Harnessing hypoxic adaptation to prevent , treat , and repair stroke The brain demands oxygen and glucose to fulfill its roles as the master regulator of body functions as diverse as bladder control and creative thinking . Chemical and electrical transmission in the nervous system is rapidly disrupted in stroke as a result of hypoxia and hypoglycemia . Despite being highly evolved in its architecture , the human brain appears to utilize phylogenetically conserved homeostatic strategies to combat hypoxia and ischemia . Specifically , several converging lines of inquiry have demonstrated that the transcription factor hypoxia-inducible factor-1 -LRB- HIF1-1 -RRB- mediates the activation of a large cassette of genes involved in adaptation to hypoxia in surviving neurons after stroke . Accordingly , pharmacological or molecular approaches that engage hypoxic adaptation at the point of one of its sensors -LRB- e.g. , inhibition of HIF prolyl 4 hydroxylases -RRB- leads to profound sparing of brain tissue and enhanced recovery of function . In this review , we discuss the potential mechanisms that could subserve protective and restorative effects of augmenting hypoxic adaptation in the brain . The strategy appears to involve HIF-dependent and HIF-independent pathways and more than 70 genes and proteins activated transcriptionally and post-transcriptionally that can act at cellular , local , and system levels to compensate for oxygen insufficiency . The breadth and depth of this homeostatic program offers a hopeful alternative to the current pessimism towards stroke therapeutics . Stroke is defined as injury to the brain accruing from a vascular etiology . Strikingly , it has emerged as the third leading cause of death and the leading cause of disability in the USA . Accordingly , the estimated financial costs of stroke are more than 50 billion dollars a year in the USA alone . These financial costs do not begin to tell the story of the personal suffering that amasses from the silent epidemic of stroke disability -- over 5 million Americans face the challenges of handicaps from stroke each day . The recognition of stroke as a leading age-associated public health issue has led the government and the pharmaceutical industry to expend enormous resources on developing interventions in the form of drugs that minimize brain damage associated with stroke . Despite their promise , these efforts have been disappointing and have left a nearly indelible sense of frustration on the biomedical research community -LSB- 1 -RSB- . In this chapter , we will discuss the pathophysiology of stroke with particular attention to one of its primary mediators , hypoxia , and attempt to revive a sense of optimism and enthusiasm for stroke therapeutics moving forward . Ischemia is a process in which perfusion to tissue is critically reduced creating a deficit in necessary brain fuels . The brain is highly vulnerable to ischemia because the eloquent functions it is assigned to carry out , in the pluralistic society of organ functions , depend integrally on energy -- specifically adenosine triphosphate -LRB- ATP -RRB- . The brain comprises only 2 % of body weight , but it utilizes nearly 20 % of cardiac output to achieve its supply of essential nutrients including oxygen and glucose . Abnormal central nervous system -LRB- CNS -RRB- symptoms begin to manifest at 40 -- 50 % of normal resting hemispheric cerebral blood flow resulting in slowing of the EEG , attenuation of evoked potentials , and reduction in the membrane potential in individual cortical neurons -LSB- 2 -RSB- . The resting membrane potential must be maintained to allow proper neuronal function , including synaptic activity and axonal conduction . Once the neuronal membrane potential begins to dissipate , neuronal function ceases . It is important to note that ATP levels at this point may be normal or only slightly reduced -LSB- 3 -RSB- . The reason for this inordinate sensitivity is not entirely clear but is likely related to the Km of neurotransmitter systems for ATP or their exquisite sensitivity to tissue acidosis -LSB- 4 -RSB- . Gross deterioration and damage requires even more severe reductions in blood flow to 20 -- 30 % of normal resting hemispheric cerebral blood flow -LRB- Fig. 1 -RRB- . With this level of ischemia , a deterioration of ionic membrane gradients ensues , and the tissue begins to accumulate hydrogen ions -LRB- acidosis -RRB- -LSB- 5 -RSB- . Changes in ionic fluxes likely accrue directly from a reduction of intracellular ATP , a failure of the Na + / K+ATP ase activity , and increases in intracellular Na + and extracellular K + . The failure of ionic homeostasis reflects loss of activity of multiple transporters that normally maintain the electrochemical gradients necessary for normal neuronal signal transduction -LSB- 6 , 7 -RSB- . Among the ions deregulated , intracellular calcium appears to play a critical role in further ion dyshomeostasis via the calmodulin-dependent activation of neuronal nitric oxide synthase -LRB- nNOS -RRB- -LSB- 8 -- 10 -RSB- . Increased nNOS activity leads to increase in the ambient levels of neuronal nitric oxide -LRB- NO -RRB- -LSB- 11 -RSB- . Changes in NO coupled with ischemia-associated increases in cytosolic and mitochondrially derived superoxide , combine to form toxic peroxynitrite . Peroxynitrite can trigger cell death pathways via DNA damage , poly -LRB- ADP-ribose -RRB- polymerase -LRB- PARP -RRB- activation , liberation of apoptosis-inducing factor -LRB- AIF -RRB- from the mitochondria , and activation of death signaling pathways leading to apoptosis -LSB- 12 , 13 -RSB- ; alternatively , non-selective cation channels such as TRPM2 and TRPM7 can be activated to ensure sustained calcium overload and death -LSB- 14 -RSB- . Extracellular acidosis is also postulated to activate acid sensing ion channels , which also contribute to destruction of the normal ionic environment -LSB- 15 -RSB- . As one can appreciate from a partial description of the sequence of events after stroke that occur in the neuron alone , targeting a single molecule in the complex parallel and serial pathways of acute hypoxia-ischemia will not maintain neuronal survival -LRB- Fig. 2 -RRB- . It is also unlikely to enhance the ability of energy-thirsty neurons to carry out their sophisticated roles in maintaining posture , movement , sequencing language , or making critical executive decisions . Therefore , how might we move forward ? One of the most important advances in the treatment of complex medical problems has been the discovery that multimodal therapies can greatly enhance therapeutic efficiency . Treatment of cancer , HIV infection , and tuberculosis with multimodal therapies yields results that are not obtained with the application of single therapeutic agents . Fig. 1Neuronal hypoxia leads to calcium overload and production of free radicals . Stroke is associated with a decrease in cerebral blood flow to the brain . The consequent loss of metabolic fuels leads to failure of sodium pumps leading to an intracellular accumulation of sodium and calcium , depolarization , and activation of voltage sensitive and ligand gated -LSB- N-methyl-d-aspartate -LRB- NMDA -RRB- -RSB- ion channels . Increased in calcium in microdomains near the NMDA receptor leads to activation of neuronal nitric oxide synthase . Global dysregulation of calcium in the neuron leads to mitochondrial overload and superoxide production . Nitric oxide and superoxide combine to form peroxynitrite . Peroxynitrite can damage DNA leading to PARP activation and consumption of NAD + . It can also activate TRPM2/7 channels leading to further calcium dysregulation . Hypoxia is sensed by decreased activity of HIF prolyl 4 hydroxylases that can lead to activation genetic responses capable of compensating for the sentinel metabolic stress -LRB- decreased cerebral blood flow -RRB- . Decrease HIF PHD activity can also prevent death via HIF-independent pathways . Acidosis and ROS can also combine with HIF regulated prodeath proteins to trigger cell deathFig . 2Contribution of neurons and astrocytes in mediating excitotoxic neuronal death . 1 Loss of ATP in ischemia leads to inhibition of the Na + / K+ATP ase and subsequent collapse of normal ionic gradients . 2 In turn , neuronal membrane depolarization activates voltage sensitive Ca2 + channels , which increase intracellular Ca2 + and stimulate vesicular glutamate release . Severe loss of ionic gradients found in certain ischemic regions may also lead to the reversal of 3 neuronal specific and 4 astrocyte specific glutamate transporters , which in the reverse mode act to release glutamate into the extracellular space . 5 Cell swelling in cerebral ischemia , which is mainly localized to astrocytes , likely activates swelling sensitive anion channels , referred to as volume regulated anion channels -LRB- VRACs -RRB- . VRACs , which are permeable to organic osmolytes , contribute to glutamate release predominantly in the ischemic penumbra . 