG) model of membrane proteins, which includes the membrane, the electrolytes and the electrodes. The CG model yields Marcus-type voltage dependent free energy parabolas for the response of the electrostatic environment (electrolytes etc.) to the transition from the initial to the final configuratinal states, leading to equilibrium free energy difference and free energy barrier that follow the trend of the equilibrium fluctuation relation and the Marcus theory of electron transfer. These energetics also allow for a direct estimation of the voltage dependence of channel activation (Q-V curve), offering a quantitative rationale for a correlation between the voltage dependence parabolas and the Q-V curve, upon site-directed mutagenesis or drug binding. Taken together, by introducing the voltage coupling as the energy gap reaction coordinate, our framework brings new perspectives to the thermodynamic models of voltage activation in voltage-sensitive membrane proteins, offering an a framework for a better understating of the structure-function correlations of voltage gating in ion channels as well as electrogenic phenomena in ion pumps and transporters. Significantly, this formulation also provides a powerful bridge between the CG model of voltage coupling and the conventional macroscopic treatments.

Insights into the structural nature of the transition state in the Kir channel gating pathway

In a previous study we identified an extensive gating network within the inwardly rectifying Kir1.1 (ROMK) channel by combining systematic scanning mutagenesis and functional analysis with structural models of the channel in the closed, pre-open and open states. This extensive network appeared to stabilize the open and pre-open states, but the network fragmented upon channel closure. In this study we have analyzed the gating kinetics of different mutations within key parts of this gating network. These results suggest that the structure of the transition state (TS), which connects the pre-open and closed states of the channel, more closely resembles the structure of the pre-open state. Furthermore, the G-loop, which occurs at the center of this extensive gating network, appears to become unstructured in the TS because mutations within this region have a ‘catalytic’ effect upon the channel gating kinetics.

A self-consistent approach for determining pairwise interactions that underlie channel activation

Net free-energy measurements can be combined with mutant cycle analysis to determine interaction energies between specific amino acid pairs during channel activation.

Signaling proteins such as ion channels largely exist in two functional forms, corresponding to the active and resting states, connected by multiple intermediates. Multiparametric kinetic models based on sophisticated electrophysiological experiments have been devised to identify molecular interactions of these conformational transitions. However, this approach is arduous and is not suitable for large-scale perturbation analysis of interaction pathways. Recently, we described a model-free method to obtain the net free energy of activation in voltage- and ligand-activated ion channels. Here we extend this approach to estimate pairwise interaction energies of side chains that contribute to gating transitions. Our approach, which we call generalized interaction-energy analysis (GIA), combines median voltage estimates obtained from charge-voltage curves with mutant cycle analysis to ascertain the strengths of pairwise interactions. We show that, for a system with an arbitrary gating scheme, the nonadditive contributions of amino acid pairs to the net free energy of activation can be computed in a self-consistent manner. Numerical analyses of sequential and allosteric models of channel activation also show that this approach can measure energetic nonadditivities even when perturbations affect multiple transitions. To demonstrate the experimental application of this method, we reevaluated the interaction energies of six previously described long-range interactors in the Shaker potassium channel. Our approach offers the ability to generate detailed interaction energy maps in voltage- and ligand-activated ion channels and can be extended to any force-driven system as long as associated “displacement” can be measured.

State-dependent network connectivity determines gating in a K+ channel

X-ray crystallography has provided tremendous insight into the different structural states of membrane proteins and, in particular, of ion channels. However, the molecular forces that determine the thermodynamic stability of a particular state are poorly understood. Here we analyze the different X-ray structures of an inwardly rectifying potassium channel (Kir1.1) in relation to functional data we obtained for over 190 mutants in Kir1.1. This mutagenic perturbation analysis uncovered an extensive, state-dependent network of physically interacting residues that stabilizes the pre-open and open states of the channel, but fragments upon channel closure. We demonstrate that this gating network is an important structural determinant of the thermodynamic stability of these different gating states and determines the impact of individual mutations on channel function. These results have important implications for our understanding of not only K⁺ channel gating but also the more general nature of conformational transitions that occur in other allosteric proteins.

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Functional validation of different crystallographic states of Kir channels

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Presence of a state-dependent gating network revealed by large-scale mutagenesis

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Biased effect of mutations on Kir channel gating due to open-state destabilization

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Long-range allosteric coupling mediated by a physically connected residue network

Differential modulations of KCNQ1 by auxiliary proteins KCNE1 and KCNE2

KCNQ1 channels play vital roles in cardiovascular, gastric and other systems. The conductance and dynamics of KCNQ1 could be modulated by different single transmembrane helical auxiliary proteins (such as KCNE1, KCNE2 and others). In this study, detail KCNQ1 function modulations by different regions of KCNE1 or KCNE2 were examined using combinational methods of electrophysiology, immunofluorescence, solution NMR and related backbone flexibility analysis. In the presence of KCNE2 N-terminus, decreased surface expression and consequent low activities of KCNQ1 were observed. The transmembrane domains (TMDs) of KCNE1 and KCNE2 were illustrated to associate with the KCNQ1 channel in different modes: Ile64 in KCNE2-TMD interacting with Phe340 and Phe275 in KCNQ1, while two pairs of interacting residues (Phe340-Thr58 and Ala244-Tyr65) in the KCNQ1/KCNE1 complex. The KCNE1 C-terminus could modulate gating property of KCNQ1, whereas KCNE2 C-terminus had only minimal influences on KCNQ1. All of the results demonstrated different KCNQ1 function modulations by different regions of the two auxiliary proteins.

