Speed, Variability, and Timing of Motor Output in ADHD: Which Measures are Useful for Endophenotypic Research?

Attention-Deficit/Hyperactivity Disorder (ADHD) shares a genetic basis with motor coordination problems and probably motor timing problems. In line with this, comparable problems in motor timing should be observed in first degree relatives and might, therefore, form a suitable endophenotypic candidate. This hypothesis was investigated in 238 ADHD-families (545 children) and 147 control-families (271 children). A motor timing task was administered, in which children had to produce a 1,000 ms interval. In addition to this task, two basic motor tasks were administered to examine speed and variability of motor output, when no timing component was required. Results indicated that variability in motor timing is a useful endophenotypic candidate: It was clearly associated with ADHD, it was also present in non-affected siblings, and it correlated within families. Accuracy (under- versus over-production) in motor timing appeared less useful: Even though accuracy was associated with ADHD (probands and affected siblings had a tendency to under-produce the 1,000 ms interval compared to controls), non-affected siblings did not differ from controls and sibling correlations were only marginally significant. Slow and variable motor output without timing component also appears present in ADHD, but not in non-affected siblings, suggesting these deficits not to be related to a familial vulnerability for ADHD. Deficits in motor timing could not be explained by deficits already present in basic motor output without a timing component. This suggests abnormalities in motor timing were predominantly related to deficient motor timing processes and not to general deficient motor functioning. The finding that deficits in motor timing run in ADHD-families suggests this to be a fruitful domain for further exploration in relation to the genetic underpinnings of ADHD.
Introduction
It has become apparent from twin- and adoption studies that the development of the Attention-Deficit/Hyperactivity Disorder (ADHD) (American Psychiatric Association 1994) is strongly genetically based (Faraone et al. 2005; Willcutt, in press). Overall heritability estimates exceed 0.70 (Faraone and Doyle 2000; Smalley 1997) and are fairly constant across studies conducted worldwide (Faraone et al. 2005). Research aimed at the molecular genetic basis of the disorder (genotype) has had success in identifying some susceptibility genes by using information from behaviorally observable symptoms (phenotype) (Faraone et al. 2005). However, the current knowledge about the genetic basis of the disorder is still limited and the causal pathway(s) leading from genotype to phenotype have yet to be revealed.
Both issues have been the aims of investigation in endophenotypic research. Endophenotypes are defined as heritable, vulnerability traits that mark a risk for the development of the disorder (Almasy and Blangero 2001; Castellanos and Tannock 2002; Doyle et al. 2005; Gottesman and Gould 2003; Skuse 2001; Waldman 2005; Zobel and Maier 2004). They are conceptualized as forming an intermediate link between the genotype and phenotype and are presumably genetically less complex compared to phenotypic symptoms (Gottesman and Gould 2003; Waldman 2005). Because of these characteristics, it is thought that, compared to phenotypic symptoms, endophenotypes are more suitable for detecting disease genes and for unraveling the modes of actions of these disease genes.
Several criteria have been proposed to discriminate an endophenotype from other biological markers that are not causally involved in the disorder but are merely associated with the disorder (Durston et al. 2004; Gottesman and Gould 2003). Although these criteria do not appear to be universally agreed upon, several key criteria have emerged from the literature (Almasy and Blangero 2001; Castellanos and Tannock 2002; Doyle et al. 2005; Gottesman and Gould 2003; Skuse 2001; Waldman 2005; Zobel and Maier 2004). First, an endophenotype should co-occur with the disorder, although given the heterogeneity of ADHD, it is unlikely that a single endophenotype will occur in all patients with ADHD (Doyle et al. 2005). Second, non-affected relatives should also exhibit the endophenotype to some extent, indicating that the endophenotype contributes to a familial susceptibility for the disorder. Because non-affected relatives share, on average, 50% of their genes with the affected family member, it is theorized that they also carry some of the susceptibility genes of ADHD which translate into subtle abnormalities in the endophenotype (Gottesman and Gould 2003; Waldman 2005). Third, the endophenotype should show familial resemblance, reflected by significant sibling correlations for the endophenotypic measure. In addition to these criteria, several other important characteristics of an endophenotype have been put forward, such as reliability of measurement, stability over time (i.e. expressed regardless whether or not the disorder is currently manifested), and acting as a mediator and/or moderator between genes and disorder (Doyle et al. 2005; Waldman 2005). The focus of our study lies on the first three key criteria of an endophenotype.
Possible endophenotypic candidates might be found in the deficits in motor output associated with ADHD. Fine motor coordination problems as well as gross motor coordination problems are frequently observed in co-occurrence with ADHD (Carte et al. 1996; Korkman and Pesonen 1994; Marcotte and Stern 1997; Piek et al. 1999; Pitcher et al. 2003; Whitmont and Clark 1996). Because of this highly frequent co-occurrence, it is feasible that motor problems might be genetically related to the risk for developing ADHD (Gillberg 2003), which has indeed been reported recently (Martin et al. 2006). This might make motor measures useful endophenotypic candidates, which was underlined by the findings of motor control difficulties in non-affected siblings of children with ADHD (Rommelse et al. 2007a; Slaats-Willemse et al. 2005).
A specific aspect of motor output that might serve as a candidate endophenotype is temporal organization (Castellanos and Tannock 2002; Waldman et al. 2006). Temporal organization of motor output refers to the timing of movements (i.e. motor timing) and seems to be predominantly mediated by the cerebellum and basal ganglia and their reciprocal connections with the cerebral cortex (Handy et al. 2003; Harrington et al. 1998; Ivry 1996; Nenadic et al. 2003). The timing of motor output is hypothesized to consist of two components: a clock component, which reflects central time keeping operations, and a motor delay component, which reflects random variability due to response implementation processes (Harrington et al. 1998; Keele et al. 1985; Wing and Kristofferson 1973). Children with ADHD seem to be predominantly impaired in the clock component, as evidenced by paradigms specifically assessing timing operations independent of motor operations, such as duration discrimination tasks (Keele et al. 1985; see for review Toplak et al. 2006). The motor component is possibly best assessed using simple reaction time tasks and free Tapping tasks in which timing is minimized. Some have found no impairments in children with ADHD (Kalff et al. 2003; Seidman et al. 1997, 2000), others have (Kalff et al. 2005). By combining both components, one can assess timing that is predominantly related to motor output, which reflects the interplay between timing and motor skills. Studies using these motor timing tasks have, however, not revealed consistent results of impairments in children with ADHD, possibly due to inconsistencies in methodological approaches across studies (Toplak et al. 2006). However, greater variability in motor output when a timing component is required is a frequently reported finding in children with ADHD (Leth-Steensen et al. 2000; Pitcher et al. 2002; Rubia et al. 1999, 2003; Toplak et al. 2006; Van Meel et al. 2005). None of these studies, however, used a measure of basic motor speed/variability (without requirements regarding timing/rhythm) in addition to the motor timing measure. Therefore, it remains unclear whether the variability in motor timing is primarily due to variability of motor processes, or due to variability of timing processes or both. Here, we administered two simple motor tasks in addition to the motor timing task, in order to investigate whether deficits were specifically related to the timing of motor output or whether deficits were also observed in tasks that do not require timing of motor output.
