SBML Level 3: an extensible format for the exchange and reuse of biological models.

Systems biology has experienced dramatic growth in the number, size, and complexity of computational models. To reproduce simulation results and reuse models, researchers must exchange unambiguous model descriptions. We review the latest edition of the Systems Biology Markup Language (SBML), a format designed for this purpose. A community of modelers and software authors developed SBML Level 3 over the past decade. Its modular form consists of a core suited to representing reaction-based models and packages that extend the core with features suited to other model types including constraint-based models, reaction-diffusion models, logical network models, and rule-based models. The format leverages two decades of SBML and a rich software ecosystem that transformed how systems biologists build and interact with models. More recently, the rise of multiscale models of whole cells and organs, and new data sources such as single-cell measurements and live imaging, has precipitated new ways of integrating data with models. We provide our perspectives on the challenges presented by these developments and how SBML Level 3 provides the foundation needed to support this evolution.

PICs in motoneurons do not scale with the size of the animal: a possible mechanism for faster speed of muscle contraction in smaller species.

The majority of studies on the electrical properties of neurons are carried out in rodents, and in particular in mice. However, the minute size of this animal compared with humans potentially limits the relevance of the resulting insights. To be able to extrapolate results obtained in a small animal such as a rodent, one needs to have proper knowledge of the rules governing how electrical properties of neurons scale with the size of the animal. Generally speaking, electrical resistances of neurons increase as cell size decreases, and thus maintenance of equal depolarization across cells of different sizes requires the underlying currents to decrease in proportion to the size decrease. Thus it would generally be expected that voltage-sensitive currents are smaller in smaller animals. In this study, we used in vivo preparations to record electrical properties of spinal motoneurons in deeply anesthetized adult mice and cats. We found that PICs do not scale with size, but instead are constant in their amplitudes across these species. This constancy, coupled with the threefold differences in electrical resistances, means that PICs contribute a threefold larger depolarization in the mouse than in the cat. As a consequence, motoneuronal firing rate sharply increases as animal size decreases. These differences in firing rates are likely essential in allowing different species to control muscles with widely different contraction speeds (smaller animals have faster muscle fibers). Thus from our results we have identified a possible new mechanism for how electrical properties are tuned to match mechanical properties within the motor output system.NEW & NOTEWORTHY The small size of the mouse warrants concern over whether the properties of their neurons are a scaled version of those in larger animals or instead have unique features. Comparison of spinal motoneurons in mice to cats showed unique features. Firing rates in the mouse were much higher, in large part due to relatively larger persistent inward currents. These differences likely reflect adaptations for controlling much faster muscle fibers in mouse than cat.

Across-muscle coherence is modulated as a function of wrist posture during two-digit grasping.

The purpose of this study was to investigate the extent to which correlated neural inputs, quantified as EMG-EMG coherence across intrinsic and extrinsic hand muscles, varied as a function of wrist angle during a constant force precision grip task. Eight adults (5 males; mean age 29 years) participated in the experiment. Subjects held an object using a two-digit precision grip at a constant force at a flexed, neutral, and extended wrist posture, while the EMG activity from intrinsic and extrinsic hand muscles was recorded through intramuscular fine-wire electrodes. The integral of z-transformed coherence computed across muscles pairs was greatest in the flexed wrist posture and significantly greater than EMG-EMG coherence measured in the neutral and extended wrist posture (P < 0.01 and 0.05, respectively). Furthermore, EMG-EMG coherence did not differ statistically between the extrinsic and intrinsic muscle pairs, even though it tended to be greater for the extrinsic muscle pair (P ≥ 0.063). These findings lend support to the notion of a functional role of correlated neural inputs to hand muscles for the task-dependent coordination of hand muscle activity that is likely mediated by somatosensory feedback.

Differential contributions of somatic and dendritic calcium-dependent potassium currents to the control of motoneuron excitability following spinal cord injury.

