Morphogenesis as Bayesian inference: A variational approach to pattern formation and control in complex biological systems

Recent advances in molecular biology such as gene editing [1], bioelectric recording and manipulation [2] and live cell microscopy using fluorescent reporters [3], [4] – especially with the advent of light-controlled protein activation through optogenetics [5] – have provided the tools to measure and manipulate molecular signaling pathways with unprecedented spatiotemporal precision. This has produced ever increasing detail about the molecular mechanisms underlying development and regeneration in biological organisms. However, an overarching concept – that can predict the emergence of form and the robust maintenance of complex anatomy – is largely missing in the field. Classic (i.e., dynamic systems and analytical mechanics) approaches such as least action principles are difficult to use when characterizing open, far-from equilibrium systems that predominate in Biology. Similar issues arise in neuroscience when trying to understand neuronal dynamics from first principles. In this (neurobiology) setting, a variational free energy principle has emerged based upon a formulation of self-organization in terms of (active) Bayesian inference. The free energy principle has recently been applied to biological self-organization beyond the neurosciences [6], [7]. For biological processes that underwrite development or regeneration, the Bayesian inference framework treats cells as information processing agents, where the driving force behind morphogenesis is the maximization of a cell's model evidence. This is realized by the appropriate expression of receptors and other signals that correspond to the cell's internal (i.e., generative) model of what type of receptors and other signals it should express. The emerging field of the free energy principle in pattern formation provides an essential quantitative formalism for understanding cellular decision-making in the context of embryogenesis, regeneration, and cancer suppression. In this paper, we derive the mathematics behind Bayesian inference – as understood in this framework – and use simulations to show that the formalism can reproduce experimental, top-down manipulations of complex morphogenesis. First, we illustrate this ‘first principle’ approach to morphogenesis through simulated alterations of anterior-posterior axial polarity (i.e., the induction of two heads or two tails) as in planarian regeneration. Then, we consider aberrant signaling and functional behavior of a single cell within a cellular ensemble – as a first step in carcinogenesis as false ‘beliefs’ about what a cell should ‘sense’ and ‘do’. We further show that simple modifications of the inference process can cause – and rescue – mis-patterning of developmental and regenerative events without changing the implicit generative model of a cell as specified, for example, by its DNA. This formalism offers a new road map for understanding developmental change in evolution and for designing new interventions in regenerative medicine settings

Scaling properties of granular materials

Given an assembly of viscoelastic spheres with certain material properties, we raise the question how the macroscopic properties of the assembly will change if all lengths of the system, i.e. radii, container size etc., are scaled by a constant. The result leads to a method to scale down experiments to lab-size.Comment: 4 pages, 2 figure

Functionally Relevant Maculopathy and Optic Atrophy in Spinocerebellar Ataxia Type 1

Background: Spinocerebellar ataxia type 1 (SCA-ATXN1) is an inherited progressive ataxia disorder characterized by an adult-onset cerebellar syndrome combined with nonataxia signs. Retinal or optic nerve affection are not systematically described. Objectives: To describe a retinal phenotype and its functional relevance in SCA-ATXN1. Methods: We applied optical coherence tomography (OCT) in 20 index cases with SCA-ATXN1 and 22 healthy controls (HCs), investigating qualitative changes and quantifying the peripapillary retinal nerve fiber layer (pRNFL) thickness and combined ganglion cell and inner plexiform layer (GCIP) volume as markers of optic atrophy and outer retinal layers as markers of maculopathy. Visual function was assessed by high- (HC-VA) and low-contrast visual acuity (LC-VA) and the Hardy-Rand-Rittler pseudoisochromatic test for color vision. Results: Five patients (25%) showed distinct maculopathies in the ellipsoid zone (EZ). Furthermore, pRNFL (P < 0.001) and GCIP (P = 0.002) were reduced in patients (pRNFL, 80.86 ± 9.49 μm; GCIP, 1.84 ± 0.16 mm3) compared with HCs (pRNFL, 97.02 ± 8.34 μm; GCIP, 1.98 ± 0.12 mm3). Outer macular layers were similar between groups, but reduced in patients with maculopathies. HC-VA (P = 0.002) and LC-VA (P < 0.001) were reduced in patients (HC-VA [logMAR]: 0.01 ± 010; LC-VA [logMAR]: 0.44 ± 0.16) compared with HCs (HC-VA [logMAR]: –0.12 ± 0.08; LC-VA [logMAR]: 0.25 ± 0.05). Color vision was abnormal in 2 patients with maculopathies. Conclusions: A distinct maculopathy, termed EZ disruption, as well as optic atrophy add to the known nonataxia features in SCA-ATXN1. Whereas optic atrophy may be understood as part of a widespread neurodegeneration, EZ disruption may be explained by effects of ataxin-1 gene or protein on photoreceptors. Our findings extend the spectrum of nonataxia signs in SCA-ATXN1 with potential relevance for diagnosis and monitoring

