Fully automated minicolumn chromatography.

Miniaturized chromatography columns (minicolumns) operated by automated liquid handlers are an integral part of bioprocess purification development. However, these systems can be limited in both their efficiency and accessibility. Because the minicolumn chromatography operation itself is higher throughput, the lower throughput pre- and post-operation activities become the bottleneck of the workflow. Additionally, method writing and operation of the systems while varying multiple parameters, using a design of experiments approach for example, can be error-prone and resource intensive. Here, we have developed a fully automated minicolumn chromatography system to both address these bottlenecks and improve the accessibility of these systems by allowing users to enter chromatography-relevant information through a simplified user interface. Methods have been developed to automate buffer preparation and protein solution titration leveraging modeling and integrated pH probes with feedback control. Chromatogram generation and fraction pooling has additionally been automated to improve the efficiency of post-chromatography operations. We have also demonstrated the flexibility of the system through an example run where both bind-and-elute chromatography and flowthrough chromatography experiments were performed in parallel. Additionally, all methodology and parameters to operate the system have been shared. We hope this will help interested parties improve the efficiency and accessibility of their minicolumn chromatography systems.

In vivo cortical diffusion imaging relates to Alzheimer's disease neuropathology.

BACKGROUND: There has been increasing interest in cortical microstructure as a complementary and earlier measure of neurodegeneration than macrostructural atrophy, but few papers have related cortical diffusion imaging to post-mortem neuropathology. This study aimed to characterise the associations between the main Alzheimer's disease (AD) neuropathological hallmarks and multiple cortical microstructural measures from in vivo diffusion MRI. Comorbidities and co-pathologies were also investigated. METHODS: Forty-three autopsy cases (8 cognitively normal, 9 mild cognitive impairment, 26 AD) from the National Alzheimer's Coordinating Center and Alzheimer's Disease Neuroimaging Initiative databases were included. Structural and diffusion MRI scans were analysed to calculate cortical minicolumn-related measures (AngleR, PerpPD+, and ParlPD) and mean diffusivity (MD). Neuropathological hallmarks comprised Thal phase, Braak stage, neuritic plaques, and combined AD neuropathological changes (ADNC-the "ABC score" from NIA-AA recommendations). Regarding comorbidities, relationships between cortical microstructure and severity of white matter rarefaction (WMr), cerebral amyloid angiopathy (CAA), atherosclerosis of the circle of Willis (ACW), and locus coeruleus hypopigmentation (LCh) were investigated. Finally, the effect of coexistent pathologies-Lewy body disease and TAR DNA-binding protein 43 (TDP-43)-on cortical microstructure was assessed. RESULTS: Cortical diffusivity measures were significantly associated with Thal phase, Braak stage, ADNC, and LCh. Thal phase was associated with AngleR in temporal areas, while Braak stage was associated with PerpPD+ in a wide cortical pattern, involving mainly temporal and limbic areas. A similar association was found between ADNC (ABC score) and PerpPD+. LCh was associated with PerpPD+, ParlPD, and MD. Co-existent neuropathologies of Lewy body disease and TDP-43 exhibited significantly reduced AngleR and MD compared to ADNC cases without co-pathology. CONCLUSIONS: Cortical microstructural diffusion MRI is sensitive to AD neuropathology. The associations with the LCh suggest that cortical diffusion measures may indirectly reflect the severity of locus coeruleus neuron loss, perhaps mediated by the severity of microglial activation and tau spreading across the brain. Recognizing the impact of co-pathologies is important for diagnostic and therapeutic decision-making. Microstructural markers of neurodegeneration, sensitive to the range of histopathological features of amyloid, tau, and monoamine pathology, offer a more complete picture of cortical changes across AD than conventional structural atrophy.

[Autism. Neurobiological aspects]. / Autismo. Aspectos neurobiológicos.