The hyperexcitability of alpha-motoneurons and accompanying spasticity following spinal cord injury (SCI) have been attributed to enhanced persistent inward currents (PICs), including L-type calcium and persistent sodium currents. Factors controlling PICs may offer new therapies for managing spasticity. Such factors include calcium-activated potassium (KCa) currents, comprising in motoneurons an after-hyperpolarization-producing current (I KCaN) activated by N/P-type calcium currents, and a second current (I KCaL) activated by L-type calcium currents (Li and Bennett in J neurophysiol 97:767-783, 2007). We hypothesize that these two currents offer differential control of PICs and motoneuron excitability based on their probable somatic and dendritic locations, respectively. We reproduced SCI-induced PIC enhancement in a two-compartment motoneuron model that resulted in persistent dendritic plateau potentials. Removing dendritic I KCaL eliminated primary frequency range discharge and produced an abrupt transition into tertiary range firing without significant changes in the overall frequency gain. However, I KCaN removal mainly increased the gain. Steady-state analyses of dendritic membrane potential showed that I KCaL limits plateau potential magnitude and strongly modulates the somatic injected current thresholds for plateau onset and offset. In contrast, I KCaN had no effect on the plateau magnitude and thresholds. These results suggest that impaired function of I KCaL may be an important intrinsic mechanism underlying PIC-induced motoneuron hyperexcitability following SCI.

Modulation of inhibitory strength and kinetics facilitates regulation of persistent inward currents and motoneuron excitability following spinal cord injury.

Spasticity is commonly observed after chronic spinal cord injury (SCI) and many other central nervous system disorders (e.g., multiple sclerosis, stroke). SCI-induced spasticity has been associated with motoneuron hyperexcitability partly due to enhanced activation of intrinsic persistent inward currents (PICs). Disrupted spinal inhibitory mechanisms also have been implicated. Altered inhibition can result from complex changes in the strength, kinetics, and reversal potential (E(Cl(-))) of γ-aminobutyric acid A (GABA(A)) and glycine receptor currents. Development of optimal therapeutic strategies requires an understanding of the impact of these interacting factors on motoneuron excitability. We employed computational methods to study the effects of conductance, kinetics, and E(Cl(-)) of a dendritic inhibition on PIC activation and motoneuron discharge. A two-compartment motoneuron with enhanced PICs characteristic of SCI and receiving recurrent inhibition from Renshaw cells was utilized in these simulations. This dendritic inhibition regulated PIC onset and offset and exerted its strongest effects at motoneuron recruitment and in the secondary range of the current-frequency relationship during PIC activation. Increasing inhibitory conductance compensated for moderate depolarizing shifts in E(Cl(-)) by limiting PIC activation and self-sustained firing. Furthermore, GABA(A) currents exerted greater control on PIC activation than glycinergic currents, an effect attributable to their slower kinetics. These results suggest that modulation of the strength and kinetics of GABA(A) currents could provide treatment strategies for uncontrollable spasms.

Assessment of across-muscle coherence using multi-unit vs. single-unit recordings.

Coherence between electromyographic (EMG) signals has been used to identify correlated neural inputs to motor units (MUs) innervating different muscles. Simulations using a motor-unit model (Fuglevand et al. 1992) were performed to determine the ability of coherence between two multi-unit EMGs (mEMG) to detect correlated MU activity and the range of correlation strengths in which mEMG coherence can be usefully employed. Coherence between motor-unit and mEMG activities in two muscles was determined as we varied the strength of a 30-Hz periodic common input, the number of correlated MU pairs and variability of MU discharge relative to the common input. Pooled and mEMG coherence amplitudes positively and negatively accelerated, respectively, toward the strongest and most widespread correlating inputs. Furthermore, the relation between pooled and mEMG coherence was also nonlinear and was essentially the same whether correlation strength varied by changing common input strength or its distribution. However, the most important finding is that while the mEMG coherence saturates at the strongest common input strengths, this occurs at common input strengths greater than found in most physiological studies. Thus, we conclude that mEMG coherence would be a useful measure in many experimental conditions and our simulation results suggest further guidelines for using and interpreting coherence between mEMG signals.

