Elsevier

Neural Networks

Volume 116, August 2019, Pages 110-118
Neural Networks

The place cell activity is information-efficient constrained by energy

https://doi.org/10.1016/j.neunet.2019.04.001Get rights and content

Abstract

Spatial representation is a crucial function of animal’s brain. However, there is still no uniform explanation of how the spatial code is formed in different dimensional spaces to date. The main reason why place cell exhibits unique activity pattern is that the animal needs to retrieve and process spatial information. In this paper, we constructed a constrained optimization model based on information theory to explain the place field formation across species in different dimensional spaces. We proposed the following question that, using only limited amount of neural energy, how to organize the spiking locations (place field) in the available environment to obtain the most efficient spatial information representation? We solved this conditional functional extremum problem by variational techniques. The results showed that on the condition of limited neural energy, the place field will comply with a Gaussian-form distribution automatically to convey the largest amount information per spike. We also found that the animal’s natural habitat property and locomotion experience statistics affected the symmetry of spatial representation in different dimensions. These findings not only reconcile the argument of whether the spatial codes of place cell are isotropic, but also provide an explanation of place field formation by an information-theoretic approach. Furtherly, this research revealed the energy economical and information efficient properties underlie the spatial representation system of the brain.

Introduction

The mammalian hippocampus plays a crucial role in the spatial cognition, based on a cognitive map of the environment, which was proposed by Tolman (1948). The discovery of place cells (O’Keefe & Nadel, 1978) whose firing is tuned to specific locations in an animal’s locomotion environment lays a solid foundation for this view. The hippocampus is a critical area to memory (Clark & Squire, 2013) as well as to the brain’s spatial representation (Eichenbaum, 2017, Moser et al., 2008). Spatial information during navigation is encoded by hippocampal place cells using rate and temporal codes (Moser et al., 2008, O’Keefe and Burgess, 2005). Place cell (PC) exhibits a location-specific firing distribution, i.e. a given cell fires only when the animal is in a particular part of its environment. This set of locations is named place field (PF). Different cells are tuned to fire at different locations forming PFs of diverse sizes. As a result, the environment is represented by a cognitive map providing by place cell population in hippocampus (Wilson & McNaughton, 1993). Many interesting features of place cell have been revealed during some forty years’ pursuing. When animals are exploring various environments, different combinations of place cells are recruited, implying independent representation and hippocampal remapping (Almea, Miao, et al., 2014). During mice running on a treadmill enriched with visual-tactile landmarks, place cells are more strongly modulated by landmark-associated sensory inputs in deeper regions of CA1 pyramidal layer (Geiller et al., 2017). The lateral entorhinal area is involved in modulating how the dorsal hippocampus utilizes visual environmental cues, and increase the influence of the cue on place cells (Kristin et al., 2017). Depolarization and rate changes in grid cells lead to locational changes of hippocampal place fields and further produce hippocampal remapping (Kanter et al., 2017, Kubie and Fox, 2015). Place cells can also serve as a route planner in advance when animal is in the different initial locations of a familiar environment (Yates, 2013). And evidence has shown that autoassociative dynamics are emerged in sequence generation by place cells (Pfeiffer & Foster, 2015). Other than grid cells, head direction cells are also driving place cells. Directional information provided by the head direction cell system is essential for the angular disambiguation by place cells (Harland, Grieves, et al., 2017). Suppression-generating cell populations are found to minimize aberrant place cell activation, and limit the number of active place cells during traversal of a given field (Jayet Bray, Quoy, et al., 2010). Rate and temporal codes of place cell are featured by intracellular dynamics during navigation (Harvey, Collman, et al., 2009). Recent researches have also started to emphasize the impact of spatial dimensions on the place cell activity (Finkelstein et al., 2016, Hayman et al., 2011).