The current study is, to our knowledge, the first to examine motor timing abilities in not only children with ADHD, but also in their siblings, in order to investigate whether motor timing measures might be suitable endophenotypic candidates. Previous studies on related topics have shown that non-affected siblings of children with ADHD have comparable problems in time reproduction skills as their affected siblings (Rommelse et al. 2007b) and that variability in reaction time shows familial overlap with ADHD (Andreou et al. 2007), giving support to the hypothesis that motor timing measures may be suitable endophenotypic candidates. It was expected that (1) children with ADHD would be impaired on motor timing measures and not (or to a lesser extent) on motor measures without a timing component, indicating an association between ADHD and motor timing deficits. Furthermore, we expected (2) to find similar findings in the non-affected siblings of the children with ADHD, suggesting motor timing deficits are not merely associated with the disorder. Last, we expected (3) to find correlations between siblings indicating familial resemblance on motor timing measures.
Method
Participants
Families with at least one child with the combined subtype of ADHD (proband) and at least one additional sibling (regardless of possible ADHD-status) were recruited in order to participate in the Dutch part of the International Multicenter ADHD Genes study (IMAGE). The IMAGE project is an international collaborative study that aims to identify genes that increase the risk for ADHD using QTL linkage and association strategies (Brookes et al. 2006). Additional control families were recruited from primary and high schools from the same geographical regions as the participating ADHD-families. Controls and their first degree relatives had no formal or suspected ADHD diagnosis. A total of 238 ADHD-families and 147 control-families fulfilled inclusion and exclusion criteria. Within the ADHD-families, 238 probands (all with combined subtype of ADHD), 112 affected siblings (64 with combined subtype, 28 with inattentive subtype and 20 with hyperactive-impulsive subtype of ADHD) and 195 non-affected siblings participated. Control-families consisted of 271 children. For 51 control children, no additional control sibling could be recruited for the study (see for an overview Tables 1, 2).
Table 1Distribution of family sizesNumber of siblings within a familyADHDControlFamilies (n)Individuals (n)Families (n)Individuals (n)100515121773547214435315920604832416Total238545147271Note: ADHD = Attention-Deficit/Hyperactivity DisorderTable 2Distribution of affected and non-affected siblings within ADHD-familiesTotal number of children within a familyDiagnostic statusADHD-families (n)Proband (n)Affected siblings (n)Non-affected siblings (n)211–621–1115312–7111241–222413–2121111241–31Total238Note: ADHD = Attention-Deficit/Hyperactivity Disorder
All children were between the ages of 5 and 19 years and were of European Caucasian descent. Participants were excluded, if they had an IQ < 70, a diagnosis of autism, epilepsy, brain disorders or known genetic disorders, such as Down syndrome or Fragile-X-syndrome.
Within an ADHD-family, both proband and siblings were similarly screened using the standard procedures of the IMAGE project described by Brookes et al. (2006). Briefly, screening questionnaires (parent and teacher Conners’ long version rating scales [Conners 1996] and parent and teacher Strengths and Difficulties Questionnaires [SDQ, Goodman 1997]), were used to identify children with ADHD symptoms. T-scores ≥ 63 on the Conners’-N-scale (DSM-IV total symptom score) and scores > 90th percentile on the SDQ-hyperactivity scale were considered as clinical. For all children within a family scoring clinically on any of the questionnaires, a semi-structured, standardized, investigator-based interview was administered separately for each child: the Parental Account of Children’s Symptoms (PACS; Taylor 1986). The PACS covers DSM-IV symptoms of ADHD, conduct disorder, oppositional defiant disorder, anxiety, mood, and other internalizing disorders. The section on autistic behaviour traits was administered, if a clinical score (raw score ≥ 15) was obtained on the Social Communication Questionnaire (SCQ; Berument et al. 1999). A standardised algorithm was applied to the PACS and parent rated Conners’ to derive each of the 18 DSM-IV ADHD items, providing operational definitions for each behavioural symptom. These were combined with items that were scored 2 (‘pretty much true’) or 3 (‘very much true’) in the teacher rated Conners’ ADHD subscale to generate the total number of hyperactive-impulsive and inattentive symptoms of the DSM-IV. Situational pervasiveness was defined as at least one symptom occurring within two or more different situations as indicated by the parents in the PACS interview as well as the presence of at least one symptom scoring 2 or 3 on the ADHD subscale as indicated by teachers on the Conners’. Siblings were regarded as non-affected, if they obtained scores in the non-clinical range on both the parent and teacher questionnaires (Conners’-N-scale: T-score ≤ 62, SDQ < 90th percentile). No PACS interview was administered concerning non-affected siblings.
The Conners’ long version for both parents and teachers was completed for control children. Control children had to obtain non-clinical scores on both the parent and teacher version (Conners’-N-scale: T-score ≤ 62). Table 3 provides the characteristics of the four groups.
Table 3Sample characteristicsProbandsAffected siblingsNon-affected siblingsNormal controlsF3,812Contrastsn = 238n = 112n = 195n = 271MSDMSDMSDMSDAge in years12.02.512.03.411.53.611.63.2ns% Right handed91.187.589.285.5nsa% Male84.556.345.140.6113.9*a1 > 2,3,42 = 3 & 2 > 43 = 4Estimated full scale IQ97.913.0100.710.6103.810.9106.010.223.5*1 = 2 & 1 < 3 = 42 = 3 & 2 < 43 = 4Conners’ parent DSM-IV    Inattentive71.18.466.011.647.97.046.54.8585.4*1 > 2 > 3 = 4    Hyperactive-impulsive79.19.267.813.649.06.947.35.1767.3*1 > 2 > 3 = 4    Total76.98.668.311.648.26.846.54.5875.7*1 > 2 > 3 = 4Conners’ teacher DSM-IV    Inattentive66.09.161.710.248.36.046.44.6386.3*1 > 2 > 3 = 4    Hyperactive-impulsive70.210.763.513.348.36.547.25.0378.1*1 > 2 > 3 = 4    Total69.89.863.811.448.35.846.44.5485.8*1 > 2 > 3 = 4ADHD diagnosis    Inattentive–28––    Hyperactive-impulsive–20––    Combined23864––Note: 1 = Probands; 2 = Affected siblings; 3 = Non-affected siblings; 4 = Normal controlsADHD = Attention-Deficit/Hyperactivity Disorder; DSM-IV = Diagnostic and Statistical Manual for Mental Disorders (4th edition)* P < 0.001; a χ2; Contrasts based on p-values of 0.05
Measures
Motor Timing Task
This task was designed to measure the accuracy and variability of motor timing (Van Meel et al. 2005). Subjects were instructed to press a button with their preferred index finger when they thought a 1-second time interval had elapsed. The start of the interval was announced by a tone. After the subject’s response, visual feedback concerning the accuracy of the response was presented on the screen, indicating whether the response was correct, too short or too long. A response was regarded as correct, if it fell between the lower and upper boundary set by a dynamic tracking algorithm. Boundaries were set at 500 to 1,500 ms at the beginning of the task. If the response fell within these boundaries, the boundaries of the subsequent trial were narrowed by 100 ms. Likewise, the boundaries of the subsequent trial were widened with 100 ms, if the response on the previous trial fell outside the boundaries.
The practice session consisted of 20 trials, the experimental session of 80 trials. Both sessions were preceded by presenting 10 times a cartoon figure for exactly 1 s on the screen to demonstrate the duration of 1 s (Van Meel et al. 2005). Dependent measures were accuracy (median of productions in ms, which reflects under- versus over-production) and variability (SD of productions in ms).
Baseline Speed task
This task was designed to measure the speed and variability of motor output in response to an external cue and comparable to a simple reaction time task (De Sonneville 1999). Subjects were required to press a key as quickly as possible, when a fixation cross in the centre of a computer screen changed into a white square. Immediately following the response, the white square changed back into the fixation cross. The time interval between a response and the emergence of the next white square varied randomly between 500 and 2,500 ms in order to prevent anticipation strategies.