Influence of fatigue on hand muscle coordination and EMG-EMG coherence during three-digit grasping.

Fingertip force control requires fine coordination of multiple hand muscles within and across the digits. While the modulation of neural drive to hand muscles as a function of force has been extensively studied, much less is known about the effects of fatigue on the coordination of simultaneously active hand muscles. We asked eight subjects to perform a fatiguing contraction by gripping a manipulandum with thumb, index, and middle fingers while matching an isometric target force (40% maximal voluntary force) for as long as possible. The coordination of 12 hand muscles was quantified as electromyographic (EMG) muscle activation pattern (MAP) vector and EMG-EMG coherence. We hypothesized that muscle fatigue would cause uniform changes in EMG amplitude across all muscles and an increase in EMG-EMG coherence in the higher frequency bands but with an invariant heterogeneous distribution across muscles. Muscle fatigue caused a 12.5% drop in the maximum voluntary contraction force (P < 0.05) at task failure and an increase in the SD of force (P < 0.01). Although EMG amplitude of all muscles increased during the fatiguing contraction (P < 0.001), the MAP vector orientation did not change, indicating that a similar muscle coordination pattern was used throughout the fatiguing contraction. Last, EMG-EMG coherence (0-35 Hz) was significantly greater at the end than at the beginning of the fatiguing contraction (P < 0.01) but was heterogeneously distributed across hand muscles. These findings suggest that similar mechanisms are involved for modulating and sustaining digit forces in nonfatiguing and fatiguing contractions, respectively.

Persistent currents and discharge patterns in rat hindlimb motoneurons.

We report here the first direct measurements of persistent inward currents (PICs) in rat hindlimb motoneurons, obtained from ketamine-xylazine anesthetized rats during slow voltage ramps performed by single-electrode somatic voltage clamp. Most motoneurons expressed PICs and current-voltage (I-V) relations often contained a negative-slope region (NSR; 13/19 cells). PICs activated at -52.7 ± 3.89 mV, 9 mV negative to spike threshold. NSR onset was -44.2 ± 4.1 mV. PIC amplitudes were assessed by maximum inward currents measured relative to extrapolated leak current and to NSR-onset current. PIC conductance at potentials just positive to activation was assessed by the relative change in slope conductance (g(in)/g(leak)). PIC amplitudes varied widely; some exceeded 5 and 10 nA relative to current at NSR onset or leak current, respectively. PIC amplitudes did not vary significantly with input conductance, but PIC amplitudes normalized by recruitment current decreased with increasing input conductance. Similarly, g(in)/g(leak) decreased with increasing input conductance. Currents near resting potential on descending limbs of I-V relations were often outward, relative to ascending-limb currents. This residual outward current was correlated with increases in leak conductance on the descending limb and with input conductance. Excluding responses with accommodation, residual outward currents matched differences between recruitment and derecruitment currents, suggesting a role for residual outward current in frequency adaptation. Comparison of potentials for PIC activation and NSR onset with interspike trajectories during discharge demonstrated correspondence between PIC activation and frequency-current (f-I) range boundaries. Contributions of persistent inward and outward currents to motoneuron discharge characteristics are discussed.

Characteristics and organization of discharge properties in rat hindlimb motoneurons.