Many inspiring and interesting models have been developed in order to study the various properties of place cells, using tools and techniques such as Gaussian function (Foster et al., 2000, Hartley et al., 2000, O’Keefe and Burgess, 1996, Touretzky and Redish, 1996), back-propagation algorithm (Shapiro & Hetherington, 1993), auto-associative memory (Recce & Harris, 1996), competitive learning (Brown and Sharp, 1995, Sharp, 1991), neural architecture based on landmark recognition (Gaussier, Revel, Banquet, & Babeau, 2002), neuronal plasticity (Arleo and Gerstner, 2000, Arleo et al., 2004, Krichmar et al., 2005, Sheynikhovich et al., 2005, Strösslin et al., 2005), independent component analysis (Franzius et al., 2007, Takács and Lorincz, 2006), self-organizing map (Chokshi et al., 2003, Ollington and Vamplew, 2004), Kalman filter (Balakrishnan et al., 1999, Bousquet et al., 1998) and odor supported model (Kulvicius et al., 2008). All these models will eventually depict the most distinguishing activity pattern of place cells which is the emergence of PF. The place cell will be activated intensely in some particular locations on in the environment and these locations tend to cluster and be centralized. As the animal moves away from this area, the firing rate or activity power (Wang, Wang and et al., 2017) will decay as the distance from the center grows. This is also the main reason that Gaussian function is chosen directly to describe the behavior of place cell in many theoretical and modeling studies (Foster et al., 2000, glum and Abbott, 1996, Hartley et al., 2000, Kulvicius et al., 2008, O’Keefe and Burgess, 1996, O’Keefe and Burgess, 2005, Rolls, 2017, Samsonovich and McNaughton, 1997, Touretzky and Redish, 1996, Wang, Wang et al., 2017). However, how this pattern is formed and why this activity pattern is designed still remain to be furtherly answered.

There is no doubt that the main function of place cell system is to express and convey spatial information. Since the sensory cues (Kristin et al., 2017), grid cell activities (Kanter et al., 2017, Kubie and Fox, 2015) and head directional information (Harland et al., 2017) as well as the spatial topology are all driving the place cells, it is an effective but complex approach to study the place cell activity by neuronal connections and synaptic changes. Focusing on the information itself conveyed by place cell is an alternative. Based on the information theory, Skaggs, McNaughton, et al. (1993) deduced a measurement to quantify the amount of information conveyed by the firing rate of a place cell, which has been extensively used in experimental studies (Finkelstein et al., 2015, Fu et al., 2017, Hayman et al., 2011). However, this formula is rather a quantitative tool than an explanatory theory. Another approach to study the neuronal system is the recently developed energy coding method (Wang et al., 2015, Wang, Wang et al., 2017, Wang and Zhu, 2016) which proposed that neural information can be expressed by neural energy. The brain is a highly energy-efficient system (Wang et al., 2015), 1 petabyte of information flowed throughout the whole brain within 1 s (Bartol, Bromer, Kinney, Chirillo, Bourne, Harris, & Sejnowski, 2015) while the energy consumption is limited. Both experimental and computational evidences suggest that neural systems may maximize the efficiency of energy consumption during neural information processing (Wang et al., 2015, Wang, Wang et al., 2017, Yu and Yu, 2017). And efficiency is a basic principle to explain the design and function of brains on all levels of neural organization (Sterling & Laughlin, 2015). So based on these researches, it is a reasonable assumption that, under the pressure of natural selection, the neural systems such as the hippocampal networks will maximize the amount of information conveyed by neuronal activities with limited energy consumption. And the neuronal activity can even be changed by economic considerations (Tryon, Penner, et al., 2017). Based on these considerations, we will survey the energy and information properties underlie the place cell activity pattern and provide a possible explanation for the PF formation.

Section snippets

Model and method

Suppose that a PC fires on a certain half part of the environment, then whether the PC fires or not will reduce the uncertainty of the animal’s location. In this case, it can be considered that a spike conveys one bit of information about the spatial location. If the firing rate is f and the PC is observed for a sufficiently short time dt, on average fdt bits of information will be obtained. Detailed discussion was initially made by Skaggs et al. (1993), and this leads to the formula: I=xf(x)

Results

Based on the method introduced above, we simulate the behavior of PC in some special cases. Calculation has estimated that a typical neuron will consume 188 nJ energy to generate an action potential (Wang, Wang et al., 2017), so E0 is taken randomly from a normal distribution N(188, 102) nJ to introduce some uncertainty of the firing (Wang, Xu, & Wang, 2018).

Case 1 PC in 1D space

When a rat is exploring a 1D tube which can be expressed by an interval [a, b], it will probably move everywhere in

Discussion

Hippocampal PC is one of the most important components of the spatial cognition system. Numerous theoretical and experimental studies try to get a deeper understanding of PC’s properties. However, how the activity pattern of PC is formed? What is the relationship and difference of firing properties of different species in different dimensional spaces? Does the behavior statistical property of an animal affect the PC’s activity? All these interesting questions have not yet been answered

Acknowledgments

This work is supported by the National Natural Science Foundation of China (Nos. 11802095, 11702096, 11232005, 11472104, 11872180) and the Fundamental Research Funds for the Central Universities of China (Nos. 222201814025 & 222201714020)

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