A practice session (10 trials) and an experimental session (32 trials) were administered for both hands separately. The task was first practised and executed with the index finger of the non-preferred hand, thereafter practised and executed with the index finger of the preferred hand. Dependent measures were the speed (mean reaction time in ms) and variability (SD of reaction times in ms) of responses.
Tapping task
This task measured the speed and variability of self-generated motor output (without internal or external cues) (De Sonneville 1999). Subjects were required to tap as frequently as possible within an interval of 18 s. The beginning and end of the interval were announced by a tone. During tapping, the number of taps was continuously counted and displayed on the screen.
A practice session (5 s) and an experimental session (18 s) were administered for both hands separately. The task was first practised and executed with the index finger of the non-preferred hand, thereafter practised and executed with the index finger of the preferred hand. Dependent measures were speed (mean intertap interval in ms) and variability (SD of intertap intervals in ms) of motor output.
Intelligence
Full-scale IQ was estimated by four subtests of the WISC-III (Wechsler 2002) or WAIS-III (Wechsler 2000) (depending on the child’s age): Vocabulary, Similarities, Block Design and Picture Completion. These subtests are known to correlate between .90–.95 with the Full-scale IQ (Groth-Marnat 1997).
Procedure
Testing of ADHD children and their siblings took place at the VU University Amsterdam or at the Radboud University Nijmegen Medical Centre and was conducted simultaneously for children within a family. Psychostimulants were discontinued for at least 48 h before testing took place (Pelham et al. 1999). Participants that took other medication than stimulants to suppress their symptoms of ADHD were also off medication during testing. The medication of these children was gradually decreased in line with standard procedures to allow for sufficient wash-out. Children were motivated with small breaks. At the end of the session, a gift worth approximately € 4, was given. Control children were tested in a similar way in a quiet room at their school. The study had medical-ethical approval.
Analyses
The percentage of missing data was less than 5% for each of the dependent variables. Missing data were replaced by using the Estimation Maximization procedure (Tabachnick and Fidell 2001). None of the dependent variables was normally distributed. Therefore, variables were successfully normalized by applying a Van der Waerden transformation (Statistical Package for the Social Sciences [SPSS] version 14). The Van der Waerden transformation transforms raw scores into z-scores corresponding to the estimated cumulative proportion of the distribution corresponding to a particular rank. It is defined by the formula r/(w + 1), in which w is the sum of the case weights and r is the rank, ranging from 1 to w (Lehmann 1975). Cases are given different weights by means of simulated replication. The value of the new standardized variable equals the sum of case weights (SPSS version 14). This transformation has two important advantages: It handles the (extreme) influence outliers may have on the data, by ranking them as (very) high or low within the normal distribution, and the comparison between the variables was facilitated since the variables were all depicted on the same scale. Homogeneity of variance was tested by calculating Fmax (ratio of the largest cell variance to the smallest). Since sample sizes were relatively equal (i.e. within a ratio of 4 to 1 or less), an Fmax of 10 and lower was acceptable (Tabachnick and Fidell 2001). For all six normalized variables, the ratio was well within acceptable limits (all below 1.37). Alpha was set at .01 for all tests. Following Cohen’s guidelines (Cohen 1988), effect sizes were defined in terms of the percentage of explained variance: 1, 9 and 25% were used to define small, medium, and large effects. These figures translate into η2-values of 0.01, 0.06 and 0.14.
Linear mixed models were used for the analyses. The linear mixed model expands the general linear model so that the data are permitted to exhibit correlated variability. This model allows for the investigation of group differences while correcting for the non-independency of data (i.e. more than one child participated per family, which resulted in related measurements within groups and between groups). In first instance, we tested the main effects of possible confounders (hand, gender, IQ, and age) on performance on the three different tasks. This was done within the control group to avoid dependency with the factor group. Thereafter, interactions between group and the confounders were examined to investigate whether effects of possible confounders were comparable across groups. In second instance, we investigated whether group differences existed for each task measure. Group was used as factor (four groups: proband, affected sibling, non-affected sibling, and control), age (linear and/or curvilinear) as covariate(s), and family as random effect to account for within family correlation. Pairwise comparisons were used to compare groups and it was analyzed whether a linear trend was present in polynomial group contrasts. It was expected that probands and affected siblings performed worse than controls (mainly on the motor timing measures but not or to a lesser extent on the other motor measures), indicating an association between motor timing deficits and ADHD. It was also expected that the non-affected siblings performed worse than controls and formed an intermediate group in between their affected siblings and controls, suggesting motor timing deficits were related to a familial susceptibility to the disorder. The Conners’ Total ADHD scale (averaged across parents and teachers) was used as an additional covariate in the analyses to rule out that possible deficits in the non-affected siblings group could be attributed to sub-clinical ADHD symptoms in this group. Correlations (with 95% confidence intervals) were calculated between siblings to test the familial resemblance of the motor measures (Statistical Analysis for Genetic Epidemiology [S.A.G.E] 5.3.1, 2007).
Results
Testing of possible confounders
Main effects of hand, gender, IQ, and age
We tested for the effects of hand, gender, IQ, and age within the control group to avoid dependency with the factor group. No significant effect of hand was found on the Baseline Speed task (F(1, 271.0) = 0.05, P = .83, ηp2 < .01), but there was a significant effect on the Tapping task (F(1, 271.0) = 5.99, P = .02, ηp2 = .02). Control children were faster and less variable, when performing the Tapping task with their right hand than their left hand, likely reflecting an effect of hand dominance. The Motor Timing task was only performed with the preferred hand. Gender had no effect on the Motor Timing task and Baseline Speed task (F(1, 241.5) = 0.03, P = .87, ηp2 < .01 and F(1, 229.5) = 0.36, P = .55, ηp2 < .01, respectively), but had an effect on the Tapping task (F(1, 225.1) = 14.91, P < .001, ηp2 = .05). Control boys were faster and less variable in their tapping performance than control girls. No effect of IQ was found on the Motor Timing task, Baseline Speed task, or Tapping task (F(1, 258.4) = 0.20, P = .66, ηp2 < .01, F(1, 254.8) = 0.06, P = .81, ηp2 < .01 and F(1, 259.9) = 0.95, P = .33, ηp2 < .01, respectively). In order to assess whether age could be best modeled in linear and/or curvilinear terms, we first analyzed the linear effect of age and then in a second model analyzed the quadratic effect of age, while keeping the linear term for age in the model. In this manner, the incremental contribution of the curvilinear relation with age over and above the linear relation was tested. Age (in linear terms) had a strong effect on the Motor Timing task, Baseline Speed task, and Tapping task (F(1, 252.7) = 26.65, P < .001, ηp2 = .22, F(1, 239.1) = 292.38, P < .001, ηp2 = .57, and F(1, 244.5) = 278.31, P < .001, ηp2 = .57, respectively). Older control children were more accurate, faster and less variable in their motor output. Results indicated that when both age terms were implemented in the model, no curvilinear effect of age was present on the Motor Timing task (F(1, 259.3) = 1.34, P = .25), but there was on the Baseline Speed task and Tapping task (F(1, 257.8) = 20.59, P < .001 and F(1, 258.3) = 12.47, P < .001, respectively). No significant interactions were present between gender and age, whether age was modelled in linear or curvilinear terms.
