Walking through the looking glass: Adapting gait patterns with mirror feedback

Clinical locomotor research seeks to facilitate adaptation or retention of new walking patterns by providing feedback. Within a split-belt treadmill paradigm, sagittal plane feedback improves adaptation but does not affect retention. Representation of error in this manner is cognitively demanding. However, it is unknown in this paradigm how frontal plane feedback, which may utilize a unique learning process, impacts locomotor adaptation. Frontal plane movement feedback has been shown to impact retention of novel running mechanics but has yet to be evaluated in gait conditions widely applicable within neurorehabilitation, such as walking. The purpose of this study was to investigate the effects of frontal plane mirror feedback on gait adaptation and retention during split-belt treadmill walking. Forty healthy young adults were divided into two groups: one group received mirror feedback during the first split-belt exposure and the other received no mirror feedback. Individuals in the mirror feedback group were asked to look at their legs in the mirror, but no further instructions were given. Individuals with mirror feedback displayed more symmetric stance time during the first strides of adaptation and maintained this pattern into the second split-belt exposure when no feedback was provided. Individuals with mirror feedback also demonstrated more symmetric double support time upon returning to normal walking. Lastly, the mirror feedback also allowed individuals to walk with smaller gait variability during the final steps of both split-belt exposures. Overall, mirror feedback allowed individuals to reduce their stance time asymmetry and led to a more consistent adapted pattern, suggesting this type of feedback may have utility in gait training that targets symmetry and consistency in movement.     

Stochastic thermodynamic limit on E. coli adaptation by information geometric approach

Biological systems process information under noisy environment. Sensory adaptation model of E. coli is suitable for investigation because of its simplicity. To understand the adaptation processing quantitatively, stochastic thermodynamic approach has been attempted. Information processing can be assumed as state transition of a system that consists of signal transduction molecules using thermodynamic approach, and efficiency can be measured as thermodynamic cost. Recently, using information geometry and stochastic thermodynamics, a relationship between speed of the transition and the thermodynamic cost has been investigated for a chemical reaction model. Here, we introduce this approach to sensory adaptation model of E. coli, and examined a relationship between adaptation speed and the thermodynamic cost, and efficiency of the adaptation speed. For increasing external noise level in stimulation, the efficiency decreased, but the efficiency was highly robust to external stimulation strength. Moreover, we demonstrated that there is the best noise to achieve the adaptation in the aspect of thermodynamic efficiency. Our quantification method provides a framework to understand the adaptation speed and the thermodynamic cost for various biological systems.     

Migratory costs and the evolution of egg size and number in introduced and indigenous salmon populations

The trade-off between reproductive investment and migration should be an important factor shaping the evolution of life-history traits among populations following their radiation into habitats with different migratory costs and benefits. An experimentally induced difference in migratory rigor for families of chinook salmon (Oncorhynchus tshawytscha), of approximately 86 km and 413 m elevation, exacted a cost to somatic energy reserves (approximately 17% reduction in metabolizable mass) and ovarian investment (13.7% reduction in ovarian mass). This cost was associated with a reduction in egg size and paralleled the phenotypic pattern of divergence between two introduced New Zealand populations of common origin, presently breeding at sites with different migration distances. The genetic pattern of divergence of these same populations, detected under common rearing, was consistent with compensation for migratory costs (the population that migrates farther invested more in ovarian mass), but egg number more than egg size was associated with this evolution. These evolutionary patterns are consistent with what is known of the inheritance of these traits and with trade-offs and constraints favoring initial evolution in offspring number over offspring size. Analysis of egg number-size patterns of other Pacific salmon populations in their native range supported the hypothesis that migration strongly influences patterns of reproductive allocation, favoring a higher ratio of egg number to egg size with greater migration distance.     

2'Halo-ATP and -GTP analogues: rational phasing tools for protein crystallography

The solution of the crystallographic macromolecular phase problem requires incorporation of heavy atoms into protein crystals. Several 2'-halogenated nucleotides have been reported as potential universal phasing tools for nucleotide binding proteins. However, only limited data are available dealing with the effect of 2'-substitution on recognition by the protein. We have determined equilibrium dissociation constants of 2'-halogenated ATP analogues for the ATP binding proteins UMP/CMP kinase and the molecular chaperone DnaK. Whereas the affinities to UMP/CMP kinase are of the same order of magnitude as for unsubstituted ATP, the affinities to DnaK are drastically decreased to undetectable levels. For 2'-halogenated GTP analogues, the kinetics of interaction were determined for the small GTPases p21ras(Y32W) (fluorescent mutant) and RabS. The rates of association were found to be within about one order of magnitude of those for the nonsubstituted nucleotides, whereas the rates of dissociation were accelerated by factors of approximately 100 (p21ras) or approximately 10(5) (Rab5), and the resulting equilibrium dissociation constants are in the nm or microM range, respectively. The data demonstrate that 2'halo-ATP and -GTP are substrates or ligands for all proteins tested except the chaperone DnaK. Due to the very high affinities of a large number of GTP binding proteins to guanine nucleotides, even a 10(5)-fold decrease in affinity as observed for Rab5 places the equilibrium dissociation constant in the microM range, so that they are still well suited for crystallization of the G-protein:nucleotide complex.     

Phase locking in integrate-and-fire models with refractory periods and modulation

It is known [8, 11, 16, 26] that phase locking can entrain frequency information when the leaky integrate-and-fire (IF) model of a neuron is forced by a periodic function. We show that this is still the case when the IF model is made more biologically realistic. We incorporate into our model spike dependent threshold modulation and refractory periods. Consecutive firing times from this model and their respective interspike intervals are related by an annulus map. We prove a general theorem concerning orientation reversing annulus twist homeomorphisms, which shows that our map admits a unique rotation number. This implies, in particular, that chaotic behaviour is not possible in our model and phase locking is predicted.This research was partially supported by NSF EIA-BITS grant 426411This research was partially supported by the Summer Undergraduate Research Program sponsored by IGERT grant NSF-DGE 9972824 and the Undergraduate Scholars Program at MSU-BozemanAcknowledgement The authors would like to thank Marcy Barge for discussions of prime ends and Sherry Heis for formatting the diagrams.     

