Degeneracy in hippocampal physiology and plasticity

Degeneracy, defined as the ability of structurally disparate elements to perform analogous function, has largely been assessed from the perspective of maintaining robustness of physiology or plasticity. How does the framework of degeneracy assimilate into an encoding system where the ability to change is an essential ingredient for storing new incoming information? Could degeneracy maintain the balance between the apparently contradictory goals of the need to change for encoding and the need to resist change towards maintaining homeostasis? In this review, we explore these fundamental questions with the mammalian hippocampus as an example encoding system. We systematically catalog lines of evidence, spanning multiple scales of analysis, that demonstrate the expression of degeneracy in hippocampal physiology and plasticity. We assess the potential of degeneracy as a framework to achieve the conjoint goals of encoding and homeostasis without cross-interferences. We postulate that biological complexity, involving interactions among the numerous parameters spanning different scales of analysis, could establish disparate routes towards accomplishing these conjoint goals. These disparate routes then provide several degrees of freedom to the encoding-homeostasis system in accomplishing its tasks in an input- and state-dependent manner. Finally, the expression of degeneracy spanning multiple scales offers an ideal reconciliation to several outstanding controversies, through the recognition that the seemingly contradictory disparate observations are merely alternate routes that the system might recruit towards accomplishment of its goals. Against the backdrop of the ubiquitous prevalence of degeneracy and its strong links to evolution, it is perhaps apt to add a corollary to Theodosius Dobzhansky’s famous quote and state “nothing in physiology makes sense except in the light of degeneracy”. Highlights Degeneracy is the ability of structurally distinct elements to yield similar function We postulate a critical role for degeneracy in the emergence of stable encoding systems We catalog lines of evidence for the expression of degeneracy in the hippocampus We suggest avenues for research to explore degeneracy in stable encoding systems Dobzhansky wrote: “nothing in biology makes sense except in the light of evolution” A corollary: “nothing in physiology makes sense except in the light of degeneracy”

The pervasive question on the relationship between structure and function spans every aspect of 2 life, science and philosophy: from building architectures to the mind-body problem, from 3 connectomics to genomics to proteomics, from subatomic structures to cosmic bodies and from 4 biomechanics to climate science. Even within a limited perspective spanning only neuroscience, 5 the question has been posed at every scale of brain organization spanning the genetic to 6 behavioral ends of the spectrum. Efforts to address this question have resulted in extensive 7 studies that have yielded insights about the critical roles of protein structure and localization, 8 synaptic ultrastructure, dendritic morphology, microcircuit organization and large-scale synaptic 9 connectivity in several neural and behavioral functions. 10 The question on the relationship between structure and function has spawned wide-11 ranging debates, with disparate approaches towards potential answers. At one extreme is the 12 suggestion that structure defines function (Buzsaki, 2006): 13 "The safest way to start speculating about the functions of a structure is to inspect 14 its anatomical organization carefully. The dictum "structure defines function" never 15 fails, although the architecture in itself is hardly ever sufficient to provide all the 16 necessary clues." 17 18 Within this framework, the following is considered as a route for understanding neural systems 19 and behavior (Buzsaki, 2006): 20 "First, we need to know the basic "design" of its circuitry at both microscopic and 21 macroscopic levels. Second, we must decipher the rules governing interactions 22 among neurons and neuronal systems that give rise to overt and covert behaviors." 23 24 The other extreme is the assertion that "form follows function", elucidated by Bert Sakmann 25 (Sakmann, 2017), quoting Louis Sullivan: 26 "Whether it be the sweeping eagle in his flight, or the open apple-blossom, the 27 toiling work-horse, the blithe swan, the branching oak, the winding stream at its 28 base, the drifting clouds, over all the coursing sun, form ever follows function, and 29 this is the law. Where function does not change, form does not change". 30 31 Within this framework, the approach to understanding neural structure function relations was 32 elucidated as (Sakmann, 2017): 33 "The approach we took, in order to discover structure-function relations that help to 34 unravel simple design principles of cortical networks was, to first determine 35 functions and then reconstruct the underlying morphology assuming that "form 36 follows function", a dictum of Louis Sullivan and also a Bauhaus design principle." 