6 Glutamate regulated NMDA receptors -LRB- NMDA-R -RRB- are activated by -LRB- 1 -RRB- extracellular glutamate and -LRB- 2 -RRB- release of Mg2 + from its pore after membrane depolarization -LRB- in part due to activation of glutamate regulated AMPA receptors , not shown -RRB- . 7 NMDA-Rs are permeable to Ca2 + and as such , overabundant NMDA-R activation leads to an intracellular Ca2 + overload . This increase in intracellular Ca2 + then contributes to neuronal death via several mechanisms As stroke does not represent a single homogeneous category of injury , it is also a poor candidate for a single approach to treatment -LSB- 16 -RSB- . Challenges involved in promoting recovery from stroke involve reducing the extent of damage that occurs in acute injury . Moreover , many different kinds of damage are found in individuals with stroke ranging from necrotic , apoptotic , or parthanatotic death of neurons -LSB- 17 , 18 -RSB- , demyelination of otherwise functional axons -LSB- 19 -RSB- , and transection of axons and subsequent loss of critical neuronal populations -LSB- 20 -RSB- . Acute injury itself is extremely complex , including waves of cell death , inflammatory responses , edema , and scarring . Indeed , experimental studies have continued to demonstrate that interventions that target single aspects of the complex cascade , including blocking ion gradients , scavenging free radicals , or enhancing growth factors on their own are insufficient to overcome the considerable barriers to protection against hypoxia and ischemia in acute stroke -LSB- 21 -RSB- . Instructive data from the experimental paradigm of ischemic preconditioning has pointed the way towards novel strategies that can address the heterogeneity and complexity inherent in stroke pathophysiology -LSB- 22 -RSB- . Animals subjected to a non-lethal exposure to hypoxia are found to be more resistant to a host of subsequent lethal stresses , including cerebral ischemia . The mechanism by which a sublethal exposure to hypoxia can render the brain resistant to cerebral ischemia and a host of other insults is a topic of active investigation and debate . However , one point appears irrefutable : The tolerance that develops after a short duration of hypoxia involves not only the activation or inactivation of pre-existing proteins but also de novo gene expression -LSB- 23 , 24 -RSB- . These transcriptional and post-transcriptional mechanisms reflect a cassette of genes and proteins that work collectively at the cellular , local , and systemic levels to compensate for a discrepancy in oxygen supply and demand . The findings suggest that under conditions where adaptive homeostatic mechanisms are appropriately engaged , damage to the brain can be substantially lessened or even prevented -LRB- Fig. 3 -RRB- . Stroke is , almost by definition , a failure of homeostasis . Accordingly , identification of small molecules that augment endogenous adaptive strategies provides a mechanism to tilt the balance away from cell damage and death and toward cell survival and repair -LRB- Fig. 3 -RRB- . Fig. 3Drugs that augment endogenous homeostatic mechanisms will more effectively neutralize the heterogeneity inherent in stroke pathophysiology . As these pathways are already used by the body , their activation can occur with decreased threat of toxicity . The term `` homeostasis '' was coined by Walter Canon in the early twentieth century . It refers to the innate tendency of organisms to mobilize adaptive responses physiological and pathological perturbations that ultimately return the system to a set point that is consistent with survival . a The experimental paradigm of `` ischemic preconditioning '' has shown that a short , sublethal exposure to hypoxia , or hypoxia-ischemia induces homeostatic responses that make the organism `` immune '' or `` tolerant '' to a lethal ischemic insult . Mechanistic studies have revealed that tolerance is the consequence of activation of pre-existing proteins and de novo gene expression . b According to this model , stroke can be conceptualized as a failure of homeostasis . Consequently , neurons die and the brain is permanently damaged . c By extension , small molecules that engage homeostatic mechanisms designed to alleviate hypoxia/ischemia early or enhance their activation should tip the balance away from cell death and toward survival and repair . Such small molecules are currently being developed and represent a new generation of stroke therapies Examination of adaptive responses to hypoxia in the central nervous system has affirmed that the family of transcriptional regulators known as the hypoxia-inducible factors are central players -LSB- 25 -- 27 -RSB- . HIF-1 was purified and cloned as a result of a search for proteins that regulate the expression of genes involved in hypoxic adaptation , such as erythropoietin , vascular endothelial growth factor , and glycolytic enzymes -LSB- 27 -RSB- . HIF is a heterodimeric transcriptional activator composed of an inducible HIF-1α subunit and a constitutively expressed HIF-1β subunit -LSB- 28 , 29 -RSB- . HIF-1α stability is regulated via the activity of a class of oxygen , 2-oxoglutarate , and iron dependent enzymes known as the HIF prolyl-4 hydroxylases -LRB- HIF PHDs , Fig. 4 -RRB- -LSB- 30 -RSB- . As intracellular oxygen levels drop below a critical threshold , these enzymes fail to hydroxylate HIF-1α . As hydroxylation is required for the recruitment of the constitutively active E3 Ubiquitin Ligase , Von Hippel Lindau protein , HIF-1α becomes stabilized . HIF-1α can partner with its constitutively expressed but induced partner HIF-1β and translocate to the nucleus to regulate the expression of a host of genes involved in hypoxic adaptation -LSB- 31 -RSB- . Consistent with this model , several groups have shown that HIF-1α immunoreactivity increases in areas of the cortex that become hypoxic due to stroke -LSB- 25 , 32 -RSB- An unanswered question has been whether HIF is also upregulated in areas connected to but remote from the site of ischemia . Indeed , neurons projecting to an area of infarction are at risk for cell death due to a loss of trophic support from their damaged targets . Moreover , neurons projecting from an area of damage are at risk for cell death due to a loss of trophic excitatory input from their targets . An elegant recent study in non-human primates demonstrated a dramatic increase in neuronal immunoreactivity for HIF-1α and one of its target genes in the infarct and peri-infarct region -LSB- 33 , 34 -RSB- . Indeed , the neuronal immunoreactivity for HIF-1α increased from less than 5 % to nearly 90 % in both regions . Interestingly , areas remote to the area of hypoxia and ischemia also experience increased HIF and vascular endothelial growth factor -LRB- VEGF -RRB- levels but to a quantitatively much smaller extent . Together , the published rodent and primate histochemical studies support the hypothesis that increased HIF protein levels resulting from direct hypoxia and non-hypoxic mediators such as IGF-1 are a marker for surviving and regenerating neurons after ischemia -LSB- 32 -RSB- . Fig. 4HIF prolyl 4 hydroxylases sense hypoxia and transduce a critical insufficiency in oxygen in the brain into transcriptional and post-transcriptional signal changes that mediate protection and repair . Hypoxia regulates the activity of HIF PHDs via direct or indirect mechanisms ; production of peroxide via reduction in mitochondrial ATP production and electron transport chain -LRB- ETC -RRB- impairment -LRB- 1 , 2 -RRB- ; accumulation of the tricarboxylic cycle -LRB- TCA -RRB- intermediates succinate and fumarate -LRB- 3 -RRB- ; or direct inhibition of the activity of PHDs due to lack of oxygen -LRB- 4 -RRB- . Accumulation of hydrogen peroxide , succinate or fumarate can inhibits the activity of PHDs by competing with 2-oxoglutarate or by oxidizing the active site iron -LRB- 5 -RRB- . Among its numerous downstream effects , inhibition of HIF PHD activity leads to stabilization of HIF-1α . Stabilized HIF-1α dimerizes with HIF-1β in the nucleus and increases gene transcription -LRB- 6 -RRB- Pharmacological and molecular studies have provided additional support for the notion that stabilization of HIF-1 after ischemia is associated with enhanced survival of neurons . Small molecule hypoxia mimics , deferoxamine , and cobalt chloride , were found to stabilize HIF-1α levels , increase DNA binding to a cognate hypoxia response element , and increase the expression of HIF target genes in vitro cultured neurons -LRB- Zaman et al. -LSB- 31 -RSB- -RRB- and in vivo in the intact brain -LRB- Fig. 4 ; -LSB- 35 -RSB- -RRB- . Pretreatment or post-treatment with desferrioxamine or cobalt chloride resulted in reduced cell loss in models of focal or global ischemia in vitro and in vivo -LSB- 25 , 31 , 36 -- 39 -RSB- . Subsequent studies have confirmed that hypoxia , iron chelation , or cobalt chloride appear to confer protective