Optic chiasm measurements may be useful markers of anterior optic pathway degeneration in neuromyelitis optica spectrum disorders

OBJECTIVES: We aimed to evaluate optic chiasm (OC) measures as potential imaging marker for anterior optic pathway damage assessment in the context of neuromyelitis optica spectrum disorders (NMOSD). MATERIALS AND METHOD: This cross-sectional study included 39 patients exclusively with aquaporin 4-IgG seropositive NMOSD of which 25 patients had a history of optic neuritis (NMOSD-ON) and 37 age- and sex-matched healthy controls (HC). OC heights, width, and area were measured using standard 3D T1-weighted MRI. Sensitivity of these measures to detect neurodegeneration in the anterior optic pathway was assessed in receiver operating characteristics analyses. Correlation coefficients were used to assess associations with structural measures of the anterior optic pathway (optic nerve dimensions, retinal ganglion cell loss) and clinical measures (visual function and disease duration). RESULTS: OC heights and area were significantly smaller in NMOSD-ON compared to HC (NMOSD-ON vs. HC p < 0.0001). An OC area smaller than 22.5 mm(2) yielded a sensitivity of 0.92 and a specificity of 0.92 in separating chiasms of NMOSD-ON from HC. OC area correlated well with structural and clinical measures in NMOSD-ON: optic nerve diameter (r = 0.4, p = 0.047), peripapillary retinal nerve fiber layer thickness (r = 0.59, p = 0.003), global visual acuity (r = − 0.57, p = 0.013), and diseases duration (r = − 0.5, p = 0.012). CONCLUSION: Our results suggest that OC measures are promising and easily accessible imaging markers for the assessment of anterior optic pathway damage. KEY POINTS: (1) Optic chiasm dimensions were smaller in neuromyelitis optica spectrum disorder patients compared to healthy controls. (2) Optic chiasm dimensions are associated with retinal measures and visual dysfunction. (3) The optic chiasm might be used as an easily accessible imaging marker of neurodegeneration in the anterior optic pathway with potential functional relevance

Foveal changes in aquaporin‐4 antibody seropositive neuromyelitis optica spectrum disorder are independent of optic neuritis and not overtly progressive

Background and purpose: Foveal changes were reported in aquaporin-4 antibody (AQP4-Ab) seropositive neuromyelitis optica spectrum disorder (NMOSD) patients; however, it is unclear whether they are independent of optic neuritis (ON), stem from subclinical ON or crossover from ON in fellow eyes. Fovea morphometry and a statistical classification approach were used to investigate if foveal changes in NMOSD are independent of ON and progressive. Methods: This was a retrospective longitudinal study of 27 AQP4-IgG + NMOSD patients (49 eyes; 15 ON eyes and 34 eyes without a history of ON [NON eyes]), follow-up median (first and third quartile) 2.32 (1.33-3.28), and 38 healthy controls (HCs) (76 eyes), follow-up median (first and third quartile) 1.95 (1.83-2.54). The peripapillary retinal nerve fibre layer thickness and the volume of combined ganglion cell and inner plexiform layer as measures of neuroaxonal damage from ON were determined by optical coherence tomography. Nineteen foveal morphometry parameters were extracted from macular optical coherence tomography volume scans. Data were analysed using orthogonal partial least squares discriminant analysis and linear mixed effects models. Results: At baseline, foveal shape was significantly altered in ON eyes and NON eyes compared to HCs. Discriminatory analysis showed 81% accuracy distinguishing ON vs. HCs and 68% accuracy in NON vs. HCs. NON eyes were distinguished from HCs by foveal shape parameters indicating widening. Orthogonal partial least squares discriminant analysis discriminated ON vs. NON with 76% accuracy. In a follow-up of 2.4 (20.85) years, no significant time-dependent foveal changes were found. Conclusion: The parafoveal area is altered in AQP4-Ab seropositive NMOSD patients suggesting independent neuroaxonal damage from subclinical ON. Longer follow-ups are needed to confirm the stability of the parafoveal structure over time