Interactions between group and possible confounders
Group did not interact with hand on the Baseline Speed task (F(3, 816.0) = 1.14, P = .33, ηp2 < .01), but did interact marginally significantly with hand on the Tapping task (F(3, 816.0) = 2.73, P = .04, ηp2 = .01). Group did not interact with gender on the Motor Timing, Baseline Speed, or Tapping tasks (F(3, 762.9) = 1.96, P = .12, ηp2 < .01, F(3, 743.3) = 0.52, P = .67, ηp2 < .01, and F(3, 751.8) = 0.53, P = .66, ηp2 < .01, respectively) nor with IQ (F(3, 730.1) = 2.01, P = .11, ηp2 = .01, F(3, 714.3) = 1.28, P = .28, ηp2 = .01, and F(3, 727.2) = 2.11, P = .09, ηp2 = .01, respectively), nor with linear age (F(3, 732.0) = 1.67, P = .17, ηp2 = .01, F(3, 731.1) = 0.88, P = .45, ηp2 < .01, and F(3, 755.2) = 1.36, P = .26, ηp2 = .01, respectively), nor with curvilinear age (F(3, 727.1) = 1.61, P = .19, ηp2 < .01, F(3, 733.2) = 0.51, P = .67, ηp2 < .01, and F(3, 754.4) = 1.21, P = .31, ηp2 < .01, respectively).
Based on the results of these analyses, it was decided to average the measures across hands to simplify results, since no group differences were found for the percentage of right- and left-handed (Table 3) and since there was only a marginal significant interaction of small effect between group and hand for one of the tasks (Tapping). Furthermore, not included as covariates were IQ (had no effect on motor performance and did not interact with group) and gender (had only a small effect on one of the tasks and even in the opposite direction i.e. boys performing better than girls, and gender did not interact with group). Both the linear and curvilinear effects of age were included as covariates in the analyses for the Baseline Speed task and Tapping task. Only the linear effect of age was included as covariate in the analyses for the Motor Timing task. Raw means and SDs are presented in Table 4.
Table 4Means and standard deviations of the motor measures in msDependent variableProbandAffected siblingNon-affected siblingControlηp2ContrastsMSDMSDMSDMSDMotor timing    Accuracy98199997961,0071141,020100.031 = 2 > 3 = 4    Variability389265375265344260295218.101 = 2 > 3 > 4Baseline Speed    Speed35575356853538135178.021 = 2 > 3 = 4    Variability13285131871238211775.031 = 2 > 3 = 4Tapping    Speed23939248482565124948.01ns    Variability4620482345204418.01nsNote: 1 = Probands; 2 = Affected Siblings; 3 = Non-Affected Siblings; 4 = Controls. ns = not significantScores were averaged across hands for the Baseline Speed and TappingOutliers (|z| > 3) were removed
Endophenotypic analyses
Motor Timing task
A significant small effect of group was found for accuracy (F(3, 532.9) = 7.21, P < .001, ηp2 = .03). Pairwise comparisons indicated that probands and affected siblings did not differ from each other (P = .21). Both differed significantly from controls (P < .001 and P = .02, respectively): probands and (to a lesser extent) affected siblings tended to under-produce the 1,000 ms interval (M = 981 ms and M = 997 ms, respectively) compared to controls (M = 1,020 ms). A tendency to under reproduce appeared to be associated with ADHD, but was not convincingly related to a familial predisposition for the disorder, since non-affected siblings did not show this tendency: they differed significantly from probands (P < .001), marginally significantly from affected siblings (P = .02) but not from controls (P = .08) (see Fig. 1). Using the Conners’ Total ADHD score as covariate did not change the difference between non-affected siblings and controls (P = .04). However, a polynomial group contrast indicated a linear trend to be present (Contrast Estimate [CE] = 0.29, P < .001), suggesting probands performed most abnormal, followed by affected siblings, then non-affected siblings and then controls. Siblings marginally significantly resembled each other (r = .11 confidence interval [CI = .02–.19], P = .02).
Fig. 1Accuracy and variability of motor timing (adjusted for the linear effect of age) in probands, affected siblings, non-affected siblings and control children. Error bars represent 1 standard error from the mean
Groups also differed with respect to the variability of motor timing (medium effect) (F(3, 524.6) = 25.12, P < .001, ηp2 = .10). Pairwise comparisons indicated that probands and affected siblings were equally variable (P = .45) and both were more variable than controls (both P < .001), suggesting ADHD and variability in motor timing were associated. Moreover, variability in motor timing appeared related to a familial predisposition for the disorder, since non-affected siblings formed an intermediate group: They significantly differed from probands, affected siblings, and controls (P < .001, P = .009 and P < .001, respectively). Using the Conners’ Total ADHD score as covariate did not change the difference between non-affected siblings and controls (P = .001). A linear group contrast was present (CE = −0.49, P < .001). A significant familial resemblance was found for variability (r = .29 [CI = .20–.38], P < .001). These findings lend support for variability of motor timing as endophenotype, though the accuracy of motor timing appears only to be associated with ADHD and not conclusively related to a familial susceptibility for the disorder (Fig. 1).
Baseline Speed task
A small but significant effect of group was found for speed (F(3, 537.2) = 6.92, P < .001, ηp2 = .02). Pairwise comparisons revealed that probands and affected siblings did not differ from each other (P = .82) and both were slower than controls (P < .001 and P = .007, respectively), indicating a relationship between speed and ADHD. It appeared that speed was not related to a familial vulnerability for ADHD, since non-affected siblings differed from probands and affected siblings (P < .001 and P = .01, respectively), but not from controls (P = .84). Using the Conners’ Total ADHD score as covariate did not change the difference between non-affected siblings and controls (P = .99). Nevertheless, polynomial group contrasts indicated a linear trend (CE = −0.14, P = .001), suggesting probands to perform most abnormal, followed by affected siblings, then non-affected siblings, and then controls. A significant correlation between siblings was found (r = .29 [CI = .20–.38], P < .001).
Groups differed somewhat (small effect size) in the variability on the Baseline Speed task (F(3, 555.1) = 6.96, P < .001, ηp2 = .03). Pairwise comparisons indicated that probands and affected siblings were equally variable (P = .74) and both groups were more variable than normal controls (P < .001 and P = .003, respectively), signaling an association between ADHD and variability in self generated motor output. Again, non-affected siblings did differ from probands (P = .003) and affected siblings (P = .04), but not from controls (P = .38). Using the Conners’ Total ADHD score as covariate did not change the difference between non-affected siblings and controls (P = .41). Nevertheless, a linear group contrast was present (CE = −0.22, P < .001). Variability correlated between siblings (r = .16 [CI = .07–.25], P < .001). These findings suggest slow and variable motor output in response to an external cue is associated with ADHD, but probably not related to a familial vulnerability for ADHD, since motor output of non-affected siblings resembles that of normal controls more than that of their affected siblings (Fig. 2).
Fig. 2Speed and variability of Baseline Speed (adjusted for the linear and curvilinear effects age) in probands, affected siblings, non-affected siblings and control children. Error bars represent 1 standard error from the mean. Scores were averaged across hands
Tapping Task
No significant effect of group was found for speed (F(3, 547.4) = 1.88, P = .13, ηp2 = .01) or variability (F(3, 553.6) = 1.95, P = .12, ηp2 = .01). No significant linear trend was present in polynomial group contrasts for speed or variability (CE = 0.10, P = .04 and CE = −0.12, P = .03, respectively). Siblings did resemble each other in the speed and variability of tapping (speed: r = .27 [CI = .18–.36], P < .001; variability: r = .18 [CI = .09–.27], P < .001). These findings indicated that speed and variability in self generated motor output were not familially associated with ADHD (Fig. 3).