effects on neurons via their ability to inhibit HIF PHDs -LSB- 35 -RSB- . Emerging data indicate that inhibition of each of the three of the HIF PHD isoforms -LRB- 1 -- 3 -RRB- may lead to cell survival in the nervous system . Of note , inhibition of each isoform may enhance survival via distinct but mutually supportive pathways . Our studies demonstrate that pharmacological inhibition of PHDs , in vitro , leads to inhibition of oxidative stress-induced death , an established mediator of neural injury and death in stroke -LSB- 35 -RSB- . More recent studies indicate that molecular suppression of HIF PHD 1 alone can mimic this effect -LRB- Siddiq et al. , unpublished observations -RRB- . Interestingly , while HIF-1 , HIF-2 , and cAMP response element-binding protein are stabilized by PHD inhibition in neurons or astrocytes , the molecular deletion or inhibition of each of these three transcription factors fails to abrogate the protective effects of PHD inhibition suggesting that other , as yet unidentified , pathways are important in protection -LRB- Siddiq et al. , unpublished observations -RRB- . Studies are underway to clarify whether molecular deletion of PHD1 selectively in the CNS confers resistance to stroke in a HIF-independent manner . In contrast to PHD1 , PHD2 appears to be the isoform most important for tagging HIF for degradation . Deletion of PHD2 but not PHD1 or PHD3 results in increased HIF and VEGF protein and consequent angiogenesis in multiple organs including the brain -LSB- 40 -RSB- . Underscoring PHD2 's important role in HIF signaling , the expression level of this isoform is significantly higher as compared to its brethren -LSB- 41 -RSB- . Ischemia-induced PHD2 inhibition stabilizes HIF and enhances expression of genes that mediate cellular -LRB- e.g. , glycolytic enzymes -RRB- , local -LRB- vascular endothelial growth factor -RRB- , and systemic -LRB- erythropoietin , Epo -RRB- adaptive responses to hypoxia or hypoxia-ischemia -LSB- 42 -RSB- . While Epo is best known as a hematopoietic growth factor that can enhance oxygen carrying capacity to tissue , it also has organ-autonomous roles in the nervous system . Epo is produced in astrocytes in response to hypoxia or ischemia and mediates a number of responses critical to stroke prevention and recovery -LSB- 43 , 44 -RSB- . Epo can inhibit neuronal death due to excitotoxicity or growth factor deprivation -LSB- 45 -- 49 -RSB- . It can also stimulate the proliferation of neural progenitors in the germinal zones of the brain and enhance their migration to sites of injury -LSB- 50 , 51 -RSB- . The concomitant HIF-dependent increase in VEGF expression provides , among other things , the appropriate angiogenic niche for neural progenitors to survive -LSB- 52 -RSB- . New neurons could mediate recovery responses via paracrine effects or due to direct participation in functional circuits . A recent study affirmed the requisite role for HIF transcription factors in mediating some of the salutary effects of low molecular weight PHD inhibitors given after cerebral ischemia -LSB- 53 -RSB- . Available evidence suggests that these inhibitors are likely targeting PHD2 to induce HIF and its gene targets in the CNS . Inhibition of the third isoform of PHDs -LRB- PHD3 -RRB- by hypoxia or hypoxia mimetics has also been linked to neuronal survival -LSB- 54 -RSB- . Freeman and colleagues first identified PHD3 -LRB- then known as SM-20 -RRB- as a message and protein that is highly upregulated in sympathetic neurons after growth factor deprivation . Subsequent studies have shown that pharmacological or molecular deletion of HIF PHD3 prevents apoptosis associated with trophic loss in neurons and that the protection is HIF independent -LSB- 55 -RSB- . As target -LRB- post-synaptic -RRB- derived trophic factors appear to be lost after stroke and result in cell death remote from the infarct site , HIF PHD3 inhibition may be a rational strategy for maintaining the viability of these neurons in evolving or stable stroke . From the above discussion , a model begins to emerge whereby inhibition of HIF PHD1 , 2 , or 3 by hypoxia or consequences of hypoxia can mediate HIF-dependent and HIF-independent compensatory responses via distinct but clearly reinforcing mechanisms . How does one reconcile this model with observations from several laboratories , including our own , that HIF PHD inhibition or HIF activation leads to the upregulation of prodeath , Bcl-2 family proteins such as Puma , Bnip3 , and NIX -LSB- 56 -RSB- ? Moreover , constitutive HIF activation has been associated with potentiation and suppression of death -LSB- 56 -RSB- . These findings appear to make perfect sense if one considers apoptosis as an adaptive response to stress . After stroke , oxygen may fall below a critical level rendering the prolyl hydroxylases inactive . Accordingly , HIF is stabilized and it translocates to the nucleus to upregulate genes involved in preventing and executing death . The anthropomorphized cell can be visualized stepping to the edge of a steep cliff in response to a potentially lethal stress -LRB- Fig. 5 -RRB- . If adequate compensation for hypoxia occurs , prodeath proteins are not activated and the cell survives as a functional component of a complex neural network -- the cell moves away from the cliff to survival promoting , terra firma . By contrast , if oxidative stress , hypoxia , and acidosis dominate , indicating that compensatory mechanisms have failed , then proapoptotic proteins such as BNIP3 undergo a conformational change , insertion into the mitochondrial membrane and activation of permeabilization transition and release of apoptotic effectors -LSB- 57 -- 59 -RSB- . In the latter scenario , the cell jumps off the cliff to preserve limiting resources for its neighbors . The model suggests that state changes in the cell -LRB- e.g. , redox and pH -RRB- that follow the initial ischemic insult will determine the fate of the tissue and potential for recovery -LRB- Fig. 5 -RRB- . Of note , low molecular weight or peptide inhibitors of the PHDs , antioxidants , and a small interfering RNA to BNIP3 prevent the prodeath effects of HIF -LRB- Amino et al. , personal communication -RRB- . These findings suggest that engaging the adaptive response at an upstream point where stress is detected by the cell -LRB- the stress sensor -RRB- is going to be more effective in stemming cell loss and facilitating repair than at the point of the transcription factor -LRB- HIF -RRB- . It is our hypothesis that engaging the adaptive response at an upstream point in the pathway results in post-transcriptional changes essential for the homeostatic response . These changes in concert with transcriptional changes optimally alleviate the discrepancy between oxygen supply and demand . Fig. 5Adaptation to hypoxia-cell fate and beyond . Expression of HIF in neurons leads to the constitutive expression of proteins associated with cell death -LRB- BNIP3 , NIX , and PUMA -RRB- and cell survival -LRB- VEGF , glycolytic enzymes , Epo , and p21 waf1/cip1 -RRB- . Similar prodeath gene expression is found in neurons exposed to hypoxia or hypoxia mimetics despite the absence of cell death . It appears the oxygen `` starved '' neurons have stepped to the edge of the cliff . If during the ensuing hours to days the neuron becomes acidotic or oxidized , then prodeath proteins such as BNIP3 undergo a conformational change , insertion into the mitochondrial membrane , release of apoptotic effectors , and death . By contrast , if the survival genes are effective in neutralizing the hypoxic stress -LRB- e.g. , no acidosis or oxidative stress -RRB- , then the death genes never get activated . Our studies indicate that antioxidants , short interfering RNAs to BNIP3 or inhibitors of the HIF prolyl 4 hydroxylases tip the balance toward survival -LRB- away from the cliff -RRB- The model has some clear predictions . First , low molecular weight global inhibitors of the HIF prolyl 4 hydroxylases will be more effective at preventing injury and repairing damage after stroke than selective isoform inhibitors . These inhibitors will engage HIF-dependent and HIF-independent pathways at cellular , local , and systemic levels and ultimately alleviate the discrepancy in nutrient supply and demand . They can also -LRB- via mechanisms that are only beginning to be defined -RRB- divert HIF away from its tendencies as a prodeath transcription factor . The ability of single `` drugs '' to target an oligopoly of proteins -LRB- HIF PHD1 -- 3 -RRB- to affect a concerted program of neuroprotection involving more than 70 genes and larger number of proteins suggests a strategy for overcoming the heterogeneity inherent in stroke pathophysiology in the short term . While a significant amount of work needs to be done to adequately assess the viability of this strategy for human therapeutics , the notion of augmenting endogenous adaptive programs via HIF PHDs to thwart disease continues to gain currency .