Autism is a neurodevelopmental disorder with a neurobiological basis, characterized by a qualitative disturbance in social interaction and communication, associated with restricted interests and stereotyped behaviors. The genesis of autism cannot be interpreted through a single theory, and we can't compartmentalize brain areas as the only ones responsible for it. Among the neurobiological bases we can include: deficit in the social reward system, which generates poor social initiative; dysfunctions and disorders of the amygdala and the mirror neuron system, related to compromised empathy and social cognition; abnormalities in the minicolumns related to hyper-systematization; persistent inflammatory phenomena of the central nervous system related to microglia; alterations of neuropeptides such as oxytocin, vasopressin and cortisol, which compromise socialization, and neuronal inhibition disorders, expressed in GABAergic dysfunctions in interneurons, linked to autistic behaviors, epilepsy and sensory phenomena. Understanding the neurobiological bases of autism is complex and there is no single explanation or specific biological marker. However, identifying processes related to social cognition, molecular, inflammatory, neuromodulation mechanisms and bases linked to sensory disorders are fundamental elements.

El autismo es un trastorno del neurodesarrollo de base neurobiológica, caracterizado por una alteración cualitativa en la interacción social y la comunicación, asociado a intereses restringidos y conductas estereotipadas. La génesis del autismo no puede interpretarse a través de una sola teoría, tampoco podemos compartimentalizar áreas del cerebro como únicos responsables de la misma. Entre las bases neurobiológicas podemos incluir: déficit en el sistema de recompensa social, lo cual genera pobre iniciativa social; disfunciones y trastornos de la amígdala y el sistema de neuronas espejo, relacionadas al compromiso en la empatía y la cognición social; anormalidades en las minicolumnas relacionadas con la hiper-sistematización; fenómenos inflamatorios persistentes del sistema nervioso central relacionados a la microglía; alteraciones de los neuropéptidos como oxitocina, vasopresina y cortisol, que comprometen la socialización, y trastornos en la inhibición neuronal, expresados en disfunciones gabaérgicas en las inteneuronas, vinculadas a conductas autistas, epilepsia y fenómenos sensoriales. La comprensión de las bases neurobiológicas del autismo son complejas y no existe un marcador biológico específico. Sin embargo, identificar procesos relacionados a la cognición social, mecanismos moleculares, inflamatorios, de neuromodulación y bases vinculadas a trastornos sensoriales son elementos fundamentales.

Understanding the effects of system differences for parameter estimation and scale-up of high throughput chromatographic data.

In this paper, we evaluate how employing fraction collection and multistep gradients with RoboColumns® (Repligen, formally Atoll) affects both comparison to benchtop experimental data and column simulation parameter estimation. These operational differences arise from the RoboColumn® system (operated on an automated liquid handling device) requiring offline analysis for determination of elution profiles rather than the continuous in-line UV curves obtained with larger scale systems. In addition, multistep gradients are used to model the smooth linear gradients of larger scale systems because sequential injections are used to provide liquid flow. Comparisons of two sets of column simulations was first carried out to demonstrate that fraction collection reduced the first moments of the elution peaks by 1/2 of the fraction volumes. Additional column simulations determined that the effect of a multistep gradient approximation on retention volume was dependent upon the gradient step length. An empirical transformation was then developed to correct the first moments obtained from gradient experimental data using the RoboColumn® system. These corrected values provided a more direct comparison of the experimental data at different scales and resulted in a significant improvement in agreement with results obtained using a 20 mL benchtop column. Linear steric mass-action (SMA) parameters were then estimated using the corrected values and employed to successfully predict the performance of the benchtop system data. Finally, these parameters were demonstrated to be well suited for modeling the RoboColumn® gradient data when properly accounting for multistep gradients and fraction collection. This work continues previous investigations into understanding system differences associated with robotic liquid handling devices and proposes a methodology for properly accounting for operational differences to predict operation at larger scales using conventional chromatography systems.

