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Spatial performance is more sensitive to ethanol than nonspatial performance regardless of cue proximity.

In rodents, ethanol produces a greater impact on the ability to perform spatial reference memory tasks than nonspatial reference memory tasks. Such evidence may reflect a selective disruption in the use of previously acquired spatial information. However, a nonmnemonic explanation has yet to be ruled out Tasks used to study ethanol's effects on spatial memory commonly require subjects to utilize distal, or extramaze, cues to respond correctly. In contrast, many previously used nonspatial tasks could be solved using cues located on the maze itself. Because ethanol has been shown to disrupt sensory processing, it is possible that previously observed differences in the effects of ethanol on spatial and nonspatial performance were actually due to differences in the proximity of relevant cues in the spatial and nonspatial tasks and not to a selective disruption in spatial memory. The present study compares the effects of ethanol on the performance of spatial and nonspatial reference memory tasks that require subjects to discriminate among extramaze cues for correct responding. Subjects were trained while sober to navigate to a goal arm on a 12-arm maze. In the spatial task, the goal arm was defined by its location with respect to a number of extramaze cues. In the nonspatial task, the goal arm was defined by the presence of a single extramaze cue located directly beyond the end of the arm. Subjects were tested under 1 of 4 doses of ethanol (0.0, 0.7, 1.4, and 2.1 g/kg). Performance on the nonspatial task was more resistant to the effects of ethanol than performance on the spatial task. The results suggest that differences in the effects of ethanol on spatial and nonspatial performance are not due to differences in the proximity of relevant cues in previously used spatial and nonspatial tasks.

Alcoholic Intoxication↗

Dissociation of the effect of spatial behaviors on the phosphorylation of cAMP-response element binding protein (CREB) within the nucleus accumbens.

Several studies have reported a role for the nucleus accumbens (NAcc) in learning and synaptic plasticity. Many of them suggest that the NAcc is involved in translating cortico-limbic information to the motor system mediating spatial learning and memory processes. Previous studies from our laboratory have shown that protein kinase C is activated following training in a food search spatial learning task. The present study further characterizes the molecular substrates associated with NAcc-dependent spatial behavior. The cyclic AMP-response element binding protein (CREB), a transcription factor implicated in the formation of long-term memory, was studied in the NAcc following spatial training in a food search spatial learning task. Western blots were performed to detect phosphorylated (activated) and total CREB protein levels. Our results show that CREB is significantly phosphorylated in the NAcc 48 h after habituation and at 5 min and 1 h after the first spatial training session in comparison with the naive animals that remained in their home cages. Since published data show that NAcc plays a role in novelty detection and reactivity, we conducted further experiments in order to dissociate the effect on CREB phosphorylation and expression of spatial novelty (single exposure), exploration, and spatial learning in the food search apparatus. Results show that CREB phosphorylation is significantly increased 48 h after exposure to a novel environment. The present study suggests that CREB phosphorylation observed in the NAcc during habituation and spatial training may be mainly triggered by detection of spatial novelty.

Animals↗

Accelerated senescence prone mouse-8 shows early onset of deficits in spatial learning and memory in the radial six-arm water maze.

Available data indicate that the senescence-accelerated prone mouse 8 (SAMP8) is an appropriate model of brain aging, with impairments in nonspatial learning and memory beginning as early as 2 months of age, and spatial learning and memory deficiencies not becoming apparent until after 4 months of age. However, with other strains (e.g., C57BL mice), the impairment in spatial memory was found earlier than that in nonspatial memory. We considered the possibility that the observed differences could be due to strain-specific differences in the training equipment. In the present study, a new optimized testing apparatus-the radial six-arm water maze (RAWM)-for detecting spatial learning and memory in mice, was employed, to determine whether there is impairment of spatial learning and memory in young SAMP8. The relationship between the spatial learning measures observed with the RAWM and the Morris maze, a classic spatial learning and memory testing apparatus, was also explored. It was found that, in the RAWM, rather than in the Morris maze, the impairment in spatial learning could be measured in SAMP8 mice as early as 3 months old, and the impairment in spatial memory in SAMP8 mice aged 5 months. These results suggested that the spatial learning and memory deficiencies could be found in early life of SAMP8 mice, and that RAWM and Morris maze each detect different aspects of spatial learning and memory.