O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B B O B O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O B O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O O B B O O O O O O O O O O O O O O O O O O O O B O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O B O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O


Evidence of molecular alignment fluctuations in aqueous dilute liquid crystalline media Protein dynamics can be studied by NMR measurements of aqueous dilute liquid crystalline samples . However , the measured residual dipolar couplings are sensitive not only to internal fluctuations but to all changes in internuclear vectors relative to the laboratory frame . We show that side-chain fluctuations and bond librations in the ps -- ns time scale perturb the molecular shape and charge distribution of a small globular protein sufficiently to cause a noticeable variation in the molecular alignment . The alignment variation disperses the bond vectors of a conformational ensemble even further from the dispersion already caused by internal fluctuations of a protein . Consequently RDC-probed order parameters are lower than those obtained by laboratory frame relaxation measurements . Introduction Native proteins are customarily pictured as highly structured entities ; a view that is supported by many lines of evidence . Nonetheless , all proteins exhibit internal motions on various time scales and amplitudes . Fast internal motions , i.e. bond vibrations and librations as well as peptide plane movements , take place in picoseconds to nanoseconds -LRB- Bouvignies et al. 2005 ; Kay et al. 1989 ; Lakomek et al. 2006 -RRB- . Slow internal motions , i.e. secondary structure and protein domain motions , occur at a sedate pace in microseconds to milliseconds . NMR coherence decays have revealed that bond librations and side-chain reorientations amount only to a small reduction in structural order . The associated Lipari -- Szabo order parameter -LRB- SLS2 -RRB- -LRB- Lipari and Szabo 1982a , b -RRB- in well-structured parts of a protein is typically above 0.85 for amide moieties -LRB- Kay et al. 1989 -RRB- , 0.9 for backbone bonds -LRB- Ferrage et al. 2006 -RRB- and 0.2 -- 0.9 for side-chain methyl groups depending on the length of the side-chain -LRB- Millet et al. 2002 ; Skrynnikov et al. 2002 -RRB- . On slower time scales , in the μs-regime and above , relaxation dispersion and exchange rate measurements -LRB- Palmer 2004 -RRB- have revealed larger but infrequent excursions away from the most populated states . Recently , residual dipolar coupling -LRB- RDC -RRB- data has revealed -LRB- Lakomek et al. 2005 ; Meiler et al. 2001 ; Tolman et al. 2001 -RRB- in the intervening time-scale , below μs and above τc , anisotropic and correlated motions , that have been associated with order parameters in the range 0.6 -- 1.0 . RDCs -LRB- Tjandra and Bax 1997 -RRB- can be regarded as ideal motional probes as they respond explicitly to all motions of internuclear vectors . Non-zero RDCs arise first when molecular tumbling in solution is slightly anisotropic . To that end a dilute liquid crystalline -LRB- LC -RRB- medium is used to impose a subtle alignment on a biological macro-molecule solute via steric and electrostatic interactions -LRB- Prestegard et al. 2004 -RRB- . RDC observables are , of course , averages over a dynamic conformational ensemble -LRB- Bax et al. 2001 ; Louhivuori et al. 2006 -RRB- . The high structural similarity among the most populated states prompts to think that on average all conformations would , to an excellent approximation , adopt a similar alignment . This is the implicit assumption underlying the many structural and dynamic data analyses of weak alignment NMR spectroscopy -- a method that is widely used today in structural biology -LRB- Bax and Grishaev 2005 ; Blackledge 2005 -RRB- . Indeed it seems reasonable to imagine that the dispersion of molecular alignments among the conformations is small , perhaps negligible , in particular as no apparent inconsistencies have been noticed in protein structure determination . Furthermore it may also seem reasonable to use in the analysis of dynamics an effective alignment frame because usually the conformations are in a fast exchange compared to molecular reorientation . In this study we inspect critically the concept of a common alignment frame for a protein structure on the basis of experimental data . We find that a variation in molecular alignment due to the ps -- ns fluctuations can contribute significantly to the RDC-probed order parameter in the case of a small globular protein . Theory Protein motions captured by RDCs A residual dipolar coupling reports essentially on the average direction of an internuclear vector , e.g. a chemical bond , relative to the main magnetic field of a NMR spectrometer . Both fast and slow internal motions perturb the directions of a chemical bond and since RDCs are measured as an average over a longer time period this reflects directly into the observed RDC . Besides internal motions , the molecule experiences also rotational and translational diffusion in the liquid sample . Anisotropic orientational sampling in a dilute liquid crystalline medium is the basis for observing a residual of a dipolar coupling -LRB- Tjandra and Bax 1997 -RRB- . In practice , it may not be possible to de-convolute the observed data to distinct motional modes , but their identification will clarify the analysis . From a molecular perspective , i.e. from the perspective of an observer on a single molecule , external motions are incidental and of no particular interest -- at least if we assume that molecule -- medium interactions are negligible . It would therefore be sufficient to consider any disorder present in molecular structures only in terms of internal motions -LRB- Fig. 1 -RRB- . The averaging due to the fast ps -- ns bond fluctuations when inspected in the local sub-molecular frame is given by the aforementioned values . The recently proposed -LRB- Bernadó and Blackledge 2004 ; Lakomek et al. 2006 ; Meiler et al. 2003 ; Peti et al. 2002 ; Tolman 2002 -RRB- substantial and frequent fluctuation of secondary structures , i.e. α-helices or β-sheets , relative to a molecular frame will cause additional down-scaling of the order parameter . We denote the corresponding order parameter as and note that it has been reported to range from 0.6 to 1.0 . Fig. 1In the molecular perspective internal motions like -LRB- a -RRB- bond fluctuations , -LRB- b -RRB- peptide plane motions and -LRB- c -RRB- secondary structure movements all contribute to disperse a chemical bond away from its average direction . -LRB- d -RRB- In the ensemble perspective both internal and external motions contribute to fill the available state space . In a RDC measurement the available state space is reduced to effective alignment tensors of the constituent conformations From an ensemble perspective , i.e. from the perspective of an observer regarding every molecule in the sample , both internal and external motions are manifestations of the state space of the system -LRB- Louhivuori et al. 2006 -RRB- . Internal motions cause the conformational diversity and external motions are responsible for the various orientations and positions the molecules inhabit . A conformational change is , from the ensemble perspective , tied to a change in the effective alignment of that molecule . This connection between the alignment and the conformation seems like non-sense from the molecular perspective since a conformational change does not instantly change the orientation of the molecule . Since RDCs are a time and ensemble average the ensemble perspective is an appropriate choice . In the vicinity of a liquid crystalline particle conformations are not energetically equivalent -LRB- Louhivuori et al. 2006 -RRB- and therefore e.g. some side-chain conformations are not in a fast exchange . This means that conformational changes due to internal motions couple to the alignment and appear as fluctuations in the effective alignment frame of a molecule . We mark the corresponding order parameter as It should be emphasised that the alignment is not a property of a free molecule , i.e. a molecule in void , but rather a property of the whole sample including the LC-particles . does not therefore correspond to any intrinsic