Cytochrome oxidase "blobs": a call for more anatomy.

An ordered relation of structure and function has been a cornerstone in thinking about brain organization. Like the brain itself, however, this is not straightforward and is confounded both by functional intricacy and structural plasticity (many routes to a given outcome). As a striking case of putative structure-function correlation, this mini-review focuses on the relatively well-characterized pattern of cytochrome oxidase (CO) blobs (aka "patches" or "puffs") in the supragranular layers of macaque monkey visual cortex. The pattern is without doubt visually compelling, and the semi-dichotomous array of CO+ blobs and CO- interblobs is consistent with multiple studies reporting compartment-specific preferential connectivity and distinctive physiological response properties. Nevertheless, as briefly reviewed here, the finer anatomical organization of this system is surprisingly under-investigated, and the relation to functional aspects, therefore, unclear. Microcircuitry, cell type, and three-dimensional spatiotemporal level investigations of the CO+ CO- pattern are needed and may open new views to structure-function organization of visual cortex, and to phylogenetic and ontogenetic comparisons across nonhuman primates (NHP), and between NHP and humans.

Relationship between HETP measurements and breakthrough curves in short chromatography columns.

An analysis of the relationship between the number of plates measured with a small molecule tracer and the breakthrough curve of a strongly bound protein in short laboratory chromatography columns (1-5 cm) considering flow nonuniformity is presented. For practical conditions, while axial dispersion has only a small impact on the breakthrough curve, radial flow nonuniformity has a profound effect. Radial parabolic velocity profiles lead to tailing tracer peaks and broader breakthrough curves. Profiles where the velocity varies radially only in a thin region near the column wall lead to fronting tracer peaks and early breakthrough when the velocity at the wall is higher than the average and to tailing peaks and tailing breakthrough curves when the velocity at the wall is lower than the average. Experiments conducted in laboratory minicolumns (0.5-1 cm diameter, 0.5-1 ml volume) show tracer peaks and protein breakthrough curves that are consistent with higher velocities at the wall. The model presented in this work provides a tool to model experimental breakthrough data and to assess the degree of flow uniformity required to obtain meaningful dynamic binding capacity measurements using minicolumns in a high-throughput lab setting.

Translational Neuroscience in Autism: From Neuropathology to Transcranial Magnetic Stimulation Therapies.

The presence of heterotopias, increased regional density of neurons at the gray-white matter junction, and focal cortical dysplasias all suggest an abnormality of neuronal migration in autism spectrum disorder (ASD). The abnormality is borne from a dissonance in timing between radial and tangentially migrating neuroblasts to the developing cortical plate. The uncoupling of excitatory and inhibitory cortical cells disturbs the coordinated interactions of neurons within local networks, thus providing abnormal patterns of brainwave activity in the gamma bandwidth. In ASD, gamma oscillation abnormalities and autonomic markers offer measures of therapeutic progress and help in the identification of subgroups.

Cellular and Network Mechanisms for Temporal Signal Propagation in a Cortical Network Model.