Fig. 3Speed and variability of tapping (adjusted for the linear and curvilinear effects of age) in probands, affected siblings, non-affected siblings and control children. Error bars represent 1 standard error from the mean. Scores were averaged across hands
Since there were group differences for speed and variability of externally cued motor output (Baseline Speed task), the issue was raised whether the deficits found on the Motor Timing task were primarily related to these group differences in basic motor output. Therefore, analyses were undertaken whereby the speed on the Baseline Speed task was used as an additional covariate in the analyses on accuracy on the Motor Timing task. The variability on the Baseline Speed task was used as additional covariate for the analyses on variability on the Motor Timing task.
The effect of group on accuracy on the Motor Timing task remained significant after accounting for speed on the Baseline Speed task (F(3, 532.4) = 7.51, P < .001, ηp2 = .03). The unadjusted means of the raw (unstandardized) data of the accuracy on the Motor Timing task for probands, affected siblings, non-affected siblings, and controls were: 981, 997, 1,007, and 1,020 ms, respectively. The adjusted means after covarying for speed on the Baseline Speed task were: 979, 998, 997, and 1,018 ms, respectively.
The same was true for variability of motor timing: the medium effect of group remained significant after accounting for variability on the Baseline Speed task (F(3, 528.2) = 21.72, P < .001, ηp2 = .09). The unadjusted means of the raw (unstandardized) data of the variability on the Motor Timing task for probands, affected siblings, non-affected siblings, and controls were: 389, 375, 344, and 295 ms, respectively. The adjusted menas after covarying for the variability on the Baseline Speed task were: 438, 428, 424, and 316 ms, respectively. Group contrasts for accuracy and variability as reported above also remained unchanged. These findings suggest that the deficits found on the Motor Timing task can not be explained by the deficits found in basic motor output.
Discussion
There was investigated whether accuracy and variability of motor timing were viable endophenotypic candidates as reflected by poor performance on these measures in children with ADHD (i.e. indicating an association between the deficits and the disorder), reflected by poor performance in non-affected siblings in between their affected siblings and controls (i.e. suggesting a relation between the deficits and a familial susceptibility for the disorder), and reflected by sibling correlations (i.e. signalling familial resemblance for deficits). We administered two motor tasks in addition to a motor timing task, in order to investigate whether deficits were specifically related to the timing of motor output or whether deficits were also observed in tasks requiring motor output without any timing demands.
Probands and affected siblings were dissociated from controls with respect to accuracy of motor timing. Both groups tended to under-produce the 1,000 ms compared to control children (who tended to over-produce the interval). This finding has been reported previously using exactly the same task (Van Meel et al. 2005) and is comparable to some other studies documenting on under estimation/(re)production in patients with ADHD compared to controls (see for review Toplak et al. 2006). These findings suggest a relation between under reproduction (possibly reflecting a somewhat speeded internal clock and/or impulsivity) and ADHD. The findings were less convincing with respect to non-affected siblings: despite a linear trend in group contrasts, their accuracy of motor timing was more like controls than that of affected siblings. Furthermore, correlations between siblings on accuracy were also modest suggesting familial resemblance for accuracy was present but not strongly. Therefore, accuracy of motor timing seems not to be a strong endophenotypic candidate.
Variability of motor timing, however, convincingly met all characteristics of an endophenotype as investigated in our study: Probands and affected siblings were clearly more variable in their motor output than controls, non-affected siblings also differed significantly from controls and had variability scores in between their affected siblings and controls, and greater variability in motor timing was evidently familial. Greater variability in motor timing in children with ADHD compared to controls concurs with previous studies (Pitcher et al. 2002; Rubia et al. 1999, 2003; Toplak et al. 2006; Van Meel et al. 2005) and suggests variability in motor timing is characteristic of ADHD. Our study adds important knowledge to this topic, showing that non-affected siblings portray a similar type of variability in their motor timing and that siblings resemble each other in the variability of motor timing. These findings suggest the variability in motor timing is not only associated with the disorder, but is related to familial vulnerability for ADHD, which may make it a useful tool in future studies aimed at unraveling the genetic underpinnings of ADHD.
All in all, variability of motor timing may form a fruitful endophenotypic candidate. However, group differences were also present on motor measures that did not require a timing component, suggesting motor deficits not to be specifically related to timing but to be more generalized. Probands and affected siblings were significantly slower and more variable than controls concerning motor output in response to an external cue (Baseline Speed). These findings of slow and variable responding are in line with a study using the same task in young children at risk for ADHD (Kalff et al. 2005) and suggests slow and variable responding are characteristic of ADHD. However, in contrast to variability of motor timing, non-affected siblings did not differ from controls with respect to speed and variability of externally cued motor output. So, despite the finding that slow and variable motor output is associated with ADHD, it does not appear to be convincingly associated with a familial vulnerability for the disorder.
Given that poor motor output was observed in probands and affected siblings (Baseline Speed), it was surprising that no such abnormalities were found in self-generated motor output (Tapping). Probands and affected siblings had a normal speed and variability in self generated motor output. The discrepancy in results between both tasks may lie in the suggestion that Baseline Speed may have required some form of cognitive processing (i.e. registering a stimulus and responding to it), whereas Tapping only required executing a motor action. The normal performance of children with ADHD on the Tapping task is in line with some studies (Seidman et al. 1997, 2000), but in contrast with others (Toplak et al. 2006). This might be explained by the important difference in timing requirements necessary in the Tapping task used here and in some previous studies. Here, no timing was required to execute the Tapping task. The instruction was simply to press the button as often as possible within a certain time interval. However, in other studies the child was required to modify his/her tapping rate to be in synchrony with the stimulus and maintain the rhythm in the absence of the stimulus (Rubia et al. 1999; Toplak et al. 2006). These tasks load differently on timing processes. Our findings suggest that self-generated motor output does not form a viable area of endophenotypic research, even though speed and variability of self-generated motor output correlate within families.
Since group differences were not only present on measures of motor timing, but also on measures of motor output (Baseline Speed), it was investigated whether motor timing impairments may be due to deficits in basic motor output. This appeared not to be the case. Even when speed and variability of basic motor output were used as covariates in the analyses on motor timing, group differences for motor timing remained. These findings suggest abnormalities in the accuracy and variability of motor timing are relatively independent of general deficits in basic motor output (Keele et al. 1985) and suggest abnormalities in motor timing are predominantly related to timing operations and not to motor functioning. Since motor timing appears predominantly regulated by the cerebellum, basal ganglia and their reciprocal connections with the cerebral cortex (Handy et al. 2003; Harrington et al. 1998; Ivry 1996; Nenadic et al. 2003), subcortical regions in addition to cortical regions might be important in the etiology of ADHD (Halperin and Schulz 2006).
Limitations
We did not administer the PACS interview for nonaffected siblings. This might have resulted in undetected ADHD cases in the nonaffected sibling group, which in turn might explain the deficits of this group. However, we do not believe this to be the case, because (1) all siblings were thoroughly screened and, if they scored clinically on any of the screening questionnaires, the PACS interview was administered, and (2) even when symptom severity was used as a covariate, group differences between nonaffected siblings and controls remained significant. Furthermore, including measures aimed at isolating aspects of timing performance, such as time estimation and reproduction paradigms, in addition to the measure of time production would have enhanced the comprehensiveness of our findings with respect to the internal clock. Some previous studies using time estimation and reproduction tasks have reported that children with ADHD performed abnormally (see for review Toplak et al. 2006). We documented previously on time reproduction deficits present in both children with ADHD as well as their non-affected siblings (Rommelse et al. 2007b), suggesting familial deficits in timing in ADHD generalize across timing paradigms and extent beyond motor timing as reported in the current study.