molecular motion , even though it might appear as one if the molecular perspective is chosen for RDC data interpretation . Finally , we remind that molecular tumbling in solution is the most effective averaging process with respect to the laboratory frame . The associated order parameter Sτ2 is on the order of 10 − 6 in a dilute LC-medium -LRB- Bax et al. 2001 ; Tjandra and Bax 1997 -RRB- . The order parameters are usually normalized relative to Sτ2 . Dynamics modulated alignment We reason that the variation in molecular alignment originates from the dynamics-induced modulation of van der Waals and Coulomb interactions between the protein conformations and the nematogens -LRB- Louhivuori et al. 2006 -RRB- . It may appear paradoxical that a transient conformation could align as the internal ps -- ns fluctuations are much faster than the molecular translational and rotational diffusion . This quandary is resolved as explained above in what is formally referred to as Boltzmann 's ergodic hypothesis of the equivalence between time and ensemble averages . The suppression of some of the molecules internal fluctuations by the presence of the LC-particle imposes an unique alignment on each transient conformation . In other words , a transient conformation does not align per se but rather may only exist if it is energetically allowed . It is thus mistaken to justify the use of a single , effective alignment frame solely on the fact that internal fluctuations are much faster than translational or rotational diffusion . It is clear then that dynamics modulated alignment -LRB- DMA -RRB- is a conceivable phenomenon and could very well be expressed in experimental data . We will therefore proceed to search for experimental evidence of it . Our analysis will be restricted to the ps -- ns protein dynamics that is well characterized by NMR relaxation measurements . On such short time scales primarily bonds fluctuate and side-chains reorientate while motions of secondary structure elements are negligible -LRB- Palmer 2004 -RRB- . Signature of dynamics modulated alignment Of the many motions captured by residual dipolar couplings , bond fluctuations and the overall molecular tumbling are well understood . These two contributions should be removed from the total order to expose any additional motion attributable to either DMA or additional intrinsic motion , e.g. in the form of secondary structure fluctuations , or to both . If the additional motion is an exclusive property of the protein , i.e. independent of the LC-medium that was used in measurements , then it is likely evidence of the reported sub-μs intrinsic secondary structure fluctuations . On the other hand , if a change in LC-media makes a difference then the excess motion may just as well result from the alignment frame dispersion in DMA . Obviously neither secondary structure nor alignment fluctuations are mutually exclusive and indeed it is quite conceivable that both contribute to the observed additional motions . The presence of DMA does not therefore disprove for example the recent findings -LRB- Lakomek et al. 2005 -RRB- of correlated backbone motions . All order examined by RDCs is captured by an overall molecular measure called the general degree of order -LRB- GDO -RRB- -LRB- Tolman et al. 2001 -RRB- . We employ its squared value , The components ϑij are obtained from the measured RDCs , e.g. by singular value decomposition -LRB- SVD -RRB- -LRB- Losonczi et al. 1999 -RRB- , using a set of equationswhere the refined structural model is given by cicj , i.e. internuclear vectors in the Cartesian -LCB- x , y , z -RCB- frame . The constants for the two nuclei A and B are the gyromagnetic ratios γA and γB , the internuclear distance rAB and as usual Planck 's constant h and the permeability of vacuum μo . We aim to determine the ps -- ns fluctuations , i.e. the SLS2 contribution to ϑ2 , on the basis of the intrinsic difference between amide -LRB- NH -RRB- and backbone -LRB- CαCO -RRB- bond fluctuations . This difference is not large , but it is significant -LRB- Ferrage et al. 2006 -RRB- . We find from molecular dynamics -LRB- MD -RRB- simulations of ubiquitin and the B3 domain of protein G that the NH order parameter squared is on the average and the corresponding CαCO value when flexible tails and loops are excluded from the evaluation . These values are consistent with the average model-free order parameter SLS2 for NH obtained from laboratory frame relaxation measurements -LRB- Hall and Fushman 2003 ; Tjandra et al. 1995 -RRB- . The fluctuations of CαCO bonds are being investigated by cross correlated relaxation measurements -LRB- Chang and Tjandra 2005 ; Ferrage et al. 2006 ; Wang et al. 2003 -RRB- . It follows that when ϑ2 is determined using only the NH couplings the result should be slightly smaller than when only the CαCO couplings are used , provided that no other motions play a role . Conversely , any additional motion will partially mask the intrinsic bond fluctuations and perturb the difference Asymmetric motions , i.e. motions that affect the two bonds unequally , will either increase or decrease this difference , or even keep it invariant , whereas symmetric motions will only decrease it . Any change in that is due to the intrinsic secondary structure fluctuations , i.e. Sαβ2 , will be independent of the alignment medium . Any medium-dependent variation in can not arise from medium-independent intrinsic molecular motions and must be attributed either to DMA or to some unknown , novel medium-induced motion . In order to remove contributions from Sτ2 and such superfluous factors as LC-medium density and sample temperature that are present equally in ϑNH2 and we normalize by Furthermore we should note that the sample conditions of the data sets used in this study to illustrate DMA are so similar -LRB- cf. Clore and Schwieters 2004a , b ; Cornilescu et al. 1998 ; Tossavainen et al. 2003 ; Ulmer et al. 2003 -RRB- that we can not see how they could have any significant effect on the results to be presented . Alignment tensors are determined from RDC data e.g. by using SVD -LRB- Losonczi et al. 1999 -RRB- . The δ parameter and its error are then obtained using Eq . 2 . Amount of intrinsic bond fluctuations Based on the MD simulation derived and values , the normalized difference between the average NH and CαCO bond fluctuations is without any additional motion If the measured differs substantially from the simulated value of 0.955 , this value should be adjusted accordingly . It should also be noted that if the internal bond fluctuations were highly molecule dependent , it might be more sensible to consider δo separately for each molecule rather than the general δo shown here . Nevertheless , a δo parameter derived from a system outside the influence of any alignment medium serves to establish a numeric value that includes all intrinsic motions and nothing else . Any deviation from this baseline is then a sign of additional motions . Local alignment frames It may appear strange to use the general degree of order , a molecular quantity , as a motional probe because local order parameters are more informative . A locus-specific measure of RDC-probed dynamics is obtained by combining , via transformations , a non-redundant data set of at least five alignments -LRB- Tolman et al. 2001 -RRB- . The obtained local GDOs provide a clear measure of residue-specific dynamics , but unfortunately the procedure would also mix up the eventual fluctuations in alignments -- the very effect we aim to address . To differentiate between internal and alignment fluctuations it only matters to observe whether δ varies from one medium to another . To this end ϑ2 is a robust measure that samples various bond directions . By taking care to account for alignment frame fluctuations and population differences between the conformations -LRB- Louhivuori et al. 2006 -RRB- , one could arrive at more precise local order parameters . Methods The conformational ensembles of GB1 -LRB- 850 members -RRB- , GB3 -LRB- 150 members -RRB- and ubiquitin -LRB- 2,400 members -RRB- were generated by molecular dynamics using the CHARMM22 parameter set -LRB- MacKerell et al. 1998 -RRB- with a modified backbone potential -LRB- MacKerell et al. 2004 -RRB- and generalized Born model -LRB- Im et al. 2003 -RRB- . The proteins were first heated to 300 K during 200 ps and