Structural basis for calcium and magnesium regulation of a large conductance calcium-activated potassium channel with β1 subunits

Large conductance Ca(2+)- and voltage-activated potassium (BK) channels, composed of pore-forming α subunits and auxiliary β subunits, play important roles in diverse physiological activities. The β1 is predominately expressed in smooth muscle cells, where it greatly enhances the Ca(2+) sensitivity of BK channels for proper regulation of smooth muscle tone. However, the structural basis underlying dynamic interaction between BK mSlo1 α and β1 remains elusive. Using macroscopic ionic current recordings in various Ca(2+) and Mg(2+) concentrations, we identified two binding sites on the cytosolic N terminus of β1, namely the electrostatic enhancing site (mSlo1(K392,R393)-β1(E13,T14)), increasing the calcium sensitivity of BK channels, and the hydrophobic site (mSlo1(L906,L908)-β1(L5,V6,M7)), passing the physical force from the Ca(2+) bowl onto the enhancing site and S6 C-linker. Dynamic binding of these sites affects the interaction between the cytosolic domain and voltage-sensing domain, leading to the reduction of Mg(2+) sensitivity. A comprehensive structural model of the BK(mSlo1 α-β1) complex was reconstructed based on these functional studies, which provides structural and mechanistic insights for understanding BK gating.

Enhanced amino acid selection in fully evolved tryptophanyl-tRNA synthetase, relative to its urzyme, requires domain motion sensed by the D1 switch, a remote dynamic packing motif

We previously showed (Li, L., and Carter, C. W., Jr. (2013) J. Biol. Chem. 288, 34736-34745) that increased specificity for tryptophan versus tyrosine by contemporary Bacillus stearothermophilus tryptophanyl-tRNA synthetase (TrpRS) over that of TrpRS Urzyme results entirely from coupling between the anticodon-binding domain and an insertion into the Rossmann-fold known as Connecting Peptide 1. We show that this effect is closely related to a long range catalytic effect, in which side chain repacking in a region called the D1 Switch, accounts fully for the entire catalytic contribution of the catalytic Mg(2+) ion. We report intrinsic and higher order interaction effects on the specificity ratio, (kcat/Km)Trp/(kcat/Km)Tyr, of 15 combinatorial mutants from a previous study (Weinreb, V., Li, L., and Carter, C. W., Jr. (2012) Structure 20, 128-138) of the catalytic role of the D1 Switch. Unexpectedly, the same four-way interaction both activates catalytic assist by Mg(2+) ion and contributes -4.4 kcal/mol to the free energy of the specificity ratio. A minimum action path computed for the induced-fit and catalytic conformation changes shows that repacking of the four residues precedes a decrease in the volume of the tryptophan-binding pocket. We suggest that previous efforts to alter amino acid specificities of TrpRS and glutaminyl-tRNA synthetase (GlnRS) by mutagenesis without extensive, modular substitution failed because mutations were incompatible with interdomain motions required for catalysis.

Inter-subunit interactions across the upper voltage sensing-pore domain interface contribute to the concerted pore opening transition of Kv channels

The tight electro-mechanical coupling between the voltage-sensing and pore domains of Kv channels lies at the heart of their fundamental roles in electrical signaling. Structural data have identified two voltage sensor pore inter-domain interaction surfaces, thus providing a framework to explain the molecular basis for the tight coupling of these domains. While the contribution of the intra-subunit lower domain interface to the electro-mechanical coupling that underlies channel opening is relatively well understood, the contribution of the inter-subunit upper interface to channel gating is not yet clear. Relying on energy perturbation and thermodynamic coupling analyses of tandem-dimeric Shaker Kv channels, we show that mutation of upper interface residues from both sides of the voltage sensor-pore domain interface stabilizes the closed channel state. These mutations, however, do not affect slow inactivation gating. We, moreover, find that upper interface residues form a network of state-dependent interactions that stabilize the open channel state. Finally, we note that the observed residue interaction network does not change during slow inactivation gating. The upper voltage sensing-pore interaction surface thus only undergoes conformational rearrangements during channel activation gating. We suggest that inter-subunit interactions across the upper domain interface mediate allosteric communication between channel subunits that contributes to the concerted nature of the late pore opening transition of Kv channels.