Aging↗

Comprehension of spatial language terms in Williams syndrome: evidence for an interaction between domains of strength and weakness.

Individuals with Williams syndrome show an unusual neuropsychological profile, with relatively strong language abilities and impoverished visual and spatial abilities. Two studies are reported that examine the interaction between these two domains in Williams syndrome by assessing individuals' comprehension of spoken language with a spatial component. In a first study, the Test for Reception of Grammar (Bishop, 1983) was given to 32 individuals with Williams syndrome and to controls matched individually for total number of errors on the task. Individuals with Williams syndrome had particular problems when asked to comprehend sentences containing spatial prepositions, making significantly more errors on these items than control groups. A second study examined in more detail comprehension of sentences with spatial and non-spatial components, comparing the performance of 15 individuals with Williams syndrome and control groups matched for vocabulary ability. Individuals with Williams syndrome again showed impaired comprehension of spoken spatial terms. In contrast, they were unimpaired in comprehending utterances without a spatial component, with the exception of descriptions testing comprehension of non-spatial comparatives (lighter than and darker than). These results suggest that the spatial difficulties experienced by individuals with Williams syndrome may constrain language comprehension in certain circumstances. They also shed light on the ways in which spatial cognition may interact with language comprehension more generally.

Adolescent↗

Visual reaction time of cats to different spatial frequencies.

If physiological mechanisms similar to cat Y and X cells explain faster detection of low spatial frequencies by humans, then cats should show the same effect. We have tested this prediction by determining the visual reaction time of cats over a range of spatial frequencies and contrasts by training them to respond quickly when a vertical sine-wave grating was presented. At 50% contrast, the cat's visual reaction time increased monotonically from 0.25-2.0 cpd (cycle/deg). At every spatial frequency tested, the cat's reaction time increased monotonically as contrast decreased. By determining contrast threshold (70% detection) at each spatial frequency, it was possible to determine reaction times for different spatial frequencies at equal physical contrasts and equal "threshold equivalent" contrasts. Some of the cat's faster detection of low spatial frequencies was due to sensitivity differences and some was not. To determine if faster detection of low spatial frequencies was based upon Y cells, we took advantage of the fact that Y cells show a strong peripheral effect while X cells do not. Low and high spatial frequencies were detected in the presence of a flickering (7 Hz) or steady (70 Hz) surround. Surround frequency had no effect upon reaction times to 2.0 cpd but the flickering surround increased reaction times to 0.25 cpd. These results indicate that, in cats, rapid detection of low spatial frequencies is by Y cells and slower detection of high spatial frequencies is by X cells.

Animals↗

The burgeoning spatial multi-omics in human gastrointestinal cancers.

The development and progression of diseases in multicellular organisms unfold within the intricate three-dimensional body environment. Thus, to comprehensively understand the molecular mechanisms governing individual development and disease progression, precise acquisition of biological data, including genome, transcriptome, proteome, metabolome, and epigenome, with single-cell resolution and spatial information within the body's three-dimensional context, is essential. This foundational information serves as the basis for deciphering cellular and molecular mechanisms. Although single-cell multi-omics technology can provide biological information such as genome, transcriptome, proteome, metabolome, and epigenome with single-cell resolution, the sample preparation process leads to the loss of spatial information. Spatial multi-omics technology, however, facilitates the characterization of biological data, such as genome, transcriptome, proteome, metabolome, and epigenome in tissue samples, while retaining their spatial context. Consequently, these techniques significantly enhance our understanding of individual development and disease pathology. Currently, spatial multi-omics technology has played a vital role in elucidating various processes in tumor biology, including tumor occurrence, development, and metastasis, particularly in the realms of tumor immunity and the heterogeneity of the tumor microenvironment. Therefore, this article provides a comprehensive overview of spatial transcriptomics, spatial proteomics, and spatial metabolomics-related technologies and their application in research concerning esophageal cancer, gastric cancer, and colorectal cancer. The objective is to foster the research and implementation of spatial multi-omics technology in digestive tumor diseases. This review will provide new technical insights for molecular biology researchers.