What is the protein design alphabet?

Selecting a protein sequence that corresponds to a specific three-dimensional protein structure is known as the protein design problem. One principal bottleneck in solving this problem is our lack of knowledge of precise atomic interactions. Using a simple model of amino acid interactions, we determine three crucial factors that are important for solving the protein design problem. Among these factors is the protein alphabet-a set of sequence elements that encodes protein structure. Our model predicts that alphabet size is independent of protein length, suggesting the possibility of designing a protein of arbitrary length with the natural protein alphabet. We also find that protein alphabet size is governed by protein structural properties and the energetic properties of the protein alphabet units. We discover that the usage of average types of amino acid in proteins is less than expected if amino acids were chosen randomly with naturally occurring frequencies. We propose three possible scenarios that account for amino acid underusage in proteins. These scenarios suggest the possibility that amino acids themselves might not constitute the alphabet of natural proteins.     

Neuronal adaptation improves the recognition of temporal patterns in a grasshopper

The recognition of the temporal structure of sound patterns by grasshopper males was investigated in behavioural experiments. Males were tested with short (165–335 ms) song models in which the characteristic subunit pattern of syllables and pauses was modified either at the beginning or at the end of the stimuli. The highly specific responses of the animals indicate that neuronal adaptation has a substantial influence on the detection of the pauses which are essential cues for the subunit structure: pauses were less likely detected shortly after the beginning of a song model than at later positions. Even adaptation in auditory neurons that was induced by unspecific stimulation (with unmodulated noise) facilitated the processing of sound envelopes. The effects of stimulus prolongation and introduction of pauses appeared to combine linearly, similar to the effects of introducing two pauses instead of a single one. In the responses to some song models large interindividual differences were observed. Comparison across stimuli and repeated testing of a smaller number of individuals indicated a considerable consistency of behavioural preferences. However, the data yielded no clear evidence for the existence of individually distinct processing types among males, that conceivably would focus on different features of the stimuli.     

Ecological role of energy taxis in microorganisms

Motile microorganisms rapidly respond to changes in various physico-chemical gradients by directing their motility to more favorable surroundings. Energy generation is one of the most important parameters for the survival of microorganisms in their environment. Therefore it is not surprising that microorganisms are able to monitor changes in the cellular energy generating processes. The signal for this behavioral response, which is called energy taxis, originates within the electron transport system. By coupling energy metabolism and behavior, energy taxis is fine-tuned to the environment a cell finds itself in and allows efficient adaptation to changing conditions that affect cellular energy levels. Thus, energy taxis provides cells with a versatile sensory system that enables them to navigate to niches where energy generation is optimized. This behavior is likely to govern vertical species stratification and the active migration of motile cells in response to shifting gradients of electron donors and/or acceptors which are observed within microbial mats, sediments and soil pores. Energy taxis has been characterized in several species and might be widespread in the microbial world. Genome sequencing revealed that many microorganisms from aquatic and soil environments possess large numbers of chemoreceptors and are likely to be capable of energy taxis. In contrast, species that have a fewer number of chemoreceptors are often found in specific, confined environments, where relatively constant environmental conditions are expected. Future studies focusing on characterizing behavioral responses in species that are adapted to diverse environmental conditions should unravel the molecular mechanisms underlying sensory behavior in general and energy taxis in particular. Such knowledge is critical to a better understanding of the ecological role of energy taxis.     

Comparing expression level-dependent features in codon usage with protein abundance: an analysis of 'predictive proteomics'

Synonymous codon usage is a commonly used means for estimating gene expression levels of Escherichia coli genes and has also been used for predicting highly expressed genes for a number of prokaryotic genomes. By comparison of expression level-dependent features in codon usage with protein abundance data from two proteome studies of exponentially growing E. coli and Bacillus subtilis cells, we try to evaluate whether the implicit assumption of this approach can be confirmed with experimental data. Log-odds ratio scores are used to model differences in codon usage between highly expressed genes and genomic average. Using these, the strength and significance of expression level-dependent features in codon usage were determined for the genes of the Escherichia coli, Bacillus subtilis and Haemophilus influenzae genomes. The comparison of codon usage features with protein abundance data confirmed a relationship between these to be present, although exceptions to this, possibly related to functional context, were found. For species with expression level-dependent features in their codon usage, the applied methodology could be used to improve in silico simulations of the outcome of two-dimensional gel electrophoretic experiments.     

Optimal growth strategies of larval helminths in their intermediate hosts

We consider optimal growth of larval stages in complex parasite life cycles where there is no constraint because of host immune responses. Our model predicts an individual's asymptotic size in its intermediate host, with and without competition from conspecific larvae. We match observed variations in larval growth patterns in pseudophyllid cestodes with theoretical predictions of our model. If survival of the host is vital for transmission, larvae should reduce asymptotic size as intensity increases, to avoid killing the host. The life history strategy (LHS) model predicts a size reduction <1/intensity, thus increasing the parasite burden on the host. We discuss whether body size of competing parasites is an evolved LHS or simply reflects resource constraints (RC) on growth fixed by the host, leading to a constant total burden with intensity. Growth under competition appears comparable with "the tragedy of the commons", much analysed in social sciences. Our LHS prediction suggests that evolution generates a solution that seems cooperative but is actually selfish.