then equilibrated for 2 ns at this temperature before sampling for 48 , 34 and 3 ns for ubiquitin , GB1 and GB3 , respectively . Subsequently the alignment of each conformation was simulated using the PALES program -LRB- Zweckstetter 2006 ; Zweckstetter and Bax 2000 ; Zweckstetter et al. 2004 -RRB- in order to achieve the alignment dispersion present in a real sample . The alignments were predicted in the presence of a neutral planar obstacle as well as using positively and negatively charged bacteriophages carrying a surface charge density 0.047 e/nm2 and 10 mM ionic strength of monovalent salt in pH 6.5 with a LC concentration of 1 mg/ml . The refined structures 1P7F -LRB- Clore and Schwieters 2004a ; Ulmer et al. 2003 -RRB- , 1D3Z -LRB- Clore and Schwieters 2004b ; Cornilescu et al. 1998 -RRB- and 1NYA -LRB- Tossavainen et al. 2003 -RRB- of the B3 domain of protein G , ubiquitin and calerythrin were used to analyse experimental RDC data available in various LC media -LRB- Table 1 -RRB- . The temperature dependence of the experimental parameters were reported -LRB- Cornilescu et al. 1998 ; Ulmer et al. 2003 -RRB- to be minimal in the temperature range used in the experiments.Table 1ϑ2 and δ of GB3 , ubiquitin and calerythrin in various alignment media . ϑ2 are shown in units of 10 − 6ProteinMediumT -LRB- K -RRB- GB3 -LRB- 1P7F -RRB- aCTAB2 .0732.3490.117 ± 0.006302 PEG0 .6140.7500.181 ± 0.009304 PAG +1.0791.2420.131 ± 0.007298 PAG − 1.1131.3200.158 ± 0.006298 Pf11 .3771.7310.205 ± 0.005302 UBI -LRB- 1D3Z -RRB- bBicelles0 .6950.7880.118 ± 0.005304 CTAB2 .2692.6850.155 ± 0.003304 CAL -LRB- 1NYA -RRB- cPf14 .4514.7280.059 ± 0.001318 Experimental temperature is shown for an easy comparison with δ variationapH 6.5 , ɛNH = 0.26 Hz , Pf1 11 mg/ml , 100 mM NaClbɛNH = 0.15 HzcpH 6.0 ; Pf1 30 mg/ml An effective alignment tensor for each ensemble was calculated using SVD -LRB- Losonczi et al. 1999 -RRB- . Either the experimental or average PALES predicted RDCs were used . Besides the refined structures -LRB- Table 1 -RRB- experimental RDCs were used also with the MD simulated -- PALES aligned structures in what we call the hybrid model -LRB- Table 5 -RRB- . PALES predicted average RDCs were used in conjunction with the MD simulated -- PALES aligned structures -LRB- Table 2 -RRB- . Table 2 and δ parameters for simulated conformational ensembles of the B1 and B3 domain of protein G and human ubiquitin based on PALES-predicted average RDCsProteinMedium -LRB- ° -RRB- -LRB- ° -RRB- δdirectδSVDGB1Negative31 .7 ± 0.231.1 ± 0.20.172 ± 0.0070.109 ± 0.008 Neutral11 .82 ± 0.047.38 ± 0.020.114 ± 0.0010.116 ± 0.008 Positive40 .36 ± 0.0536.23 ± 0.030.385 ± 0.0040.208 ± 0.002 GB3Negative12 .60 ± 0.109.54 ± 0.060.082 ± 0.0030.097 ± 0.009 Neutral11 .82 ± 0.097.75 ± 0.050.096 ± 0.0030.100 ± 0.009 Positive23 .0 ± 0.420.6 ± 0.40.119 ± 0.0100.107 ± 0.007 UBINegative13 .21 ± 0.049.87 ± 0.020.090 ± 0.0010.106 ± 0.003 Neutral16 .95 ± 0.0913.16 ± 0.080.080 ± 0.0020.085 ± 0.005 Positive15 .84 ± 0.0612.86 ± 0.050.092 ± 0.0020.104 ± 0.007 Results and discussion Analysis of experimental data The wealth of high-quality residual dipolar coupling data of the B3 domain of protein G -LRB- GB3 -RRB- and ubiquitin -LRB- UBI -RRB- and their refined structures -LRB- 1P7F and 1D3Z , respectively -RRB- allow us to determine GDOs and to calculate δ values for several cases -LRB- Table 1 -RRB- . The data for calerythrin -LRB- 1NYA -RRB- , a significantly larger protein -LRB- ∼ 20 kDa v. less than 10 kDa -RRB- , is also available -LRB- Tossavainen et al. 2003 -RRB- . The quality of the refined structures in terms of an RMSD measure , referred to as the quality factor -LRB- Clore and Garrett 1999 -RRB- , is in all these cases good . Accordingly , in the evaluation of δ we employ only the NH and CαCO couplings that were used to refine the GB3 , ubiquitin and calerythrin structures . The GDO values were calculated from the experimental dipolar coupling data using a SVD algorithm against the average structures of the refined ensembles . The two most important observations are that and that δ varies from one medium to another . Therefore it seems that there are motions in addition to bond fluctuations and we attribute them , owing to their medium-dependency , at least partly to dynamics modulated alignment . The results are subject to the following uncertainties . The errors in δ were obtained by a Monte-Carlo -LRB- MC -RRB- method from the experimental errors in RDCs . The largest ambiguity originates from the ratio between the NH and CαCO bond length . We used rNH = 1.02 Å -LRB- Jeffrey 1992 , p. 270 -RRB- and -LRB- Engh and Huber 1991 ; Lehmann et al. 1972 -RRB- . An eventual error in the bond length ratio is systematic and affects the absolute δ value , but it does not abolish the variation in δ from one medium to another . It should be noted that customarily when a structure is refined against RDCs rNH is set to 1.04 Å -LRB- Ottiger and Bax 1998 -RRB- to obtain the average directions of the more mobile amides consistent with less mobile bonds , e.g. those of the CαCO vectors . In other words , it is desirable to obtain the same magnitude of alignment tensor irrespective of the couplings employed . Further uncertainty stems from the discrete sampling of directions by the non-uniform and dissimilar distributions of NH and CαCO bonds , but as will be shown later on it does not seem to matter that much . Furthermore , as mentioned above , no motional effects including the consequences of discrete non-uniform sampling can be seen in δ when the excess fluctuations are small compared to SLS2 . Large alignment fluctuations on the other hand lead categorically to nearly uniform sampling of directions . Simple model of wobble A simple approximation of internal bond motions considers fluctuations about the mean direction only as axial , i.e. including just the zero-order spherical harmonics Y00.Assuming that the internal bond -LRB- θ -RRB- and alignment -LRB- -RRB- fluctuations are independent and on different timescales , they can be separated and treated independently -LRB- Brainard and Szabo 1981 ; Petersen and Chan 1977 -RRB- . If an isotropic sampling of bond directions is also assumed , then the combined effect of the fluctuations will be It would then be clear from Eq . 2 that δ values remain invariant even in the presence of alignment fluctuations . However , it is evident from Table 1 that the δ parameter varies from one medium to another implying a coupling between the alignment fluctuations and δ . It is therefore reasoned that can not be factorised . This is not a contradiction since neither of the previously mentioned assumptions are entirely valid in this case . -LRB- i -RRB- The two fluctuations are not completely independent since there is a slight coupling between the alignment and the ps -- ns bond motions -LRB- Louhivuori et al. 2006 -RRB- . -LRB- ii -RRB- Since alignment fluctuations are not a real motion , but rather a manifestation of the state space available in the system , alignment fluctuations can be said to affect all time-scales . Therefore we propose the following simple ad hoc model to describe the combined effect of internal bond motions and alignment frame fluctuations.Essentially this means that we are considering a model where a molecule 's wobble about an average orientation amplifies the effect of internal bond motions . As a consequence the effective opening angle of internal bond motions is increased from the initial value of θo by In the absence of alignment fluctuations -LRB- -RRB- θo can be calculated using Eq . 5 from the GDO values determined for the MD simulated ensembles.Accordingly , θo for NH and CαCO were calculated from the previously mentioned MD-derived and and found to be 11.82 ° and 9.99 ° , respectively . Then and were calculated using Eq . 4 and plotted as functions of increasing -LRB- Fig . 2 -RRB- . Finally , δ versus was calculated from and using Eq . 