Humans↗

Hippocampus and remote spatial memory in rats.

Damage to the hippocampus typically produces temporally graded retrograde amnesia, whereby memories acquired recently are impaired more than memories acquired remotely. This phenomenon has been demonstrated repeatedly in a variety of species and tasks. It has also figured prominently in theoretical treatments of memory and hippocampal function. Yet temporally graded retrograde amnesia has not been demonstrated following hippocampal damage in spatial tasks like the water maze. We have assessed recent and remote spatial memory following hippocampal lesions in three different tests of spatial memory: (1) the standard water maze; (2) the Oasis maze, a dry-land version of the water maze; and (3) the annular water maze, where training and testing occur within a circular corridor. Training protocols were developed for each task such that retention of spatial memory could be expressed after very long retention intervals. In addition, retention in each task was assessed with single probe trials so that the assessment of remote memory did not depend on the ability to relearn across multiple trials. The findings were consistent across the three tasks. In the standard water maze (Experiment 1), spatial memory was impaired after training-surgery intervals of 1 day, 8 weeks, or 14 weeks. Similarly, in the Oasis maze (Experiment 2), spatial memory was impaired after training-surgery intervals of 1 day and 9 weeks. Finally, in the annular water maze (Experiment 3), spatial memory was impaired after training-surgery intervals of 9 weeks and 14 weeks. Dorsal hippocampal lesions impaired performance to the same extent as complete lesions. The impairment in remote spatial memory could reflect disruption of previously acquired spatial information. Alternatively, it is possible that in these tasks hippocampal lesions might produce an impairment in performance that prevents the expression of an otherwise intact spatial memory.

Amnesia, Retrograde↗

A possible connection between categorical and coordinate spatial relation representations.

Kosslyn (1987) theorized that the visual system uses two types of spatial relations. Categorical spatial relations represent a range of locations as an equivalence class, whereas coordinate spatial relations represent the precise distance between two objects. Data indicate a left hemisphere (LH) advantage for processing categorical spatial relations and a right hemisphere (RH) advantage for processing coordinate spatial relations. Although generally assumed to be independent processes, this article proposes a possible connection between categorical and coordinate spatial relations. Specifically, categorical spatial relations may be an initial stage in the formation of coordinate spatial relations. Three experiments tested the hypothesis that categorical information would benefit tasks that required coordinate judgments. Experiments 1 and 2 presented categorical information before participants made coordinate judgments and coordinate information before participants made categorical judgments. Categorical information sped the processing of a coordinate task under a range of experimental variables; however, coordinate information did not benefit categorical judgments. Experiment 3 used this priming paradigm to present stimuli in the left or right visual field. Although visual field differences were present in the third experiment, categorical information did not speed the processing of a coordinate task. The lack of priming effects in Experiment 3 may have been due to methodological changes. In general, support is provided that categorical spatial relations may act as an initial step in the formation of more precise distance representations, i.e., coordinate spatial relations.

Fixation, Ocular↗

Differential activation of right superior parietal cortex and intraparietal sulcus by spatial and nonspatial attention.