On the estimation of cooperativity in ion channel kinetics: activation free energy and kinetic mechanism of Shaker K+ channel

In this paper, we have explored generic criteria of cooperative behavior in ion channel kinetics treating it on the same footing with multistate receptor-ligand binding in a compact theoretical framework. We have shown that the characterization of cooperativity of ion channels in terms of the Hill coefficient violates the standard Hill criteria defined for allosteric cooperativity of ligand binding. To resolve the issue, an alternative measure of cooperativity is proposed here in terms of the cooperativity index that sets a unified criteria for both the systems. More importantly, for ion channel this index can be very useful to describe the cooperative kinetics as it can be readily determined from the experimentally measured ionic current combined with theoretical modelling. We have analyzed the correlation between the voltage value and slope of the voltage-activation curve at the half-activation point and consequently determined the standard free energy of activation of the ion channel using two well-established mechanisms of cooperativity, namely, Koshland-Nemethy-Filmer (KNF) and Monod-Wyman-Changeux (MWC) models. Comparison of the theoretical results for both the models with appropriate experimental data of mutational perturbation of Shaker K(+) channel supports the experimental fact that the KNF model is more suitable to describe the cooperative behavior of this class of ion channels, whereas the performance of the MWC model is unsatisfactory. We have also estimated the mechanistic performance through standard free energy of channel activation for both the models and proposed a possible functional disadvantage in the MWC scheme.

Transduction of voltage and Ca2+ signals by Slo1 BK channels

Large-conductance Ca2+ -and voltage-gated K+ channels are activated by an increase in intracellular Ca2+ concentration and/or depolarization. The channel activation mechanism is well described by an allosteric model encompassing the gate, voltage sensors, and Ca2+ sensors, and the model is an excellent framework to understand the influences of auxiliary β and γ subunits and regulatory factors such as Mg2+. Recent advances permit elucidation of structural correlates of the biophysical mechanism.

Allosteric coupling of the inner activation gate to the outer pore of a potassium channel

In potassium channels, functional coupling of the inner and outer pore gates may result from energetic interactions between residues and conformational rearrangements that occur along a structural path between them. Here, we show that conservative mutations of a residue near the inner activation gate of the Shaker potassium channel (I470) modify the rate of C-type inactivation at the outer pore, pointing to this residue as part of a pathway that couples inner gate opening to changes in outer pore structure and reduction of ion flow. Because they remain equally sensitive to rises in extracellular potassium, altered inactivation rates of the mutant channels are not secondary to modified binding of potassium to the outer pore. Conservative mutations of I470 also influence the interaction of the Shaker N-terminus with the inner gate, which separately affects the outer pore.

Inter-α/β subunits coupling mediating pre-inactivation and augmented activation of BKCa(β2)

Large-conductance calcium-activated potassium (BK) channels regulate the electric properties and neurotransmitter release in excitable cells. Its auxiliary β2 subunits not only enhance gating, but also confer inactivation via a short-lived preinactivated state. However, the mechanism of enhancement and preinactivation of BK channels by β2 remains elusive. Using our newly developed methods, we demonstrated that electrostatic forces played a crucial role in forming multiple complementary pairs of binding sites between α and β subunits including a “PI site” required for channel preinactivation, an “E site” enhancing calcium sensitivity and an “E_CaB” coupling site transferring force to gate from the Ca²⁺-bowl via the β2(K33, R34, K35), E site and S6-C linker, independent of another Ca²⁺ binding site mSlo1(D362,D367). A comprehensive structural model of the BK(β2) complex was reconstructed based on these functional studies, which paves the way for a clearer understanding of the structural mechanisms of activation and preinactivation of other BK(β) complexes.

Probing the energy landscape of activation gating of the bacterial potassium channel KcsA

The bacterial potassium channel KcsA, which has been crystallized in several conformations, offers an ideal model to investigate activation gating of ion channels. In this study, essential dynamics simulations are applied to obtain insights into the transition pathways and the energy profile of KcsA pore gating. In agreement with previous hypotheses, our simulations reveal a two phasic activation gating process. In the first phase, local structural rearrangements in TM2 are observed leading to an intermediate channel conformation, followed by large structural rearrangements leading to full opening of KcsA. Conformational changes of a highly conserved phenylalanine, F114, at the bundle crossing region are crucial for the transition from a closed to an intermediate state. 3.9 µs umbrella sampling calculations reveal that there are two well-defined energy barriers dividing closed, intermediate, and open channel states. In agreement with mutational studies, the closed state was found to be energetically more favorable compared to the open state. Further, the simulations provide new insights into the dynamical coupling effects of F103 between the activation gate and the selectivity filter. Investigations on individual subunits support cooperativity of subunits during activation gating.

From systems to structure: bridging networks and mechanism

There is a wide gap between the generation of large-scale biological data sets and more-detailed, structural and mechanistic studies. However, recent studies that explicitly combine data from systems and structural biological approaches are having a profound effect on our ability to predict how mutations and small molecules affect atomic-level mechanisms, disrupt systems-level networks, and ultimately lead to changes in organismal fitness. In fact, we argue that a shared framework for analysis of nonadditive genetic and thermodynamic responses to perturbations will accelerate the integration of reductionist and global approaches. A stronger bridge between these two areas will allow for a deeper and more-complete understanding of complex biological phenomenon and ultimately provide needed breakthroughs in biomedical research.