2 . Fig. 2Calculated effective order parameters for the NH -LRB- dotted -RRB- and CαCO -LRB- dashed -RRB- bonds and the δ parameter calculated from them as the molecule is subject to a fluctuating alignment of increasing angle in addition to internal bond fluctuations When the internal bond and alignment fluctuations combined reach the magic angle the alignment is lost all together . The normalized difference in the NH and CαCO probed order , denoted by δ , is available from measurements and shown in Fig. 2 for the B3 domain of protein G in CTAB doped bicelles , positively and negatively charged stretched polyacrylamide gels , polyethylene-glycol lamella and filamentous phages , and for ubiquitin in bicelles and CTAB doped bicelles . The δ value of calerythrin was smaller than the proposed general minimum of 0.081 and is therefore omitted . The symbols in the figure are larger than the errors obtained by MC analysis . It needs to be stressed that should not be interpreted as a real measure of molecular motion since alignment fluctuations are only an ensemble property affecting RDC data . When the experimental δ values are placed on the -LRB- δ , Ω -RRB- - curve we see that for both GB3 and ubiquitin in bicelle medium the effect of DMA is small enough to be comparable to that of bond fluctuations . Non-axial bond fluctuations will naturally complicate the situation and might invalidate such a comparison . The precision in δ is modest owing to the functional form of the - curve . In other media , particularly in those carrying surface charges on the nematogen , the alignments fluctuate noticeably . For example in filamentous phages the alignment of GB3 fluctuates even more than 13 ° . Thus ϑ2 may fall even below 0.7 . However , this does not mean that the molecule is somehow reorienting itself with such large-amplitude motions . It only tells that quite likely there are more than one major alignment modes separated from each other sufficiently to give the impression of large-scale motions if the alignment fluctuations are interpreted simply as real , molecular fluctuations around an average direction as was done in Eq . 4 . Nonetheless , the medium-dependent variation in δ shows that DMA contributes to RDC-probed dynamics . Analysis of simulation data The sources of the medium-dependent variation in δ found from the experimental data can be many . Fortunately , they can be assessed via computer simulations . We consider the variation in the protein shape and charge distribution due to the ps -- ns dynamics . These fluctuations give rise to a family of conformations whose members do not all align in exactly the same way . Simultaneous variation in the shape and net electric dipole moment may lead to a substantial alignment fluctuation . However , it is also conceivable that dynamics of the nematogen contributes to the protein alignment dispersion . Other microscopic heterogeneity in obstructing nematogens may also add to the variation of protein alignments but we are unequipped to examine these effects . Neither are the possible effects of hydration fully explored in this study . The average NH and CαCO RDCs of the simulated conformational ensembles were calculated and the GDO values were determined using SVD against the average structure of the ensemble . The average of the cosine matrix cicj of Eq . 1 was taken to present the best possible average structure . In this way we aimed to mimic the experimental procedure where GDOs were determined from the measured couplings against the refined structure . Alternatively , the knowledge of all NH and CαCO vectors of the dispersed ensembles allowed us to calculate directly of Eq . 3 and hence also the order parameters and δ for the various cases . The two methods , direct and SVD , give similar δ values , with only GB1 in positive alignment medium showing a larger discrepancy -LRB- Table 2 -RRB- . Since both exhibit similar overall tendencies the methods can be assumed to be qualitatively consistent . The alignment simulations in the neutral , positively and negatively charged media were not intended to match specifically any of the experimental conditions , but nevertheless the values are somewhat comparable . The simulated δ values are more uniform , but comparable in size -LRB- Table 2 -RRB- . Only the B1 domain of protein G seems to be significantly susceptible to DMA . The lack of dispersion in δ was unexpected in light of the clear dispersion found from experimental data -LRB- Table 1 -RRB- . Because of this and since the limited sampling of GB3 leaves a shadow of doubt on the exact values reported in Table 2 , further work was done to understand the source for the lack of dispersion in δ . First , non-uniform sampling of bond directions was addressed . Second , the possible increase in PALES-predicted alignment dispersion due to hydration was considered . Third , a hybrid model was used to circumvent any shortcomings in PALES-predicted RDCs . Non-uniform bond direction sampling The finite sampling of bond directions may influence the δ parameter . Therefore , we calculated the fraction of vectors oriented along the three principal directions as suggested by Fushman et al. -LRB- 2000 -RRB- . The fractions fi are a convenient measure of the uniformity of the bond direction sampling . In the case of uniform sampling whereas a significant deviation from 1/3 is a sign of non-uniform sampling . The Fushman-fractions calculated from the MD ensembles show gratifyingly that the sampling is rather uniform -LRB- Table 3 -RRB- . Table 3The fraction of vectors oriented along the three principal axis calculated for the MD simulated ensembles of GB1 , GB3 and ubiquitinProteinBondfzfyfxGB1NH0 .540.260.20 CαCO0 .450.290.26 GB3NH0 .550.260.19 CαCO0 .450.290.26 UBINH0 .490.310.21 CαCO0 .370.340.29 Nevertheless , the possible effects of discrete , non-uniform sampling of bond directions was tested using the MD ensembles . The CαCO bonds of every conformation were first rotated one residue at a time to point , on average , at the same direction as the NH bonds did , on average . A new set of RDCs was then calculated using the twisted structures and the original Saupe matrices . Singular value decomposition was then used to obtain an effective GDO value using the twisted structures and the new average RDCs . From the NH and CαCO GDO values the δ parameter was calculated using Eq . 2 . As can be seen from Table 4 , δ parameters changed , but mostly within the margins of error . Both GB1 in positively charged medium and ubiquitin in neutral medium experience a sharp drop in δ . It seems that this is due to the fact that the CαCO bonds rotated pre-dominantly closer to the magic angle diminishing CαCO couplings sufficiently to render them much more labile in the face of the applied MC error . However , non-uniform bond direction sampling does not seem to influence δ significantly in most cases.Table 4Alignment fluctuations in the MD ensemble before -LRB- δSVD -RRB- and after -LRB- δ ′ SVD -RRB- CαCO bonds were superimposed on NH bondsProteinMediumδSVDδ ′ SVDGB1Negative0 .1090.113 ± 0.008 Neutral0 .1160.116 ± 0.007 Positive0 .2080.130 ± 0.008 GB3Negative0 .0970.116 ± 0.006 Neutral0 .1000.106 ± 0.006 Positive0 .1070.113 ± 0.006 UBINegative0 .1060.109 ± 0.003 Neutral0 .0850.018 ± 0.008 Positive0 .1040.092 ± 0.007 Table 5Hybrid modelProteinMediumδδhybridGB3CTAB0 .1170.133 ± 0.005 Pf10 .2050.265 ± 0.004 UBIBicelles0 .1180.093 ± 0.008 CTAB0 .1550.139 ± 0.006 Alignment fluctuations in simulated conformational ensembles of the B3 domain of protein G and human ubiquitin based on experimental RDCs -LRB- δhybrid -RRB- compared to those in the refined , experimental structures -LRB- δ -RRB- Hydration shell Since the MD simulated conformational ensembles seemed to be less susceptible to DMA than NMR-based ensembles , it was plausible that PALES failed to impose a realistic dispersion of alignments . We hypothesised that the addition of a hydration shell to the molecules would make them more globular and therefore more susceptible to alignment dispersion due to steric interactions . To test whether this hypothesis could account for the observed lack of dispersion , a hydration layer needed to be added to the molecules . This was done with a rough model of the hydration shell in the form of increased atomic radii in PALES . Atomic radii were increased by 1 , 2 , 3 , and 4 Å , but no increase in DMA was observed neither for GB1 nor for ubiquitin . The lack of a hydration shell does not therefore seem to be the cause for the difference in DMA between simulations and experiments . Hybrid model Another possibility was that PALES dispersed the alignments sufficiently , but that the predicted RDCs had some issues that were reflected in the effective alignment and ultimately in δ . To overcome this , we calculated the effective alignments of the MD ensembles using experimental RDCs instead of PALES-predicted ones . This was done for GB3 in Pf1 and CTAB-doped bicelle media and for ubiquitin in bicelle media with and without CTAB . As can be seen from Table 5 and Fig. 3 this seems to be the major cause for the lack of δ-dispersion . What this suggests is that when experimental RDCs are available DMA can be estimated consistently from a MD-simulated conformational ensemble even without structures refined against experimental RDCs.Fig . 