Simon N. Jacob

Notation-Independent Representation of Fractions in the Human Parietal Cortex

Although the concept of whole numbers is intuitive and well suited for counting and ordering, it is with the invention of fractions that the number system gained precision and flexibility. Absolute magnitude is encoded by single neurons that discharge maximally to specific numbers. However, it is unknown how the ratio of two numbers is represented, whether by processing numerator and denominator in separation, or by extending the analog magnitude code to relative quantity. Using functional MRI adaptation, we now show that populations of neurons in human fronto-parietal cortex are tuned to preferred fractions, generalizing across the format of presentation. After blood oxygen level-dependent signal adaptation to constant fractions, signal recovery to deviant fractions was modulated parametrically as a function of numerical distance between the deviant and adaptation fraction. The distance effect was invariant to changes in notation from number to word fractions and strongest in the anterior intraparietal sulcus, a key region for the processing of whole numbers. These findings demonstrate that the human brain uses the same analog magnitude code to represent both absolute and relative quantity. Our results have implications for mathematical education, which may be tailored to better harness our ability to access automatically a composite quantitative measure.

Relating magnitudes: the brain's code for proportions

Whereas much is known about how we categorize and reason based on absolute quantity, data exploring ratios of quantities, as in proportions and fractions, are comparatively sparse. Until recently, it remained elusive whether these two representations of number are connected, how proportions are implemented by neurons and how language shapes this code. New data derived with complementary methods and from different model systems now shed light on the mechanisms of magnitude ratio representations. A coding scheme for proportions has emerged that is remarkably reminiscent of the representation of absolute number. These novel findings suggest a sense for ratios that grants the brain automatic access to proportions independently of language and the format of presentation.

Tuning to non-symbolic proportions in the human frontoparietal cortex

Humans share with many species a non‐verbal system to estimate absolute quantity. This sense of number has been linked to the activity of quantity‐selective neurons that respond maximally to preferred numerosities. With functional magnetic resonance imaging adaptation, we now show that populations of neurons in the human parietal and frontal cortex are also capable of encoding quantity ratios, or proportions, using the same non‐verbal analog code as for absolute number. Following adaptation to visually presented constant proportions (specified by the ratio of line lengths or numerosities), we introduced novel relative magnitudes to examine the tuning characteristics of the population of stimulated neurons. In bilateral parietal and frontal cortex we found that blood oxygenation level‐dependent signal recovery from adaptation was a function of numerical distance between the deviant proportion and the adaptation stimulus. The strongest effects were observed in the cortex surrounding the anterior intraparietal sulcus, a region considered pivotal for the processing of absolute magnitudes. Overall, there was substantial overlap of frontoparietal structures representing whole numbers and proportions. The identification of tuning to non‐symbolic ratio stimuli, irrespective of notation, adds to the magnitude system a remarkable level of sophistication by demonstrating automatic access to a composite, derived quantitative measure. Our results argue that abstract concepts of both absolute and relative number are deeply rooted in the primate brain as fundamental determinants of higher‐level numerical cognition.

Dopamine Receptors Differentially Enhance Rule Coding in Primate Prefrontal Cortex Neurons

Flexibly applying abstract rules is a hallmark feature of executive functioning represented by prefrontal cortex (PFC) neurons. Prefrontal networks are regulated by the neuromodulator dopamine, but how dopamine modulates high-level executive functions remains elusive. In monkeys performing a rule-based decision task, we report that both dopamine D1 and D2 receptors facilitated rule coding of PFC neurons, albeit by distinct physiological mechanisms. Dopamine D1 receptor stimulation suppressed neuronal firing while increasing responses to the preferred rule, thereby enhancing neuronal rule coding. D2 receptor stimulation, instead, excited neuronal firing while suppressing responses to the nonpreferred rule, thus also enhancing neuronal rule coding. These findings highlight complementary modulatory contributions of dopamine receptors to the neuronal circuitry mediating executive functioning and goal-directed behavior.

Signaling Microdomains Regulate Inositol 1,4,5-Trisphosphate-Mediated Intracellular Calcium Transients in Cultured Neurons

Ca2+ signals in neurons use specific temporal and spatial patterns to encode unambiguous information about crucial cellular functions. To understand the molecular basis for initiation and propagation of inositol 1,4,5-trisphosphate (InsP3)-mediated intracellular Ca2+ signals, we correlated the subcellular distribution of components of the InsP3 pathway with measurements of agonist-induced intracellular Ca2+ transients in cultured rat hippocampal neurons and pheochromocytoma cells. We found specialized domains with high levels of phosphatidylinositol-4-phosphate kinase (PIPKIγ) and chromogranin B (CGB), proteins acting synergistically to increase InsP3 receptor (InsP3R) activity and sensitivity. In contrast, Ca2+ pumps in the plasma membrane (PMCA) and sarco-endoplasmic reticulum as well as buffers that antagonize the rise in intracellular Ca2+ were distributed uniformly. By pharmacologically blocking phosphatidylinositol-4-kinase and PIPKIγ or disrupting the CGB-InsP3R interaction by transfecting an interfering polypeptide fragment, we produced major changes in the initiation site and kinetics of the Ca2+ signal. This study shows that a limited number of proteins can reassemble to form unique, spatially restricted signaling domains to generate distinctive signals in different regions of the same neuron. The finding that the subcellular location of initiation sites and protein microdomains was cell type specific will help to establish differences in spatiotemporal Ca2+ signaling in different types of neurons.