The mechanisms underlying an effective propagation of high intensity information over a background of irregular firing and response latency in cognitive processes remain unclear. Here we propose a SSCCPI circuit to address this issue. We hypothesize that when a high-intensity thalamic input triggers synchronous spike events (SSEs), dense spikes are scattered to many receiving neurons within a cortical column in layer IV, many sparse spike trains are propagated in parallel along minicolumns at a substantially high speed and finally integrated into an output spike train toward or in layer Va. We derive the sufficient conditions for an effective (fast, reliable, and precise) SSCCPI circuit: (i) SSEs are asynchronous (near synchronous); (ii) cortical columns prevent both repeatedly triggering SSEs and incorrectly synaptic connections between adjacent columns; and (iii) the propagator in interneurons is temporally complete fidelity and reliable. We encode the membrane potential responses to stimuli using the non-linear autoregressive integrated process derived by applying Newton's second law to stochastic resilience systems. We introduce a multithreshold decoder to correct encoding errors. Evidence supporting an effective SSCCPI circuit includes that for the condition, (i) time delay enhances SSEs, suggesting that response latency induces SSEs in high-intensity stimuli; irregular firing causes asynchronous SSEs; asynchronous SSEs relate to healthy neurons; and rigorous SSEs relate to brain disorders. For the condition (ii) neurons within a given minicolumn are stereotypically interconnected in the vertical dimension, which prevents repeated triggering SSEs and ensures signal parallel propagation; columnar segregation avoids incorrect synaptic connections between adjacent columns; and signal propagation across layers overwhelmingly prefers columnar direction. For the condition (iii), accumulating experimental evidence supports temporal transfer precision with millisecond fidelity and reliability in interneurons; homeostasis supports a stable fixed-point encoder by regulating changes to synaptic size, synaptic strength, and ion channel function in the membrane; together all-or-none modulation, active backpropagation, additive effects of graded potentials, and response variability functionally support the multithreshold decoder; our simulations demonstrate that the encoder-decoder is temporally complete fidelity and reliable in special intervals contained within the stable fixed-point range. Hence, the SSCCPI circuit provides a possible mechanism of effective signal propagation in cortical networks.

Relating diffusion tensor imaging measurements to microstructural quantities in the cerebral cortex in multiple sclerosis.

To investigate whether the observed anisotropic diffusion in cerebral cortex may reflect its columnar cytoarchitecture and myeloarchitecture, as a potential biomarker for disease-related changes, we compared postmortem diffusion magnetic resonance imaging scans of nine multiple sclerosis brains with histology measures from the same regions. Histology measurements assessed the cortical minicolumnar structure based on cell bodies and associated axon bundles in dorsolateral prefrontal cortex (Area 9), Heschl's gyrus (Area 41), and primary visual cortex (V1). Diffusivity measures included mean diffusivity, fractional anisotropy of the cortex, and three specific measures that may relate to the radial minicolumn structure: the angle of the principal diffusion direction in the cortex, the component that was perpendicular to the radial direction, and the component that was parallel to the radial direction. The cellular minicolumn microcircuit features were correlated with diffusion angle in Areas 9 and 41, and the axon bundle features were correlated with angle in Area 9 and to the parallel component in V1 cortex. This may reflect the effect of minicolumn microcircuit organisation on diffusion in the cortex, due to the number of coherently arranged membranes and myelinated structures. Several of the cortical diffusion measures showed group differences between MS brains and control brains. Differences between brain regions were also found in histology and diffusivity measurements consistent with established regional variation in cytoarchitecture and myeloarchitecture. Therefore, these novel measures may provide a surrogate of cortical organisation as a potential biomarker, which is particularly relevant for detecting regional changes in neurological disorders.

The modular organization of the cerebral cortex: Evolutionary significance and possible links to neurodevelopmental conditions.

The recognition of discernible anatomical regularities that appear to self-organize during development makes apparent the modular organization of the cerebral cortex. The metabolic cost engendered in sustaining interneuronal communications has emphasized the viability of short connections among neighboring neurons. This pattern of connectivity establishes a microcircuit which is repeated in parallel throughout the cerebral cortex. This canonical circuit is contained within the smallest module of information processing of the cerebral cortex; one which Vernon Mountcastle called the minicolumn. Plasticity within the brain is accounted, in part, by the presence of weak linkages that allow minicolumns to process information from a variety of sources and to quickly adapt to environmental exigencies without a need for genetic change. Recent research suggests that interlaminar correlated firing between minicolumns during the decision phase of target selection provides for the emergence of some executive functions. Bottlenecks of information processing within this modular minicolumnar organization may account for a variety of mental disorders observed in neurodevelopmental conditions.

Understanding operational system differences for transfer of miniaturized chromatography column data using simulations.