37 38 A third approach embarks on addressing the structure-function question by recognizing the 39 existence of ubiquitous variability and combinatorial complexity in biological systems. This was 40 elucidated in a landmark review by Edelman and Gally, who presented an approach to structure-41 function relationship by defining degeneracy (Edelman and Gally, 2001): 42 "Degeneracy is the ability of elements that are structurally different to perform the 43 same function or yield the same output. Unlike redundancy, which occurs when the 44 same function is performed by identical elements, degeneracy, which involves 45 structurally different elements, may yield the same or different functions depending 46 on the context in which it is expressed. It is a prominent property of gene networks, 47 neural networks, and evolution itself. Indeed, there is mounting evidence that 48 degeneracy is a ubiquitous property of biological systems at all levels of 49 organization." 50 51 They approach degeneracy and the structure-function question from an evolutionary perspective, 52 noting (Edelman and Gally, 2001): 53 "Here, we point out that degeneracy is a ubiquitous biological property and argue 54 that it is a feature of complexity at genetic, cellular, system, and population levels. 55 Furthermore, it is both necessary for, and an inevitable outcome of, natural 56 selection." 57 58 From this perspective, the supposition that a one-to-one relationship between structure and 59 function exists is eliminated, thereby yielding more structural routes to achieving the same 60 function. This perspective posits that biological complexity should be viewed from the 61 Within the purview of degeneracy, the emergence of specific combinations of higher-126 scale functions (within the limits of biological variability) could be achieved (Fig. 1B)  Further, especially given the ubiquitous variability across animals in terms of constituent 175 components that elicit analogous behavior, it is clear that the impact of deletion of one specific 176 component would be differential. This implies that the simplistic generalizability on the presence 177 or absence of degeneracy based on a single parameter and a single measurement is untenable in 178 complex adaptive systems. Additionally, with reference to the specific example of gene deletion, 179 it is also important to distinguish between the acute impact of a lack of a protein that is tied to the 180 gene and the developmental knockout (and associated compensatory mechanisms) of the 181 specified gene (Edelman and Gally, 2001;Grashow et al., 2010;Marder, 2011;Marder and 182 Goaillard, 2006;Marder and Taylor, 2011;Taylor et al., 2009). 183 In addition to these strong arguments against a one-to-one link between compensation 184 and degeneracy, it is also important to consider the specifics of the expectations on the specific 185 function that degeneracy is defined for and what functional deficit is to be compensated. Let's 186 consider the example of the emergence of membrane potential resonance in neurons as an 187 example to illustrate this argument (Fig. 2). The emergence of resonance requires the expression 188 of a resonating conductance, and the biophysical constraints on what makes a resonating 189 conductance are well established (Cole, 1968;Hodgkin and Huxley, 1952;190 Hutcheon Mauro, 1961;Mauro et al., 1970;Narayanan and Johnston, 2008). Finally, the possibility that "stochastic" compensatory process could be homeostatic or 248 pathological and importantly on whether the challenge that is being posed to the system by the 249 experiment is "planned" from the perspective of evolutionary convergence should also be 250 considered ( Even with reference to individual neurons, the literature has defined several forms of 260 homeostasis (Gjorgjieva et al., 2016;Nelson and Turrigiano, 2008;Turrigiano, 2011;Turrigiano, 261 2008;Turrigiano and Nelson, 2004), with popular measures involving neuronal firing rate 262 (Hengen et al., 2016), cytosolic calcium (Honnuraiah and Narayanan, 2013; O'Leary et al., 263 Siegel et al., 1994; or excitation-inhibition balance (Yizhar et al., 264 2011). In addition, despite perpetual changes in afferent activity under in vivo conditions 265 (Buzsaki, 2002(Buzsaki, , 2006(Buzsaki, , 2015Tononi and Cirelli, 2006), specific 266 neuronal subtypes maintain distinct functional signatures, say in terms of their excitability or 267 oscillatory or frequency selectivity measurements, that are different from other neuronal 268 subtypes even in the same brain region (Hoffman et al., 1997 An important and necessary cynosure in the physiology of encoding systems is their ability to 317 change in a manner that promotes adaptability to the environment. In other words, the ability to 318 undergo plasticity is an important requirement for it to encode or learn newly available 319 information from the environment. Such plasticity has been shown to be ubiquitous, spanning 320 cellular and network structures across almost all regions, and could be triggered by development 321 (Desai et al., 2002;Desai et al., 1999;Luo and Flanagan, 2007;Schreiner and Winer, 2007;322 Turrigiano and Nelson, 2004;White and Fitzpatrick, 2007), by learning processes (Kandel, 2001;323 Kandel et al., 2014;Kim and Linden, 2007;Lamprecht and LeDoux, 2004;Narayanan and 324 Johnston, 2012;Titley et al., 2017;Zhang and Linden, 2003) Johnston, 2007, 2008;Shah et al., 2010;Sjostrom et al., 2008). This implies 339 plasticity profile homeostasis (Anirudhan and Narayanan, 2015;Mukunda and Narayanan, 340 2017), where synapses of the same subtype respond similarly to analogous afferent activity, 341 thereby resulting in a subtype-dependent rule for synaptic plasticity (Larsen and Sjostrom, 2015). 