Conclusions
Variability in motor timing appears a useful endophenotypic candidate: It is clearly associated with ADHD, it is also present in non-affected siblings, and it correlates within families. Accuracy (under- versus over production) in motor timing appears less useful: even though accuracy is associated with ADHD (probands and affected siblings have a tendency to under-produce compared to controls), non-affected siblings did not exhibit this tendency and sibling correlations were only marginally significant. There were group differences in motor speed and variability (Baseline Speed task): probands and affected siblings were slower and more variable in their motor output as response to an external cue. Even though siblings resembled each other in their speed and variability, non-affected siblings performed more like controls. These findings suggest that speed and variability of externally cued motor output are associated with having ADHD, but probably not related to a familial vulnerability for the disorder. Interestingly, the speed and variability in self-generated motor output (Tapping) is normal in probands and affected siblings, making it unsuitable to unravel underlying vulnerabilities leading up to ADHD. Deficits in motor timing cannot be explained by deficits already present in basic motor output without a timing component (Baseline Speed), suggesting abnormalities in motor timing are predominantly related to deficient timing operations but not to deficient motor functioning. The finding that deficits in motor timing run in ADHD-families suggests this to be a fruitful domain for further exploration in relation to the genetic underpinnings of ADHD.

adhd
endophenotype
motor timing
siblings
motor speed
motor variability


Solute transport in orthorhombic lysozyme crystals: a molecular simulation study

Long-time equilibrium molecular dynamics simulations were performed to study the passage of a substrate, l-arabinose, through nanopores of orthorhombic hen egg white lysozyme crystals. Cross-linked protein crystals (CLPC), as novel biological nanoporous media, consist of an extensive regular matrix of chiral solvent-filled nanopores via which ions and solutes, e.g. sugars and amino acids, travel in and out. We studied the diffusive motion of arabinose inside protein channels. The computed diffusion coefficients within the crystal were orders of magnitudes lower relative to the diffusion coefficient of the solute in water. This study is valuable for understanding the nature of solute–protein interactions and transport phenomena in CLPCs and provides an understanding of biocatalytic and bioseparation processes using CLPC.
Introduction
Protein crystals are conventionally thought as important elements in structure determination of biomolecules as well as in protein purification (Johnson and Philips 1965; Blundell et al. 2003; Haring and Schnrier 1991). They contain pores that range from approx. 0.3 nm to 10 nm and occupy 25–75% of the crystal volume (Bishop and Richards 1968). Their porosity is comparable to that of inorganic porous catalysts and sorbents, such as zeolites and silica-gel (Bishop and Richards 1968; Vilenchik et al. 1998; Margolin and Navia 2001). More robust cross-linked protein crystals (CLPC) have been applied successfully as extremely stable biocatalysts (Vilenchik et al. 1998) and as selective (chiral) separation media (Margolin and Navia 2001). The complex crystal structure of the protein contains many functional active sites. Moreover, it resists environmental degradation once it is cross-linked (Vilenchik et al. 1998; Margolin and Navia 2001).
Understanding the nature of transport of solutes in CLEC is relevant to many biotechnological processes (Margolin and Navia 2001; Margolin and Vilenchik 1996; Margolin et al. 2000; Vuolanto et al. 2002, 2004; Jokela et al. 2002). Properties of intracrystalline water molecules and ions, and their transport through the crystal, are essential to many of these applications. Apart from their practical use, protein crystals also provide a unique model to study transport phenomena in protein channels in cell membranes since the structure of water-filled pores in the crystals is determined to atomic resolution by X-ray diffraction (Morozova et al. 1996). There are effects of both the solute on protein and protein on the solute (Nagendra et al. 1998). The latter effect is more pronounced in protein crystals, where proteins make up the lining of small pores and water and ions affect the passage of substances through such pores (Nagendra et al. 1998; Eisenberg and Kauzmann 1969). Several studies have focused on the experimental determination of the solute and water transport in protein crystals (Bishop and Richards 1968; Morozov et al 1995; Velev et al. 2000; Cvetkovic et al. 2005a, b; O’Hara et al. 1995). Recent studies on diffusion in protein crystals still leave open questions concerning the mobility of solutes and protein–solute interactions near proteins that constitute the pore walls (Cvetkovic et al. 2005a, b). In addition to advanced experimental techniques, versatile computational tools are generally needed to correlate reactivity of the protein and transport of solute with nanoporosity of the enzyme crystals at atomistic level (Malek et al. 2004, 2005).
Molecular dynamics simulations with explicit representation of molecules and ions should, in principle, provide realistic information about the diffusive motion of water, individual solute molecules and ions at atomic resolution. These simulations, however, are only practical at longer time and length scales. Due to heterogeneity of the protein surface, it is necessary to treat transport of molecules at the protein–water interface as a local property (Bon et al. 1999). There have been a number of such studies to determine how the water molecules on the protein surface are perturbed from the bulk (Bizzari and Cannistraro 1996; Bizzari et al. 1996). To our knowledge, there have been no such studies on dynamical motion of small solute molecules in a protein crystal. The mobility of small dipolar molecules, such as sugars and amino acids, in the vicinity and far from the protein surface in a confined biological channel, exhibits different dynamical and structural behavior from that in a free protein in solution (Velev et al. 2000; Cvetkovic et al. 2005a, b; O’Hara et al. 1995; Malek et al. 2004, 2005).
In the crystalline form, proteins are in a highly ordered three-dimensional structure, where the protein molecules strongly bind to each other with specific intermolecular interactions. Protein crystals are particularly interesting materials for chiral separations (Margolin and Navia 2001; Margolin and Vilenchik 1996; Margolin et al. 2000; Vuolanto et al. 2002, 2004; Jokela et al. 2002). The crystal framework poses an asymmetric environment and is made of l-amino acids. Enzymes in crystals have also specific binding sites for the substrates and cofactors. In addition, protein crystals are nanoporous materials. Based on these properties, many CLPCs have recently been used in chiral separation of racemic mixtures (Vuolanto et al. 2004; Jokela et al. 2002). These novel insights are valuable for biotechnological applications to devise highly selective biocatalysts, biosensors and bioseparators.
Here, we use orthorhombic lysozyme as a simple model enzyme to study diffusion of a chiral substrate through pore network of the enzyme crystal. Its well-known and extremely stable molecular structure makes it a good choice for computational studies. Moreover, lysozyme belongs to a large class of enzymes known as glycosidases. These are extremely efficient glycosidic hydrolysis catalysts. Biocatalysis inside the protein lattice has advanced features of product separation and catalyst recovery. Once the catalytic reaction occurs in lysozyme crystals, understanding the transport of products (sugars) through the lattice becomes an important issue. In short, the simple and well-known structure of lysozyme as model protein, the catalytic activity of lysozyme for hydrolyzing the glycosidic bond, the practical potential of protein crystals as biochemical porous media for chiral separation and as a model for biological channels, in general, were our first motivations for choosing a simulation model based on transport of sugar substrate into orthorhombic lysozyme lattice. Here we provide, for the first time, long-time MD simulations of diffusion of l-arabinose in orthorhombic hen egg white lysozyme crystals. Fundamental questions are; do solute molecules move by translation and/or rotation? How solute–protein interactions influence transport of a chiral solute through the protein crystal? What is the detailed nature of the diffusive motion of solute molecules in a lysozyme crystal and what are the length scales and the time scales (dynamics) of all those events.