In this paper, a simulation tool was employed to identify and appropriately incorporate differences between MiniColumns and benchtop column systems. It was first demonstrated that including multi-step gradients and fraction collection into the simulations resulted in improved agreement between simulated and experimental linear gradient profiles as well as calculated first moments in the MiniColumn experiments. Step elution experiments of binary mixtures (a monoclonal antibody and one of three model proteins) were then carried out to examine comparability of the MiniColumns to the benchtop system. Although the peak shapes were qualitatively similar, peak elution began earlier in the MiniColumn system while improved separation was observed between overlapping peaks using the benchtop format. Simulations were then carried out to demonstrate that increased dispersion of the eluent breakthrough in the benchtop system could readily explain these observed differences. Importantly, by incorporating these system differences into the simulations, we were able to predict benchtop step elution performance using the parameters solely obtained from the MiniColumns. The findings presented in this paper illustrate that the appropriate consideration of system differences can facilitate the implementation of miniature chromatography columns as scale-down models for bioprocess development.

The neuroanatomy of autism - a developmental perspective.

Autism Spectrum Disorders (ASDs) are a heterogeneous group of neurodevelopmental disorders that are diagnosed solely on the basis of behaviour. A large body of work has reported neuroanatomical differences between individuals with ASD and neurotypical controls. Despite the huge clinical and genetic heterogeneity that typifies autism, some of these anatomical features appear to be either present in most cases or so dramatically altered in some that their presence is now reasonably well replicated in a number of studies. One such finding is the tendency towards overgrowth of the frontal cortex during the early postnatal period. Although these reports have been focused primarily on the presumed pathological anatomy, they are providing us with important insights into normal brain anatomy and are stimulating new ideas and hypotheses about the normal trajectory of brain development and the function of specific anatomical brain structures. The use of model systems that include genetic model organisms such as the mouse and, more recently, human induced pluripotent stem cell-derived brain organoids to model normal and pathological human cortical development, is proving particularly informative. Here we review some of the neuroanatomical alterations reported in autism, with a particular focus on well-validated findings and recent advances in the field, and ask what these observations can tell us about normal and abnormal brain development.

What Is the Evidence for Inter-laminar Integration in a Prefrontal Cortical Minicolumn?

The objective of this perspective article is to examine columnar inter-laminar integration during the executive control of behavior. The integration hypothesis posits that perceptual and behavioral signals are integrated within the prefrontal cortical inter-laminar microcircuits. Inter-laminar minicolumnar activity previously recorded from the dorsolateral prefrontal cortex (dlPFC) of nonhuman primates, trained in a visual delay match-to-sample (DMS) task, was re-assessed from an integrative perspective. Biomorphic multielectrode arrays (MEAs) played a unique role in the in vivo recording of columnar cell firing in the dlPFC layers 2/3 and 5/6. Several integrative aspects stem from these experiments: 1. Functional integration of perceptual and behavioral signals across cortical layers during executive control. The integrative effect of dlPFC minicolumns was shown by: (i) increased correlated firing on correct vs. error trials; (ii) decreased correlated firing when the number of non-matching images increased; and (iii) similar spatial firing preference across cortical-striatal cells during spatial-trials, and less on object-trials. 2. Causal relations to integration of cognitive signals by the minicolumnar turbo-engines. The inter-laminar integration between the perceptual and executive circuits was facilitated by stimulating the infra-granular layers with firing patterns obtained from supra-granular layers that enhanced spatial preference of percent correct performance on spatial trials. 3. Integration across hierarchical levels of the brain. The integration of intention signals (visual spatial, direction) with movement preparation (timing, velocity) in striatum and with the motor command and posture in midbrain is also discussed. These findings provide evidence for inter-laminar integration of executive control signals within brain's prefrontal cortical microcircuits.

Detection and spatial characterization of minicolumnarity in the human cerebral cortex.