342 In terms of non-synaptic plasticity, such plasticity profile homeostasis could be generalized to 343 subtypes of cells manifesting specific forms of neuronal plasticity (in intrinsic properties, for 344 instance). 345 Juxtaposed against the considerable variability in different constitutive components 346 across neurons of the same subtype, and given the critical dissociations between different forms 347 of homeostasis (Sec. 2.2), it is easy to deduce that the maintenance of baseline homeostasis of a 348 given measurement (say activity or calcium) does not necessarily imply that the system will 349 respond in a similar manner to identical perturbations (Fig. 3B). As the direction and strength of 350 change in activity or calcium is a critical determinant of the plasticity profile (Lisman, 1989 in the maintenance of short-and long-term plasticity profiles. Specifically, these studies have 365 shown that disparate combinations of ion channel conductances and calcium-handling 366 mechanisms could yield analogous short-or long-term plasticity profiles (Anirudhan and  367 Narayanan, 2015; Mukunda and Narayanan, 2017). Although we dealt with plasticity profile 368 homeostasis and its dissociation from baseline homeostasis, a related phenomenon that involves 369 plasticity of plasticity profiles has been defined as metaplasticity (Abraham, 2008 The function of learning systems extends beyond simple maintenance of physiological or 376 plasticity homeostasis. The functional goal in these systems is rather contrary to maintenance of 377 homeostasis, because encoding or learning of new information demands alteration in 378 physiology/behavior through continual adaptation in an experience-/activity-dependent manner. 379 This presents a paradoxical requirement where components ought to change to encode new 380 information, without perturbing the overall homeostatic balance of the system. Thus, encoding of 381 a new experience entails a tricky balance between change and homeostasis (James, 1890): 382 "Plasticity, then, in the wide sense of the word, means the possession of a structure 383 weak enough to yield to an influence, but strong enough not to yield all at once. 384 Each relatively stable phase of equilibrium in such a structure is marked by what 385 we may call a new set of habits." 386 387 From the degeneracy and physiology perspectives, this balance poses several tricky questions 388 that the literature does not present definitive answers to. For instance, could learning systems 389 accomplish this balance between encoding of new information and maintenance of homeostasis 390 within the framework of degeneracy? In other words, could the plasticity mechanisms that define 391 encoding and the homeostatic mechanisms that negate the impact of perturbation together be 392 realized through disparate combinations of constitutive components (Narayanan and Johnston,393 2012; Nelson and Turrigiano, 2008;Turrigiano, 2007Turrigiano, , 2011Turrigiano et al., 1994;Turrigiano, 394 1999;Turrigiano and Nelson, 2000)? Would the availability of more routes to achieve encoding 395 or homeostasis be detrimental or be advantageous towards accomplishing these goals together? interference working towards negating each other. Therefore, for the framework of degeneracy to 411 be relevant in learning systems, it is important that future studies assess the twin goals of 412 encoding and homeostasis to be synergistically conjoined rather than treat them as isolated 413 processes that independently achieve their respective goals. Without the recognition of such 414 synergy between encoding and homeostatic systems, assessing the ability of these two processes 415 to avoid cross-interference becomes intractable. 416 417 2.5. Curse-of-dimensionality or evolutionary robustness 418 Curse of dimensionality, coined by Bellman (Bellman, 1957) Tononi et al., 1996Tononi et al., , 1999Wagner, 2005Wagner, , 2008

474