Dopamine Regulates Two Classes of Primate Prefrontal Neurons That Represent Sensory Signals

The lateral prefrontal cortex (PFC), a hub of higher-level cognitive processing, is strongly modulated by midbrain dopamine (DA) neurons. The cellular mechanisms have been comprehensively studied in the context of short-term memory, but little is known about how DA regulates sensory inputs to PFC that precede and give rise to such memory activity. By preparing recipient cortical circuits for incoming signals, DA could be a powerful determinant of downstream cognitive processing. Here, we tested the hypothesis that prefrontal DA regulates the representation of sensory signals that are required for perceptual decisions. In rhesus monkeys trained to report the presence or absence of visual stimuli at varying levels of contrast, we simultaneously recorded extracellular single-unit activity and applied DA to the immediate vicinity of the neurons by micro-iontophoresis. We found that DA modulation of prefrontal neurons is not uniform but tailored to specialized neuronal classes. In one population of neurons, DA suppressed activity with high temporal precision but preserved signal/noise ratio. Neurons in this group had short visual response latencies and comprised all recorded narrow-spiking, putative interneurons. In a distinct population, DA increased excitability and enhanced signal/noise ratio by reducing response variability. These neurons had longer visual response latencies and were composed exclusively of broad-spiking, putative pyramidal neurons. By gating sensory inputs to PFC and subsequently strengthening the representation of sensory signals, DA might play an important role in shaping how the PFC initiates appropriate behavior in response to changes in the sensory environment.

Cell-type-specific modulation of targets and distractors by dopamine D1 receptors in primate prefrontal cortex.

The prefrontal cortex (PFC) is crucial for maintaining relevant information in working memory and resisting interference. PFC neurons are strongly regulated by dopamine, but it is unknown whether dopamine receptors are involved in protecting target memories from distracting stimuli. We investigated the prefrontal circuit dynamics and dopaminergic modulation of targets and distractors in monkeys trained to ignore interfering stimuli in a delayed-match-to-numerosity task. We found that dopamine D1 receptors (D1Rs) modulate the recovery of task-relevant information following a distracting stimulus. The direction of modulation is cell-type-specific: in putative pyramidal neurons, D1R inhibition enhances and D1R stimulation attenuates coding of the target stimulus after the interference, while the opposite pattern is observed in putative interneurons. Our results suggest that dopaminergic neuromodulation of PFC circuits regulates mental representations of behaviourally relevant stimuli that compete with task-irrelevant input and could play a central role for cognitive functioning in health and disease.

Neuronal representation of number and proportion in the primate brain

Number symbols have allowed humans to develop superior mathematical skills that are a hallmark of technologically advanced cultures. Findings in animal cognition, developmental psychology, and anthropology indicate that these numerical skills are rooted in nonlinguistic biological primitives. Recent studies in human and nonhuman primates using a broad range of methodologies provide evidence that numerical information is represented and processed by regions of the prefrontal and posterior parietal lobes, where single neurons are tuned to preferred absolute quantities. Until recently, data exploring ratios of quantities, as in proportions and fractions, were comparatively sparse. New data derived with complementary methods and from different model systems now shed light on the mechanisms of magnitude ratio representations. A coding scheme for proportions has emerged that is highly reminiscent of the representation of absolute number. The magnitude code is automatic, independent of language and the format of presentation. These findings suggest that the primate brain houses a phylogenetically old network for the representation of quantity that, during the course of human evolution, has been coopted to build our remarkable sense of number.

Structuring of Abstract Working Memory Content by Fronto-parietal Synchrony in Primate Cortex

How is neuronal activity across distant brain regions orchestrated to allow multiple stimuli to be stored together in working memory, yet maintained separate for individual readout and protection from distractors? Using paired recordings in the prefrontal and parietal cortex of monkeys discriminating numbers of items (numerosities), we found that working memory content is structured by frequency-specific oscillatory synchrony. Parieto-frontal signaling in the beta band carried information about the most recent numerical input. Fronto-parietal coupling in the theta band differentiated between multiple memorized numerosities. Task-relevant and distracting stimuli were nested in spiking activity of single prefrontal neurons, but could be separated by reading out spikes at distinct phases of parietal theta oscillations. The strength of phase-locked, cross-regional memory coding predicted task performance. Frequency-specific communication channels in the fronto-parietal network could enable serial bottom-up and parallel top-down information transmission, providing an important mechanism to protect working memory from interference.

Neurobiologische Grundlagen der Verarbeitung von Anzahlen und Proportionen im Primatengehirn

Zusammenfassung Die Erfindung von Zahlensymbolen war ein entscheidender Schritt hin zur Entwicklung ausgeprägter mathematischer Fähigkeiten des Menschen, die ihrerseits den wissenschaftlich- technologischen Fortschritt ermöglichten. Vielfältige Studien zeigen, dass das grundlegende Verständnis von Anzahlen und Mengen nicht humanspezifisch, sondern im gesamten Tierreich verbreitet ist. Die Erforschung der neuronalen Grundlagen der numerischen Kognition hat in den letzten Jahren entscheidende Fortschritte erzielt. Bildgebende Verfahren beim Menschen und Einzelzellableitungen bei nicht-humanen Primaten konnten Regionen des Gehirns identifizieren und näher charakterisieren, die eine zentrale Rolle bei der Repräsentation von Quantitäten spielen. Es zeigte sich, dass sich im Stirn- und Scheitellappen der Großhirnrinde Neurone befinden, die auf Anzahlen und Proportionen abgestimmt sind. Quantitäten werden als analoge Größen repräsentiert; dieser Code ist automatisch, unabhängig vom Darstellungsformat und nicht an Sprache gebunden. Diese Befunde legen nahe, dass unser Sinn für Zahlen auf einem phylogenetisch alten Vorläufersystem zur Repräsentation von Quantitäten basiert, dessen Netzwerke im Laufe der Evolution übernommen und weiterentwickelt wurden.