Longitudinal analysis of T1w/T2w ratio in patients with multiple sclerosis from first clinical presentation

BACKGROUND: Cross-sectional studies suggest normal appearing white matter (NAWM) integrity loss may lead to cortical atrophy in late-stage relapsing-remitting multiple sclerosis (MS). OBJECTIVE: To investigate the relationship between NAWM integrity and cortical thickness from first clinical presentation longitudinally. METHODS: NAWM integrity and cortical thickness were assessed with 3T magnetic resonance imaging (MRI) in 102 patients with clinically isolated syndrome or early MS (33.2 (20.1–60.1) years old, 68% female) from first clinical presentation over 2.8 ± 1.6 years. Fifty healthy controls (HCs) matched for age and sex were included. NAWM integrity was evaluated using the standardized T1w/T2w ratio (sT1w/T2w). The association between sT1w/T2w and cortical thickness was assessed using linear mixed models. The effect of disease activity was investigated using the No Evidence of Disease Activity (NEDA-3) criteria. RESULTS: At baseline, sT1w/T2w (p = 0.152) and cortical thickness (p = 0.489) did not differ from HCs. Longitudinally, decreasing sT1w/T2w was associated with cortical thickness and increasing lesion burden (marginal R(2) = 0.061). The association was modulated by failing NEDA-3 (marginal R(2) = 0.097). CONCLUSION: sT1w/T2w may be a useful MRI biomarker for early MS, detecting relevant NAWM damage over time using conventional MRI scans, although with less sensitivity compared to quantitative measures

Sex differences in brain atrophy in multiple sclerosis

BACKGROUND: Women are more susceptible to multiple sclerosis (MS) than men by a ratio of approximately 3:1. However, being male is a risk factor for worse disability progression. Inflammatory genes have been linked to susceptibility, while neurodegeneration underlies disability progression. Thus, there appears to be a differential effect of sex on inflammation versus neurodegeneration. Further, gray matter (GM) atrophy is not uniform across the brain in MS, but instead shows regional variation. Here, we study sex differences in neurodegeneration by comparing regional GM atrophy in a cohort of men and women with MS versus their respective age- and sex-matched healthy controls. METHODS: Voxel-based morphometry (VBM), deep GM substructure volumetry, and cortical thinning were used to examine regional GM atrophy. RESULTS: VBM analysis showed deep GM atrophy in the thalamic area in both men and women with MS, whereas men had additional atrophy in the putamen as well as in localized cortical regions. Volumetry confirmed deep GM loss, while localized cortical thinning confirmed GM loss in the cerebral cortex. Further, MS males exhibited worse performance on the 9-hole peg test (9HPT) than MS females. We observed a strong correlation between thalamic volume and 9HPT performance in MS males, but not in MS females. CONCLUSION: More regional GM atrophy was observed in men with MS than women with MS, consistent with previous observations that male sex is a risk factor for worse disease progression

Accurate automated quantitative imaging of tortoise erythrocytes using the NIS image analysis system

The standard method for assessing blood cell characteristics using an ocular micrometer is time-consuming and limited. We used the Nikon NIS Elements imaging software and May-Grünwald-Giemsa staining to determine whether automated image analysis is suitable for rapid and accurate quantitative morphometry of erythrocytes. Blood was collected during four seasons from 126 geometric tortoises and the blood smears were evaluated for cell (C) and nuclear (N) characteristics of the erythrocytes. We measured area, length (L), width (W), perimeter, elongation and pixelation intensity, and calculated L/W and N/C areas. Erythrocyte size differed among cohorts; females, the larger sex, had smaller erythrocytes than either males or juveniles. Males had more elongated erythrocytes than females and erythrocytes of adults were more elongated than those of juveniles. Erythrocyte size and shape influence the efficiency of gas exchange owing to surface area to volume ratios, which are greater for small, elongated cells than for large, round cells. The high N/C ratio and low pixelation intensities of males and juveniles indicate that they may have had more immature erythrocytes in their circulation than females. The use of pixelation intensity to indicate the presence of immature erythrocytes was validated by seasonal differences that corresponded to the biology of the tortoises. Pixelation intensity was lowest in winter. We found that automated image analysis is a rapid and reliable method for determining cell size and shape, and it offers the potential for distinguishing among developmental stages that differ in staining intensity. The method should be useful for rapid health assessments, particularly of threatened species, and for comparative studies among different vertebrates.Web of Scienc