A critical requirement in a system that is endowed with degeneracy is an error-correcting 475 feedback mechanism that regulates constituent components in an effort to achieve a specific 476 function. For instance, consider the example where the goal is to achieve calcium homeostasis in 477 a neuron. In this scenario, as the specific regulatory mechanism that is to be triggered is 478 dependent on the current state of the neuron, or more precisely the current levels of calcium, it is 479 important that the regulatory mechanism is geared towards correcting the error between the  Siegel et al., 1994;. 482 This requires a closed circuit feedback loop that initiates a compensatory mechanism that is 483 driven by the quantitative distance between the target function and the current state. This state-484 dependent perpetual error correction becomes especially important in a scenario where distinct 485 regulatory mechanisms govern the different constitute components. With the specific example at 486 hand, let's say the error correcting feedback mechanism regulates ion channel conductances by 487 altering their protein expression through several transcription factors (Srikanth and Narayanan, 488 2015). In such a scenario, calcium homeostasis could be achieved by recruiting several non-489 unique sets of these transcription factors. As each of these transcription factors could be coupled 490 to the regulation of distinct combinations of ion channels, calcium homeostasis could be 491 achieved through several non-unique combinations of ion channels. 492 Within the degeneracy framework, although distinct solutions are possible with weak 493 pairwise correlations between constitutive components, there is a strong synergistic collective 494 dependence of these components to achieve a function (Rathour and Narayanan, 2014). 495 Specifically, let's consider two neurons (neurons 1 and 2) with distinct sets of non-unique 496 parametric combinations that yielded very similar function. However, given the nonlinearities of 497 neural systems, it would be infeasible to expect similar function from a third neuron built with 498 one-half of the parameters taken from neuron 1 and the other half taken from neuron 2. This 499 collective cross-dependence is an essential component of systems manifesting degeneracy and 500 should be respected by mechanisms that regulate the constitutive components. Returning to 501 specific example under consideration, the specific ensemble of the targeted transcription factors 502 and channel conductances are important in terms of which solution is chosen within the 503 degeneracy framework. This places strong requirements on the distinct regulatory mechanisms, 504 transcription factors in this case, that they strongly interact with each other rather than acting 505 independent of each other  in a manner that is driven by the error 506 that is being fed back in a state-dependent temporally precise manner. 507 These requirements become especially important in an encoding system such as the 508 hippocampus, whose afferent activity is perpetually variable in a behavioral state-dependent 509 manner, requiring temporally proximal feedback for the continuous maintenance of robust 510 function. A simple solution to account for cross-interacting regulatory mechanisms is to assume 511 the existence of only one regulatory mechanism that governs all constitutive components (e.g.,  2008)). In summary, the ability to achieve functional robustness through 522 degeneracy in any scale of analysis requires continuous correction of functional deficits, without 523 which it is impossible to adjudge the efficacious accomplishment of a desired goal through a 524 chosen route (which is one among the many possible routes). In a system with enormous 525 complexity, this is typically achieved through an error-correcting feedback pathway that recruits 526 multiple cross-interacting regulatory mechanisms towards maintaining collective cross-527 dependence of constituent mechanisms (Rathour and Narayanan, 2014;Srikanth and Narayanan, 528 2015). 529

530
The hippocampus is a brain region that has been shown to be critically involved in spatial 531 representation of the external environment and in several forms of learning and memory 532 which in some cases have been considered to be lines of evidence that are in apparent 572 contradiction to each other, triggering expansive debates and arguments within the field. In a 573 manner similar to (Edelman and Gally, 2001), we systematically explore the expression of 574 degeneracy at distinct scales (starting at the molecular scale and moving incrementally to the 575 systems/behavioral scale) of hippocampal function (Fig. 1A), with function(s) or physiological 576 measurements assessed within the specified scale of analysis. We postulate that the recognition 577 of the ubiquitous prevalence of degeneracy would provide an evolutionarily routed framework to 578 unify the several apparently contradictory routes to achieving the same function as necessity, 579 rather than luxury, towards achieving physiological robustness. 580 networks. Therefore, it is essential that the biophysical properties and expression profiles of 593 these channels be tightly regulated to ensure functional robustness. 