Computational methodology
We use MD simulations to examine diffusion of l-arabinose (Ara) in a fully hydrated orthorhombic lysozyme crystal. Ara is an aldopentose (Fig. 1) that has been extensively used as a substrate to probe diffusion properties of protein channels (Nikaido and Rosenberg 1981). Lysozyme consists of 129 amino acids with 1001 non-hydrogen atoms. The crystal structures of lysozyme, entry 1AKI (Artymiuk et al. 1982), is taken from the Brookhaven Protein Database and used as a starting point. Hydrogen atoms attached to aliphatic carbon atoms are incorporated with the latter, but the remaining 342 hydrogen atoms are treated explicitly, leading to 1,343 (pseudo-) atoms in total. The simulations are done at pH 7. The amino acids Glu and Asp are taken to be deprotonated while Lys, Arg and His residues are protonated (Artymiuk et al. 1982; Stocker et al. 2000). This leads to +8 electron charges per protein molecule. Chloride ions are then added for electroneutrality. In an orthorhombic crystal, four protein molecules related by the crystallographic symmetry P212121 are placed in the unit cell with a = 5.9062 nm, b = 6.8451 nm, and c = 3.0517 nm. Repeating the unit cell along crystallographic axes generates the pore network (Fig. 2). Channels and cavities within the orthorhombic lysozyme lattices are determined by using a procedure explained elsewhere (Malek et al. 2004), based on HOLE and CHANNEL algorithms (Smart et al. 1996; Kisljuk et al. 1994). The radius of a pore is determined at any given distance along the pore axis by calculating the maximum size for a spherical probe to still fit in the pore without overlap with the van der Waals radii of atoms in the pore wall (Kisljuk et al. 1994).
Fig. 1Ball-and-stick model of l-arabinose. CHn groups are represented by united atomsFig. 2Computer generated images of an orthorhombic lysozyme lattice, visualized along z- crystallographic axis. The solvent channels are shown in grey. A single unit cell is labelled by square and its sphere representation is shown in (b). Red lines represent water molecules. The surface representation in (a) was computed from the electron density calculations using the crystal structure data (1AKI) available in the Brookhaven protein data bank. Hydrophilic, hydrophobic and polar regions are shown in blue, red and green respectively
Simulations are carried out using a fully atomistic 1 × 1 × 5 lysozyme lattice (a = 5.9062 nm, b = 6.8451 nm, and c = 15.2585 nm). The single unit cell in Fig. 2b is repeated five times along the z-axis, so that a long pore is constructed. We start from an initial configuration by random placing arabinose inside the lysozyme channel. The system contains 20 lysozyme molecules, 21 arabinoses, 6,239 crystallographic and non-crystallographic water molecules and 160 chloride ions, leading to 46,031 atoms in total. After that the system was equilibrated for 500 ps using harmonic position restraints (1000 kJ mol−1 nm−2). Production runs were performed for another 26 ns, the last 25 ns of which was used for the analysis. Simulations are performed using GROMOS96 force field (van Gunsteren et al. 1990, 1996). In our force field, interactions between atoms are divided into non-bonded interactions, between any pair of atoms that are within a given cut-off radius, and bonded interactions between atoms connected by chemical bonds. In case of the non-bonded interactions (electrostatic and van der Waals), a partial charge and parameters for repulsion and attraction are assigned to each atom. The bonded interaction consists of bond, angle and dihedral terms. Bond and angle bending are given by simple harmonic potentials. The torsional rotational potential for the dihedral angle is a periodic function with a 3-fold barrier. The partial charges and interaction parameters for all species are taken from GROMOS96 database (van Gunsteren et al. 1990).
In our MD simulation, a cut-off of 1.4 nm is used for Van der Waals interactions, while a cut-off of 1 nm and PME with a grid spacing of 0.12 nm and fourth order interpolation are used for electrostatics interactions (Morozova et al. 1996). During the simulations, the potential energy and the total energy are monitored in order to check if the system is in equilibrium. MD simulations are performed in a canonical (NVT) ensemble at 300 K. The temperature (300 K) is controlled by the Berendsen weak-coupling algorithm, separately for protein, Ara and solvent plus ions with a time constant of 0.1 ps. During the simulations, polar hydrogen atoms are treated as dummy atoms with an increased mass of 4 Da. This allowed the integration time step to be 5 fs. Simulations are done with the GROMACS package (Lindahl et al. 2001; Berendsen et al. 1995; http://www.gromacs.org). Visualization is done by using the VMD v1.8.3 (Humphrey et al. 1996) commercial package.
Results and discussions
Figure 2a shows an instantaneous configuration of the atomic model of the orthorhombic lysozyme lattice, constructed of 3 × 3 × 3 unit cells, whereas a single unit cell is framed in Fig. 2b. In each unit cell, there is a main pore lies along the z-axis and there are no remarkable pores in the other directions (Malek et al. 2004; Geremia et al. 2005; Falkner et al. 2005). Figure 3a visualizes part of the main pores along the z-axis. The average pore radius is about 0.88 ± 0.02 nm. Figure 3b shows the pore radius as a function of the pore axis. The profiles show that there are constricted zones inside each pore. The pore radius slowly decreases from over 0.95 nm to slightly less than 0.82 nm at its narrowest point. The charged residues Lys1, Lys13, Lys33, Lys96, Lys97, Lys116, Arg14, Arg21, Arg114, Asp87, and Asp119 belonging to the lysozyme molecules lie in the pore space. The motion of these residues may affect the pore shape and pore size during the transport of Ara. Our analysis shows that the effect of the protein fluctuations on pore shape is negligible, particularly for solutes of sizes much smaller than the pore diameter, such as Ara.
Fig. 3(a) Visualized pore along z-axis in a 1 × 1 × 5 lysozyme lattice. (b) Pore radius profile along the pore axis
The averaged root mean square fluctuation (RMSF) of C-α of each residue, calculated from the distance fluctuation matrix of a 25 ns trajectory in crystalline orthorhombic lysozyme is shown in Fig. 4a. The root mean square fluctuations from the X-ray structure are averaged over 20 proteins. The fluctuation results (Fig. 4a) are consistent with previous works on fluctuations and correlations in lysozyme crystals (Héry et al. 1997, 1998). The largest fluctuations are for the α-helix loops. The β-strand residues show a low mobility with values on the order of 0.1 nm. β-Strands exhibit a high degree of rigidity with moderate correlations, while only parts of α-helices are rigid or correlated (Héry et al. 1998). Although the protein atoms fluctuate slightly during the simulation, these are too small to cause significant changes in pore size or in diffusivity. Figure 4b shows that the RMSF patterns are similar for all twenty lysozyme molecules. The residues Gly117, Gly71 and Asp101 show fluctuations above 0.10 nm. Among these, Gly117 displays the maximum fluctuations ranging from 0.15 nm to 0.25 nm. Most of the charged residues accessible from the pore space show fluctuations around 0.05 nm. The latter confirms that the pore shape and pore size are not affected by protein fluctuations during 25 ns MD simulation.
Fig. 4(a) A typical root mean square fluctuation of the C-α atoms of each residue of one of the 20 lysozyme molecules in the simulation box with respect to their average position. (b) RMSD of each resides of all lysozyme molecules. The curves are on the same scale. The full lines are shifted by 0.2 nm in the vertical direction
In order to study the motion of solutes inside orthorhombic lysozyme crystals, we take into account that proteins affect the dynamics of solute molecules. MD simulations provide information to the dynamic picture of the solute motion in the vicinity of protein molecules. The self-diffusion coefficient D, which has been widely used in both spectroscopic experiments and MD simulations, is a suitable parameter characterizing the dynamical behavior of solute in the water filled protein channels in protein crystals. The diffusion coefficient D, is related to the slope of the mean square displacement (MSD) of water molecules by the Einstein relation, which in d dimension is: where
is the MSD of solute molecules during the time Δt, averaged over the ensemble of molecules in a d dimensional space, from the moment t0 that their motion is equilibrated in the pore space. Use of the Einstein equation for the determination of D requires a linear dependence of the MSD with time. For the determination of the solute diffusivity, the MSD–t linear relation is usually fulfilled on time scales longer than a few to hundred nanoseconds (Bizzari and Cannistraro 1996).