The discharge properties of hindlimb motoneurons in ketamine-xylazine anesthetized rats were measured to assess contributions of persistent intrinsic currents to these characteristics and to determine their distribution in motoneuron pools. Most motoneurons (30/37) responded to ramp current injections with adapting patterns of discharge and the frequency-current (f-I) relations of nearly all motoneurons included a steep subprimary range of discharge. Despite the prevalence of adapting f-I relations, responses included indications that persistent inward currents (PICs) were activated, including increased membrane noise and prepotentials before discharge, as well as counterclockwise hysteresis and secondary ranges in f-I relations. Examination of spike thresholds and afterhyperpolarization (AHP) trajectories during repetitive discharge revealed systematic changes in threshold and trajectory within the subprimary, primary, and secondary f-I ranges. These changes in the primary and secondary ranges were qualitatively similar to those described previously for cat motoneurons. Within the subprimary range, AHP trajectories often included shallow approaches to threshold following recruitment and slope of the AHP ramp consistently increased until the subprimary range was reached. We suggest that PICs activated near recruitment contributed to these slope changes and formation of the subprimary range. Discharge characteristics were strongly correlated with motoneuron size, using input conductance as an indicator of size. Discharge adaptation, recruitment current, and frequency increased with input conductance, whereas both subprimary and primary f-I gains decreased. These results are discussed with respect to potential mechanisms and their functional implications.

Force-independent distribution of correlated neural inputs to hand muscles during three-digit grasping.

The ability to modulate digit forces during grasping relies on the coordination of multiple hand muscles. Because many muscles innervate each digit, the CNS can potentially choose from a large number of muscle coordination patterns to generate a given digit force. Studies of single-digit force production tasks have revealed that the electromyographic (EMG) activity scales uniformly across all muscles as a function of digit force. However, the extent to which this finding applies to the coordination of forces across multiple digits is unknown. We addressed this question by asking subjects (n = 8) to exert isometric forces using a three-digit grip (thumb, index, and middle fingers) that allowed for the quantification of hand muscle coordination within and across digits as a function of grasp force (5, 20, 40, 60, and 80% maximal voluntary force). We recorded EMG from 12 muscles (6 extrinsic and 6 intrinsic) of the three digits. Hand muscle coordination patterns were quantified in the amplitude and frequency domains (EMG-EMG coherence). EMG amplitude scaled uniformly across all hand muscles as a function of grasp force (muscle x force interaction: P = 0.997; cosines of angle between muscle activation pattern vector pairs: 0.897-0.997). Similarly, EMG-EMG coherence was not significantly affected by force (P = 0.324). However, coherence was stronger across extrinsic than that across intrinsic muscle pairs (P = 0.0039). These findings indicate that the distribution of neural drive to multiple hand muscles is force independent and may reflect the anatomical properties or functional roles of hand muscle groups.

The PHA Depolymerase Engineering Database: A systematic analysis tool for the diverse family of polyhydroxyalkanoate (PHA) depolymerases.

BACKGROUND: Polyhydroxyalkanoates (PHAs) can be degraded by many microorganisms using intra- or extracellular PHA depolymerases. PHA depolymerases are very diverse in sequence and substrate specificity, but share a common alpha/beta-hydrolase fold and a catalytic triad, which is also found in other alpha/beta-hydrolases. RESULTS: The PHA Depolymerase Engineering Database (DED, http://www.ded.uni-stuttgart.de) has been established as a tool for systematic analysis of this enzyme family. The DED contains sequence entries of 587 PHA depolymerases, which were assigned to 8 superfamilies and 38 homologous families based on their sequence similarity. For each family, multiple sequence alignments and profile hidden Markov models are provided, and functionally relevant residues are annotated. CONCLUSION: The DED is a valuable tool which can be applied to identify new PHA depolymerase sequences from complete genomes in silico, to classify PHA depolymerases, to predict their biochemical properties, and to design enzyme variants with improved properties.

Determination of the location and magnitude of synaptic conductance changes in spinal motoneurons by impedance measurements.