BACKGROUND: Spatial characterization of vertical organization of neurons in human cerebral cortex, cortical columnarity or minicolumns, and its possible association with various psychiatric and neurological diseases has been investigated for many years. NEW METHOD: In this study, we obtained 3D coordinates of disector sampled cells from layer III of Brodmann area 4 of the human cerebral cortex using light microscopy and 140-µm-thick glycolmethacrylate sections. A new analytical tool called cylindrical K-function was applied for spatial point pattern analysis of 3D datasets to see whether there is a spatially organized columnar structure. In order to demonstrate the behaviour of the cylindrical K-function, the result from brain tissues was compared with two models: A homogeneous Poisson process exhibiting complete spatial randomness, and a Poisson line cluster point process. The latter is a point process model in 3D space, which exhibits spatial structure of points similar to minicolumns. RESULTS: The data show in three out of four samples nonrandom patterns in the 3D neuronal positions with the direction of minicolumns perpendicular to the pial surface of the brain - without a priori assuming the existence of minicolumns. COMPARISON WITH EXISTING METHODS: Studies on columnarity are difficult and have mainly been based on two-dimensional images analysis of thin sections of the cerebral cortex with the a priori assumption that minicolumns existed. CONCLUSIONS: A clear difference from complete spatial randomness in the data could be detected with the new tool, the cylindrical K-function, although classical functional summary statistics are less useful in this connection.

Use of MiniColumns for linear isotherm parameter estimation and prediction of benchtop column performance.

In this paper, a comparison between experimental chromatography data and column simulations is carried out to determine the efficacy of using miniaturized chromatography columns (MiniColumns) for both column modeling parameter estimation and process development. Normalization of the data with respect to column volumes along with appropriate translations to account for system differences is shown to result in comparability of the experimental data for the MiniColumn and benchtop systems. A parameter estimation protocol is then employed to determine the linear steric mass-action (SMA) isotherm and lumped mass transport parameters for two cation exchange resins. The models are then validated and simulations using different parameter sets from the MiniColumn and benchtop systems are shown to result in similar predicted chromatography profiles and calculated retention volumes. The parameters generated from the MiniColumn system are demonstrated to be well suited for predicting experimental data from the benchtop system. These simulation results, the ability to operate MiniColumns in parallel, and the significantly lower material requirements per experiment support an industry trend toward increased usage of miniaturized chromatography columns as a scale-down model for process development.

The autistic brain in the context of normal neurodevelopment.

The etiology of autism spectrum disorders (ASDs) is complex and largely unclear. Among various lines of inquiry, many have suggested convergence onto disruptions in both neural circuitry and immune regulation/glial cell function pathways. However, the interpretation of the relationship between these two putative mechanisms has largely focused on the role of exogenous factors and insults, such as maternal infection, in activating immune pathways that in turn result in neural network abnormalities. Yet, given recent insights into our understanding of human neurodevelopment, and in particular the critical role of glia and the immune system in normal brain development, it is important to consider these putative pathological processes in their appropriate normal neurodevelopmental context. In this review, we explore the hypothesis that the autistic brain cellular phenotype likely represents intrinsic abnormalities of glial/immune processes constitutively operant in normal brain development that result in the observed neural network dysfunction. We review recent studies demonstrating the intercalated role of neural circuit development, the immune system, and glial cells in the normal developing brain, and integrate them with studies demonstrating pathological alterations in these processes in autism. By discussing known abnormalities in the autistic brain in the context of normal brain development, we explore the hypothesis that the glial/immune component of ASD may instead be related to intrinsic exaggerated/abnormal constitutive neurodevelopmental processes such as network pruning. Moreover, this hypothesis may be relevant to other neurodevelopmental disorders that share genetic, pathologic, and clinical features with autism.

Wider minicolumns in autism: a neural basis for altered processing?