In order to study diffusion of a solute (Ara) inside pore space of an orthorhombic lysozyme crystal, we have performed extensive MD simulations of Ara transport in a fully hydrated lysozyme crystal. Protein atoms are subject to move according to the equation of motions. Ara molecules are randomly incorporated inside the main pore along z-axis (Fig. 3a). The dynamical motion of solute molecules was sampled each 10 ps during 25 ns simulation.
Figure 5a shows the displacement of nine Ara molecules along the z-axis as a function of time. The location of the solute molecules is sufficiently randomized during the simulation time, so that the diffusion properties do not depend on the arbitrary initial placement of the Ara molecules. The motion of Ara molecules displays many jumps, with little motion between jumps. A few Ara molecules travel within the pore space with displacement in the order of 5–10 nm, while a few others remain around the same axial (z) position in the pore region, moving rather in xy plane. Overall, solute molecules move freely, some travel all the way within the pore network, a few remain in the pore and some go deep into the pore and return after some time. At some points along the trajectory, a group of two or three Ara molecules establish hydrogen bonding and perform a collective motion as a united body. The latter is particularly observed in longer simulation times thereby bringing an artefact in to the diffusion analysis of single Ara molecules. To calculate the self-diffusion (D) of solute molecules in the pore, the Einstein relationship (Eq. 1) is used.
Fig. 5(a) The displacement of nine arabinose molecules along the z-axis through the pore region of lysozyme crystal shown in Fig. 2a. Different colours represent different Ara molecules. (b) Mean square displacement (MSD) of Ara molecules versus time
Figure 4b shows Mean square displacement values (MSD) values versus time for Ara molecules diffusing in the pore network of lysozyme crystal. Only trajectories of individual Ara molecules are included in calculation of MSD and therefore the collective motion of solute molecules is not included in Fig. 5b. Overall, the log-log behavior of MSD vs. time (for 5 ns < t < 20) is linear with a slope close to one. This shows that in fully hydrated pores of the lattice, the Einstein relation, Eq. 1, can describe the diffusion of Ara. The diffusion coefficient of Ara in pores along z-axis is calculated from the intercept of the log–log plot, that is (8.51 ± 0.064) × 10−13 m2 s−1. Recently, we have performed combined dynamic Monte-Carlo and Brownian dynamic (MC–BD) simulations to study electrostatic and steric confinement effects on the mobility of spherical probes in orthorhombic and tetragonal lysosyme crystals (Malek et al. 2004). The diffusion coefficient of a probe of size comparable to that of the hydrated Ara (0.86 ± 0.01 nm), calculated by MC–BD simulations is (8.85 ± 0.05) × 10−13 m2 s−1, which is in good agreement with the MD prediction. This indicates that size exclusion is the main reason for uncharged solute transport in orthorhombic lysozyme crystals. The diffusion of solutes within lysozyme crystals has also been investigated using different experimental techniques (Velev et al. 2000; Cvetkovic et al. 2005a, b; O’Hara et al. 1995). Velev et al. (2000) studied the diffusion of surfactants in lysozyme crystals using fluorescent probes by means of quantitative fluorescence microscopy. The diffusion coefficients obtained range from 2 to 30 × 10−14 m2 s−1.
By using 3-D laser scanning confocal microscopy visualizations, Cvetkovic et al. (2005a, b) investigated detailed diffusion coefficients of some solutes, fluorescein and rhodamine B, into tetragonal, orthorhombic, and triclinic lysozyme crystals. The results showed that the transport of solute molecules depends on the chemical nature of solutes (e.g., hydrophobic vs. hydrophilic), charge and size of solutes and pore network within protein crystal. The diffusion of fluorescein, with an average diameter of 0.69 ± 0.02 nm, in orthorhombic lysozyme crystals was highly anisotropic and the diffusion coefficient was calculated as approx. 7.0 ± 0.5 × 10−13 m2 s−1.
The diffusion coefficient of Ara calculated from our MD simulation is in reasonable agreement to these experiments. The diffusion rate is 4–5 orders of magnitude slower than that in free water (∼7.73 × 10−10 m2 s−1 at 298 K) (Nikaido and Rosenberg 1981; Mogi et al. 2007). The deviation is most likely as a result of single-point interactions between solute and side chains of the XI, which are usually characterized by hydrogen bindings and dipole-dipole interactions. Our preliminary analysis based on hydrogen bonds, number of contacts and minimum distance between Ara molecules and residues on the pore wall showed that the solute molecules spend considerable time in the vicinity of active site residues Lys96, Lys97, Lys116, Arg14, Arg21, and Asp87. This indicates that the orientation and translational-rotational motion of Ara play an important role in its transport through channels in orthorhombic lysozyme crystals.
These results suggest that in lysozyme lattice, and in contrast to the free lysozyme in solution, the interactions between dipolar solute and protein are mostly promoted by a large electric field on the residues far from the active site cleft (which are Asp52, Asp53, Glu35, and Asp99). Many of the latter charged amino acids that act as adsorption/desorption sites for the solute are, in fact, buried, while the residues Lys96, Lys97, Lys116, Arg14, Arg21, and Asp87 are more easily accessible. Considerable experimental and computational evidence supports several aspects of the mechanism that has been proposed for the catalytic activity of the lysozyme in solution (Dao-Pin et al. 1989; Bottoni et al. 2005). In a manner similar to that proposed for free lysozyme, our simulation results can be validated based on finding the most favorable interaction of the substrate molecules in the mixture with the catalytic active centers of the enzyme molecules in lattice. Such qualitative agreement with experimental data corroborates predictive capabilities of our model. Moreover, our study highlights the importance of the protein–solute interactions on the transport in protein crystals.
Despite its simplicity and obvious limitations, this computational study provides insight into the main features of solute transport in protein crystals. Our study allows relating transport properties of the nanopores in protein crystals to solvent and ion motion as well as to protein fluctuations. Although our findings are in good qualitative and quantitative agreement with existing experimental data, more experimental studies are still needed by which we can compare our data directly. These results in combination with experimental information provide vital insights for understanding biocatalytic and chiral separation processes in CLPC.
Conclusion
In the present study, we performed MD simulations to study the motion of an aldopentose molecule (l-arabinose) in nanopores of a fully hydrated orthorhombic lysozyme crystal. The electrostatic and steric interaction inside the crystal channel significantly influences the diffusion of solute. No clear adsorption site in the crystal was detected in the simulation, most likely due to the low solute concentration. However, our analysis show that the solute molecules spend considerable time in the vicinity of active site residues Lys96, Lys97, Lys116, Arg14, Arg21, and Asp87. According to our results, the average mobility of solute molecules in lysozyme crystal channels is reduced orders of magnitude compared to that in free water. This is why crystalline proteins are easily accessible to solute molecules that are smaller than the necks of the crystal channels. The results are of practical interest to evaluate the time necessary to impregnate the crystals with ligands, water and solutes and provide valuable insights of solute–protein interactions during solute transport in nanopores of protein crystals.

lysozyme
molecular dynamics
l-arabinose
protein crystal
diffusion