Neuropsychological and functional neuroimaging studies have implicated the right posterior parietal cortex (PPC) in human spatial attention. We tested the hypothesis that this area is also involved in nonspatial aspects of attention and working memory using positron emission tomography in healthy volunteers. In an initial experiment, digits were presented in pseudo-random spatial locations, and subjects attended either to locations or digits in order to detect single targets (attention condition) or to sequences of stimuli (working memory (WM) condition). Right superior parietal cortex (BA7) and intraparietal sulcus (IPS) were active during both spatial (locations) and nonspatial (digits) tasks compared to rest, although more so for the former. Additionally, right PPC was activated to an even greater extent during tests of WM than of attention, especially for tests of spatial WM. There were no differences in activation of dorsolateral prefrontal cortex in the spatial versus nonspatial versions of the task, contrary to many previous studies. A follow-up experiment which presented abstract objects in a fixed, central location confirmed that right IPS was active during tests of nonspatial attention and also that this activation is not due to incidental spatial representation of digit stimuli. However, BA7 was not activated by this nonspatial, nondigit attentional task. Overall, these data suggest first that right IPS is recruited for both nonspatial and spatial attention and WM. Second, right BA7 is recruited specifically for spatial (both direct and indirect) forms of attentional processing. Finally, PPC activations in spatial WM tasks are likely to be due to a combination of spatial perception, attention, and WM, rather than to any of these individually.

Adult↗

Model Analysis of Spatial Patterns in Mountain Pine Beetle Outbreaks.

The mountain pine beetle [MPB, Dendroctonus ponderosae Hopkins (Coleoptera: Scolytidae)] is an aggressive bark beetle, one that typically needs to kill host trees in order to successfully reproduce. This ecological adaptation has resulted in an organism that is both economically important and ecologically significant. Even though significant resources have been expended on MPB research, and a great deal of knowledge exists regarding individual aspects of MPB ecology, some of the most basic questions regarding outbreaks remain unanswered. In our opinion, one reason for the lack of synthesis and predictive power is the inadequate treatment of spatial dynamics in outbreak theories. This paper explicitly addresses the role of spatial dynamics in the precipitation and propagation of MPB outbreaks. We first describe a spatially dynamic model of the MPB/forest interaction that includes chemical ecology, spatial redistribution of beetles, attack, and resulting host mortality. The model is a system of 6 coupled, partial differential equations with 7 state variables and 20 parameters. It represents an attempt to capture the relatively complex predator/prey interaction between MPB and host trees by including the minimum phenomenological descriptions necessary for ecological credibility. This system of equations describes the temporal dynamics of: beetle attraction as a function of pheromone concentration; the change in numbers of flying and nesting beetles; tree resistance/susceptibility; and tree recovery from attack. Spatial dynamics are modeled by fluxes due to gradients in pheromones and kairomones, and the random redistribution of beetles in absence of semiochemicals. We then use the parameterized model to explore three issues central to the ecology of MPB/forest interaction. The first of these is in response to the need for objective ways to compare patterns of successful beetle attacks as they evolve in space. Simulation results indicate that at endemic levels, the pattern of successful attacks are determined almost exclusively by the underlying distribution of susceptible host trees (environmental determinism). As an outbreak develops, the pattern of successfully attacked trees switches to one that is dynamically driven by the self-generated semiochemical landscape (dynamic determinism). This switch from an environmentally determined spatial pattern to a dynamically driven pattern is the hallmark of an outbreak. We discuss the application of a spatial correlation coefficient that can be used to differentiate between the spatial distribution of killed trees in endemic and outbreak phases. The second issue we address through simulation is synchrony in adult emergence. Synchronous adult emergence is critical for the mass attack strategy necessary for overcoming tree defenses. Results from these simulations indicate that the degree of synchrony in adult emergence can have important consequences for assessing the risk of an outbreak. The final issue we investigate through simulation is the effect of spatial pattern of nurse trees (those successfully attacked the previous year) on outbreak potential. Simulations indicated that the spatial proximity of nurse trees was an important determinant of subsequent successful attacks. We conclude with a discussion of the general implications of our simulation experiments. Copyright 1998 Academic Press.

Journal Article↗

Single unit activity in the rat hippocampus during a spatial memory task.