Previous studies have found alterations in the columnar organization of the cortex in autism spectrum disorders. Such changes have been suggested to be limited to higher order association areas and to spare primary sensory areas. In addition, evidence from gene-expression studies have suggested that there may be an attenuation of cortical differentiation in autism spectrum disorders. The present study specifically assessed the minicolumns of cells that span the depth of the cortex in a larger sample of autism spectrum disorder cases than have been studied previously, and across a broad age range. The cortical regions to be investigated were carefully chosen to enable hypotheses about cortical differentiation and the vulnerability of association cortex to be tested. Measures of the minicolumnar arrangement of the cortex (minicolumn width, spacing and width of the associated axon bundles) were made in four regions of cortex (primary auditory cortex, auditory association cortex, orbital frontal cortex and inferior parietal lobe) for 28 subjects with autism spectrum disorder and 25 typically developing control subjects. The present study found wider minicolumns in autism spectrum disorder [F(1,28) = 8.098, P = 0.008], which was particularly pronounced at younger ages, providing evidence for an altered developmental trajectory at the microstructural level. In addition, altered minicolumn width was not restricted to higher order association areas, but was also seen in the primary sensory region investigated. Finally, this study found evidence that cortical regional differentiation was still present in autism spectrum disorder [F(3,39) = 5.486, P = 0.003], although attenuated compared to typically developing subjects [F(3,45) = 18.615, P < 0.001]. It is suggested that wider spacing of the minicolumns may relate to the enhanced discrimination seen in some individuals with autism spectrum disorders.

Molecules and mechanisms that regulate multipolar migration in the intermediate zone.

Most neurons migrate with an elongated, "bipolar" morphology, extending a long leading process that explores the environment. However, when immature projection neurons enter the intermediate zone (IZ) of the neocortex they become "multipolar". Multipolar cells extend and retract cytoplasmic processes in different directions and move erratically-sideways, up and down. Multipolar cells extend axons while they are in the lower half of the IZ. Remarkably, the cells then resume radial migration: they reorient their centrosome and Golgi apparatus towards the pia, transform back to bipolar morphology, and commence locomotion along radial glia (RG) fibers. This reorientation implies the existence of directional signals in the IZ that are ignored during the multipolar stage but sensed after axonogenesis. In vivo genetic manipulation has implicated a variety of candidate directional signals, cell surface receptors, and signaling pathways, that may be involved in polarizing multipolar cells and stabilizing a pia-directed leading process for radial migration. Other signals are implicated in starting multipolar migration and triggering axon outgrowth. Here we review the molecules and mechanisms that regulate multipolar migration, and also discuss how multipolar migration affects the orderly arrangement of neurons in layers and columns in the developing neocortex.

Laws of conservation as related to brain growth, aging, and evolution: symmetry of the minicolumn.

Development, aging, and evolution offer different time scales regarding possible anatomical transformations of the brain. This article expands on the perspective that the cerebral cortex exhibits a modular architecture with invariant properties in regards to these time scales. These properties arise from morphometric relations of the ontogenetic minicolumn as expressed in Noether's first theorem, i.e., that for each continuous symmetry there is a conserved quantity. Whenever minicolumnar symmetry is disturbed by either developmental or aging processes the principle of least action limits the scope of morphometric alterations. Alternatively, local and global divergences from these laws apply to acquired processes when the system is no longer isolated from its environment. The underlying precepts to these physical laws can be expressed in terms of mathematical equations that are conservative of quantity. Invariant properties of the brain include the rotational symmetry of minicolumns, a scaling proportion or "even expansion" between pyramidal cells and core minicolumnar size, and the translation of neuronal elements from the main axis of the minicolumn. It is our belief that a significant portion of the architectural complexity of the cerebral cortex, its response to injury, and its evolutionary transformation, can all be captured by a small set of basic physical laws dictated by the symmetry of minicolumns. The putative preservations of parameters related to the symmetry of the minicolumn suggest that the development and final organization of the cortex follows a deterministic process.