The relation between impedance change and the location and magnitude of a tonic synaptic conductance was examined in compartmental motoneuron models based on previously published data. The dependency of motoneuron impedance on system time constant (tau), electrotonic length (L), and dendritic-to-somatic conductance ratio (rho) was examined, showing that the relation between impedance phase and rho differed markedly between models with uniform and nonuniform membrane resistivity. Dendritic synaptic conductances decreased impedance magnitude at low frequencies; at higher frequencies, impedance magnitude increased. The frequency at which the change in impedance magnitude reversed from a decrease to an increase-the reversal frequency, F(r)-was a good estimator of electrotonic synaptic location. A measure of the average normalized impedance change at frequencies less than F(r), cuDeltaZ, estimated relative synaptic conductance. F(r) and cuDeltaZ provided useful estimates of synaptic location and conductance in models with nonuniform (step, sigmoidal) and uniform membrane resistivity. F(r) also provided good estimates of spatial synaptic location on the equivalent cable in both step and sigmoidal models. Variability in relations between F(r), cuDeltaZ, and conductance location and magnitude between neurons was reduced by normalization with rho and tau. The effects on F(r) and cuDeltaZ of noise in experimental recordings, different synaptic distributions, and voltage-dependent conductances were also assessed. This study indicates that location and conductance of tonic dendritic conductances can be estimated from F(r), cuDeltaZ, and basic electrotonic motoneuron parameters with the exercise of suitable precautions.

Location and magnitude of conductance changes produced by Renshaw recurrent inhibition in spinal motoneurons.

The mean location of Renshaw synapses on spinal motoneurons and their synaptic conductance were estimated from changes in impedance magnitude produced by sustained recurrent inhibition. Motoneuron impedance was determined by injecting quasi-white noise current into lumbosacral motoneurons of pentobarbital-anesthetized cats. Synaptic location and conductance were estimated by comparing observed impedance changes to simulation results obtained using standard motoneuron models and compartmental models fit to each impedance function. Estimated synaptic locations ranged from 0.10 to 0.41lambda, with a mean of 0.19 or 0.24lambda, depending on the estimation method. Average dendritic path length was 262 microm. Average synaptic conductance was 23 to 27 nS (range: 6.7 to 57.9 nS), corresponding to conductance changes of 78 to 88% of resting membrane conductance. Estimated accuracy was supported by consistency using different estimation methods, agreement with Fyffe's 1991 morphological data, and comparisons of observed and simulated recurrent IPSP amplitudes. Synaptic location, but not synaptic conductance, was correlated with rheobase, a measure of motoneuron excitability. Synaptic conductance did not depend on synaptic location. A regression analysis demonstrated that synaptic conductance and cell impedance were the principal factors determining recurrent IPSP amplitude. Simulations using the observed values and locations of Renshaw conductance demonstrate that recurrent inhibition can require as much as an additional 14 to 18% sustained excitatory synaptic conductance to depolarize motoneurons sufficiently to activate somatic or dendritic inward currents and recruit motoneurons or amplify excitatory synaptic currents.

Estimation of the electrical parameters of spinal motoneurons using impedance measurements.

Electrical parameters of spinal motoneurons were estimated by optimizing the parameters of motoneuron models to match experimentally determined impedance functions with those of the models. The model was described by soma area, somatic and dendritic membrane resistivities, and the diameter of an equivalent dendritic cable having a standard profile. The impedance functions of motoneurons and optimized models usually differed (rms error) by <2% of input resistance. Consistent estimates for most parameters were obtained from repeated impedance determinations in individual motoneurons; estimates of dendritic resistivity were most variable. The few cells that could not be fit well had reduced impedance phase lag consistent with dendritic penetrations. Most fits were improved by inclusion of a voltage-dependent conductance G(V) with time constant tau(V). A uniformly distributed G(V) with tau(V) >5 ms provided a better fit for most cells. The magnitude of this conductance decreased with depolarization. Impedance functions of other cells were adequately fit by a passive model or by a model with a somatic G(V) and tau(V) <5 ms. Most of these neurons (7/8) had resting potentials positive to -60 mV. The electrotonic parameters rho, tau, and L, estimated from model parameters, were consistent with published distributions. Most motoneuron parameters obtained in somatic shunt and sigmoidal models were well correlated, and parameters were moderately affected by changes in dendritic profile. These results demonstrate the utility and limitations of impedance measurements for estimating motoneuron parameters and suggest that voltage-dependent conductances are a substantial component of resting electrical properties.