Single unit activity was recorded from complex spike cells in the hippocampus of the rat while the animal was performing a spatial memory task. The task required the animal to choose the correct arm of a 4 arm plus-shaped maze in order to obtain reward. The location of the goal arm was varied from trial to trial and was identified by 6 controlled spatial cues which were distributed around the enclosure and which were rotated in step with the goal. On some trials these spatial cues were present throughout the trial (spatial reference memory trials) while on other trials they were present during the first part of the trial but were removed before the rat was allowed to choose the goal (spatial working memory trials). On these latter trials the animal had to remember the location of the cues and/or goal during the delay in order to choose correctly. 55 units were recorded during sufficient reference memory trials for the relationship between their firing pattern and different spatial aspects of the environment to be determined. 33 units had fields with significant relations to the controlled cues while 16 had significant relations to the static background cues, those cues in the environment which did not change position from trial to trial. Of 43 units which could be tested for their relation to the shape of the maze arms themselves, 15 showed such a relationship. Therefore the place units can be influenced by different aspects of the spatial environment but those related to the task requirement appear to be more potent. Interaction effects between the different spatial factors also influenced the firing pattern of some units. Of particular interest was the interaction between the controlled cues and the static background cues found in some cells since this might shed some light on how the hippocampus enables the rat to solve the memory task. 30 units with place fields related to the controlled cues were recorded during successful performance on spatial working memory trials as well as during spatial reference memory trials. The place fields of 90% of these units were maintained during the retention phase of the memory trials. During the recording of some units, other types of trial were given as well. On control trials, the cues were removed before the rat was placed on the maze. These trials provided controls for the potential influence of information left behind by the controlled cues and for the influence of the animal's behaviour on the unit activity.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals↗

Spatial constraints in bimanual coordination: influences of effector orientation.

Two experiments are reported that examined the influence of spatial orientation of the upper limbs in bimanual coordination. In both experiments, the upper limbs were oriented in either parallel, orthogonal, or obtuse spatial configurations and participants were asked to move their limbs continuously in temporal (1:1) synchrony, prepared in either in-phase or anti-phase modes of coordination. Bimanual coordination trials in Experiment 1 were paced by a metronome at one of four frequencies (1.0, 1.5, 2.0 or 2.5 Hz). Measures of relative phase accuracy and stability both revealed that, as metronome frequency increased, in-phase coordination dominated for the parallel spatial orientation, anti-phase coordination dominated for the orthogonal spatial orientation, and neither pattern dominated for the obtuse spatial orientations. In Experiment 2, an intentional switch method replicated and extended these influences of spatial orientation. The time to voluntarily switch from an anti-phase pattern to an in-phase pattern was faster than an in-phase to anti-phase switch (confirming support for the dominance of the in-phase pattern), but this was true only for the parallel spatial orientation. The reverse was true for the orthogonal spatial orientation (i.e., faster from in-phase to anti-phase), and no difference in switch times was observed for an obtuse spatial orientation. These findings support and extend previous research regarding the influence of spatial orientation in bimanual coordination and may be attributed to the role of, and potential interactions between, egocentric, allocentric, and mechanical constraints during action.

Adult↗

Combined deficits of saccades and visuo-spatial orientation after cortical lesions.

Functionally, saccadic eye movements are closely linked to visuo-spatial orientation. Anatomically, the network of cortical areas controlling saccades also seems to be involved in spatial attention and orientation. Consequently, lesions should cause deficits in both categories. We investigated this in 34 patients with focal unilateral lesions of the posterior parietal cortex (PPC), the frontal eye fields (FEF), the supplementary motor area (SMA), or the dorsolateral prefrontal cortex (PFC). Saccadic eye movements were recorded using infrared reflection oculography. Visual hemineglect or other visuo-spatial disorders were investigated by a series of standardized paper-pencil tests. Further, the internal spatial coordinates (subjective visual vertical and subjective straight ahead) were assessed psychophysically. Depending on the site of the lesion, different patterns of deficits were identified: lesions of the PPC impaired reflexive exploration of visual space in terms of delayed and hypometric visually triggered saccades into the contralesional hemifield, related to the severity of visual hemineglect. Further, PPC lesions specifically affected basic functions of the perceptual analysis of space, such as the internal spatial coordinates and spatial constancy across saccades. The latter was tested by applying visual double-step stimuli, where saccade-related extraretinal information had to be taken into account for achieving spatial accuracy. Frontal lesions left these functions intact. FEF lesions, however, impaired systematic intentional exploration of space, thus causing an exploratory-motor type of visual hemineglect. Prefrontal (PFC) lesions impaired the working memory for saccade-related spatial information, and SMA lesions affected temporal properties such as the timing of saccadic sequences, but did not cause specific visuo-spatial deficits. In conclusion, patients with frontal or parietal cortical lesions often exhibit combined saccadic and visuo-spatial disorders, most of which are topically specific.