3Hybrid model . Calculated effective order parameters for the NH -LRB- dotted -RRB- and CαCO -LRB- dashed -RRB- bonds and the δ parameter calculated from them as the MD simulated conformations are subject to a fluctuating alignment of increasing angle in addition to internal bond fluctuations Competition of interactions In the neutral medium only the molecular shape fluctuations contribute and DMA is comparable to the internal bond vector fluctuations . Neither in the simulation nor in the experimental data is there a lot of difference between the smaller molecules GB3 and ubiquitin . Calerythrin resembles more an oblate ellipsoid -LRB- Fig. 4 -RRB- and is expected to fluctuate less than the smaller , globular proteins in the absence of electrostatic interactions.Fig . 4Causes of molecular alignment fluctuations for -LRB- a -RRB- GB1 , -LRB- b -RRB- GB3 , -LRB- c -RRB- ubiquitin and -LRB- d -RRB- calerythrin illustrated for example conformations . The variation in the molecular shape and charge distribution are simplified by showing the molecular principle axes -LRB- grey -RRB- and net electric dipole moments -LRB- orange -RRB- It is more intricate to rationalize the reduced order parameters in a charged media as both molecular shape and charge distribution fluctuations are present . It may not be possible to simplify the dynamics of a complex set of interactions to provide lucid understanding to the causes of DMA . To begin with , GB1 , GB3 , ubiquitin and calerythrin carry under experimental conditions a net charge of − 1.22 , − 3.09 , +1.39 and − 8.45 , respectively . In the repulsive electrostatic potential the alignment is , to a crude approximation , governed by the direction and size of the net electric dipole moment in relation to the molecular shape tensor . A competition between the steric and electrostatic alignment arises when the dipole moment is mostly along the long axis of the molecule and comparatively small . GB1 is a good example of this -LRB- Fig. 4 -RRB- . In GB1 dipole moments are pointing roughly to the middle of the long and short axis in two slightly separated groups . The situation is similar in GB3 , but with the dipole moments concentrated in a single , tight group . Furthermore , the dipole moments in GB3 are larger than in GB1 and dominate the alignment . In the globular ubiquitin the dipole moments are directed along the shortest of the molecular axes . Thus both the shape and electrostatics act in synergy to narrow the cone of alignments . In spite of this the globular shape of ubiquitin ensures that modest alignment fluctuations remain in charged media . In the refined structures of calerythrin the dipole moments are spread out slightly more than in the MD simulated ensemble of GB1 and directed similarly roughly to the middle of the long and short axis . Alignment fluctuations in calerythrin are small -LRB- Table 1 -RRB- , even though the combination of an oblate ellipsoidal shape with dipole moments directed away from the short axis suggest a competition between the steric and electrostatic alignments . Calerythrin contains a flexible hinge-region that has a slightly ambiguous structure in 1NYA -LRB- Tossavainen et al. 2003 -RRB- . It is thus possible that the lack of restraints in the structural refinement has led to somewhat more compact structures with slightly distorted net dipole moments . Analysis of an attractive potential is more involved and not easily reduced to the analysis of the net electric dipole moment relative to the shape tensor . The variation in the position of the net charge influences the alignment that can fluctuate substantially as exemplified by the aforementioned δ values for GB3 . In general a small globular protein that carries many charges and yet only a small net electric dipole moment is the most vulnerable to molecular alignment fluctuations . The shape as well as the charge distribution is perturbed by dynamics of long side-chains at the molecular surface . For large proteins the effects are expected to have less impact on the overall molecular alignment . Conclusions Internal motions are , at least to a good approximation , medium-independent . Therefore one would expect that e.g. relative differences between NH and CαCO bond fluctuations , denoted by the δ parameter , would remain the same from one medium to another . However , we find that this is not the case for protein G and ubiquitin . The changes in δ from one medium to another imply the presence of an additional medium-dependent ensemble property involved in the alignment phenomenon . The simulations suggest that the effective alignment of a molecule fluctuates as a response to the variation in molecular shape and charge distribution caused by protein dynamics . This alignment modulation is at its highest when steric and electrostatic interactions compete for the dominance in a small globular protein . Also flexible loops and termini may cause a fluctuating alignment . The alignment fluctuation as a phenomenon is known and e.g. used to point out domain -- domain motions in modular proteins -LRB- Bewley and Clore 2000 ; Fischer et al. 1999 -RRB- and flexibility of polypeptides -LRB- Chou et al. 2001 ; Goto et al. 2001 -RRB- . Here we were able to consider only alignment effects due to protein dynamics that occur in the ps -- ns range owing to the limitations of molecular dynamics simulations . Other states accessible via slower motions are of course also expected to contribute to the variation in molecular alignment depending on their population , shapes and charge distributions . We also expect that dynamics of nematogens and other variation in the media contribute as well to the bond vector dispersion underlying the observed RDC signals . It is perhaps perplexing that molecular alignment fluctuations do not show up as clear inconsistencies in refinement of protein structures in particular when a number of RDCs obtained from measurements in various media are used simultaneously . It should be emphasized that the dynamics modulated alignment is a process that is nearly uncorrelated from the intrinsic vector fluctuations . Consequently it will , to an excellent approximation , only scale RDCs but leave their directional information content , used in the structure determination , intact . Thus the averaging due to DMA appears much as the averaging due to the molecular tumbling . Even a substantial wobble in the alignment can be compensated by increasing the strength of LC-medium to acquire large enough couplings for quantitative analyses . It should be stressed that the presence of DMA does not , for example , invalidate the recent finding -LRB- Bernadó et al. 2005 -RRB- of long-range interactions in α-Synuclein nor the previously mentioned supra-τc backbone motions , but gives a rationale for the low S2 values . Perhaps indicative of fluctuating alignments are the challenges in predicting precisely RDC-data on the basis of a single structure . In studies of dynamics where the dispersion of a vector direction rather than its average direction is of interest we expect that the alignment fluctuations are worth to consider as they will inevitably incorporate into the RDC-based order parameter . In this study the evidence of molecular alignment fluctuation was established using the average molecular parameter , general degree of order . Consequently the site-specific variation in the order and its correlation to the secondary structure that have been reported in the RDC-probed dynamics studies was not addressed . It is conceivable that an alignment fluctuation could result in some site-specific variation in ϑ2 depending on the direction of the bonds , but unlikely in any correlated variations .

O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

protein dynamics
residual dipolar couplings