Brain Diseases↗

In situ spatial patterns of soil bacterial populations, mapped at multiple scales, in an arable soil.

Very little is known about the spatial organization of soil microbes across scales that are relevant both to microbial function and to field-based processes. The spatial distributions of microbes and microbially mediated activity have a high intrinsic variability. This can present problems when trying to quantify the effects of disturbance, management practices, or climate change on soil microbial systems and attendant function. A spatial sampling regime was implemented in an arable field. Cores of undisturbed soil were sampled from a 3 x 3 x 0.9 m volume of soil (topsoil and subsoil) and a biological thin section, in which the in situ distribution of bacteria could be quantified, prepared from each core. Geostatistical analysis was used to quantify the nature of spatial structure from micrometers to meters and spatial point pattern analysis to test for deviations from complete spatial randomness of mapped bacteria. Spatial structure in the topsoil was only found at the microscale (micrometers), whereas evidence for nested scales of spatial structure was found in the subsoil (at the microscale, and at the centimeter to meter scale). Geostatistical ranges of spatial structure at the micro scale were greater in the topsoil and tended to decrease with depth in the subsoil. Evidence for spatial aggregation in bacteria was stronger in the topsoil and also decreased with depth in the subsoil, though extremely high degrees of aggregation were found at very short distances in the deep subsoil. The data suggest that factors that regulate the distribution of bacteria in the subsoil operate at two scales, in contrast to one scale in the topsoil, and that bacterial patches are larger and more prevalent in the topsoil.

Agriculture↗

Spatial variation in insect community and species responses to habitat loss and plant community composition.

Several experimental studies have examined species responses to manipulations of habitat area and spatial arrangement, but plant composition and spatial variation in species distributions also affect animal responses to habitat alteration. We used an experimental approach to study the combined effects of habitat area, edge, and plant community composition on the spatial structure of insect species richness and composition. The abundance of three guilds (herbivores, predators and parasitoids) and individual species were also analyzed. Habitat patches were created that differed in area and edge by selectively mowing portions of 15 mx15 m plots in a 1.7-ha old field. Spatial and environmental variables were used to predict insect responses in separate multiple regression and ordination models. The variation in species responses due to spatial and environmental variables was then partitioned by combining these variables into an overall regression or ordination. Spatial and environmental variables contributed similar percentages to the total variance in insect species richness, abundance or composition. No significant effects of habitat area were observed in any response variable. Herbivore abundance showed positive responses to legume or grass cover, as well as spatial variation that was unrelated to environmental variables. Predators and parasitoids had greater effects of plant species richness and habitat edge, and less unexplained spatial variation. Individual species differed in their responses to plant variables, depending on host specialization or intraspecific aggregation. Our study highlights the importance of plant community composition and spatial variation apart from environmental variables. Spatial variation stems both from species responses to environmental features as well as species differences in habitat specialization and intraspecific aggregation.

Animals↗

Temporal and spatial frequency tuning of the flicker motion aftereffect.

The motion aftereffect (MAE) was used to study the temporal and spatial frequency selectivity of the visual system at supra-threshold contrasts. Observers adapted to drifting sine-wave gratings of a range of spatial and temporal frequencies. The magnitude of the MAE induced by the adaptation was measured with counterphasing test gratings of a variety of spatial and temporal frequencies. Independently of the spatial or temporal frequency of the adapting grating, the largest MAE was found with slowly counterphasing test gratings (at approximately 0.125-0.25 Hz). The largest MAEs were also found when the test grating was of similar spatial frequency to that of the adapting grating, even at very low spatial frequencies (0.125 c/deg). These data suggest that MAEs are dominated by a single, low-pass temporal frequency mechanism and by a series of band-pass spatial frequency mechanisms. The band-pass spatial frequency tuning even at low spatial frequencies suggests that the "lowest adaptable channel" concept [Cameron et al. (1992). Vision Research, 32, 561-568] may be an artifact of disadvantaged low spatial frequencies using static test patterns.

Adaptation, Ocular↗

Gender, level of spatial ability, and lateralization of mental rotation.

The present study indicates that some of the inconsistencies in studies of the lateralization of mental rotation may be a consequence of uncontrolled individual differences in the general level of spatial ability. In order to investigate the relation between spatial ability and the lateralization of mental rotation, 48 subjects (24 males and 24 females) were divided into three groups based on their performance on a standardized test of spatial ability. They then performed a lateralized two-dimensional mental rotation task. The results showed the typical mental rotation function in that angle of rotation and reaction time were linearly related. A significant spatial ability by visual field interaction indicated that subjects with low spatial ability had a left field advantage, whereas subjects with medium spatial ability showed no field advantage and subjects with high spatial ability showed a right field advantage. Gender also interacted with visual field, with males showing a left visual superiority and females an insignificant right visual field advantage. A significant three-way interaction of gender, spatial ability, and angle of rotation reflected the fact that low spatial males were more profoundly affected by rotation than the other groups. The results suggest that at least some of the inconsistent findings in studies of lateralization of mental rotation may be accounted for by differences in the level of spatial ability.

Aptitude↗

Spatial modeling of dimerization reaction dynamics in the plasma membrane: Monte Carlo vs. continuum differential equations.

Bimolecular reactions in the plasma membrane, such as receptor dimerization, are a key signaling step for many signaling systems. For receptors to dimerize, they must first diffuse until a collision happens, upon which a dimerization reaction may occur. Therefore, study of the dynamics of cell signaling on the membrane may require the use of a spatial modeling framework. Despite the availability of spatial simulation methods, e.g., stochastic spatial Monte Carlo (MC) simulation and partial differential equation (PDE) based approaches, many biological models invoke well-mixed assumptions without completely evaluating the importance of spatial organization. Whether one is to utilize a spatial or non-spatial simulation framework is therefore an important decision. In order to evaluate the importance of spatial effects a priori, i.e., without performing simulations, we have assessed the applicability of a dimensionless number, known as second Damköhler number (Da), defined here as the ratio of time scales of collision and reaction, for 2-dimensional bimolecular reactions. Our study shows that dimerization reactions in the plasma membrane with Da approximately >0.1 (tested in the receptor density range of 10(2)-10(5)/microm(2)) require spatial modeling. We also evaluated the effective reaction rate constants of MC and simple deterministic PDEs. Our simulations show that the effective reaction rate constant decreases with time due to time dependent changes in the spatial distribution of receptors. As a result, the effective reaction rate constant of simple PDEs can differ from that of MC by up to two orders of magnitude. Furthermore, we show that the fluctuations in the number of copies of signaling proteins (noise) may also depend on the diffusion properties of the system. Finally, we used the spatial MC model to explore the effect of plasma membrane heterogeneities, such as receptor localization and reduced diffusivity, on the dimerization rate. Interestingly, our simulations show that localization of epidermal growth factor receptor (EGFR) can cause the diffusion limited dimerization rate to be up to two orders of magnitude higher at higher average receptor densities reported for cancer cells, as compared to a normal cell.

Algorithms↗