594 The regulation of targeting, localization and properties of these channels at specific 595 levels, however, is a problem that involves several degrees of combinatorial freedom. The 596 reasons behind this complexity are manifold. First, most of these channels are not protein 597 molecules derived from single genes, but are assembled from several possible pore-forming and 598 auxiliary subunits, expressed in different stoichiometry (Catterall, 1993(Catterall, , 1995Gurnett and 599 Campbell, 1996;Hille, 2001;Isom et al., 1994). The presence or absence of a specific pore-600 forming or auxiliary subunit, and the specific ratios of their expression are important for 601 trafficking, localization and properties of these channels. For instance, A-type K + channels in the 602 hippocampus could be assembled by the main subunits from the Kv1 or Kv4  It is now recognized across systems that there is no one-to-one relationship between 668 neurophysiological properties and the channels that regulate them (Sec. 2.1-2.3, Fig. 2-3). It is 669 established that several channels contribute to the emergence and regulation of a specific 670 physiological property, and the same channel could regulate several physiological properties, 671 resulting in a many-to-many mapping between channels and physiological properties. In addition 672 to the example assessing degeneracy in resonance properties (Sec. 2.1-2.2, Fig. 2-3), we could 673 also consider the example of maintaining neuronal firing rates at specific levels. Whereas fast 674 Na + and delayed rectifier K + channels mediate action potential firing in hippocampal neurons, The ability of multiple activity protocols (Fig. 4) to elicit similar levels of synaptic 812 plasticity might be an example of multiple realizability, but it could be argued that this does not 813 constitute an instance of degeneracy, which requires that disparate structural components elicit 814 similar function. To address this argument, we refer to established answers for one of the 815 fundamental questions on synaptic plasticity: What is the mechanistic basis for these induction 816 protocols to elicit synaptic plasticity? The influx of calcium into the cytosol is considered as the 817 first step that results in the induction of LTP or LTD Malenka et al., 1992;818 Mulkey and Malenka, 1992). Quantitatively, there have been suggestions for the amplitude, 819 spread and kinetics of cytosolic calcium elevation to be specific attributes that translate to the 820 strength and direction of plasticity (Larkman and Jack, 1995;Lisman, 1989;Lisman, 2001;821 Shouval et al., 2002). Several studies that followed up on this landmark study have now clearly shown that there are 942 disparate routes to achieving synaptic plasticity, even with very similar strength and the same 943 direction of plasticity (Fig. 7). It is now well established that the expression of synaptic plasticity 944 could recruit mechanisms spanning pre-and post-synaptic components, including 945 channels/receptors, morphological features and cytoplasmic constituents on either side (Fig. 7). 946 In other words, different combinations of changes in presynaptic channels/receptors, release 947 mechanisms and postsynaptic channels/receptors could mediate the expression of synaptic 948 plasticity. 949 The framework of degeneracy provides an ideal way to reconcile the thorny debates 950 regarding pre-and post-synaptic mechanisms that could mediate synaptic plasticity. Specifically, 951 within this framework, pre-and post-synaptic components would be considered simply as a 952 subset (see Sec. 3.6) of the broad repertoire of mechanisms that are available to the neural system 953 to alter towards achieving a specific level of synaptic plasticity or accomplishing an encoding 954 task. Disparate combinations of these components could synergistically contribute to the 955 expression of specific levels of plasticity, at times even with temporal differences in the 956 expression of plasticity in different components. The specific combination of changes that are 957 recruited to mediate plasticity for a chosen protocol or for a given behavioral task would then be 958 state-dependent, critically reliant on the specific calcium sources (Sec. 3.3) and signaling 959 cascades (Sec. 3.4) that were recruited in response to the induction protocol or a behavioral task.

985
It is now widely acknowledged that plasticity protocols and learning paradigms that were once 986 assumed to exclusively recruit or induce synaptic plasticity also induce plasticity in other 987 components (Fig. 8) components (Llinas, 1988;Marder, 2011;Marder et al., 1996;Marder and Goaillard, 2006), 1002 including neuronal spectral selectivity conferred by specific sets of ion channels (Das et al., 1003Hutcheon and Yarom, 2000) and calcium wave propagation mediated by receptors on the 1004 endoplasmic reticulum (Ross, 2012). These distinct intrinsic properties, including excitability, 1005 have been shown to undergo bidirectional changes in a manner that is local to specific neuronal 1006 locations or is global spanning all locations (Brager and Johnston, 2007;1007 Johnston andJohnston, 2007, 2008). 1008 As the protocols employed for inducing non-synaptic (including intrinsic and structural) 1009 plasticity are at most instances identical to synaptic plasticity induction protocols, the broad 1010 mechanisms involved in the induction and in the translation of induction to expression are very 1011 similar to those for synaptic plasticity (Fig. 8) As a direct consequence of the similarity in the protocols employed in inducing synaptic 1027 and intrinsic plasticity, the downstream mechanisms that mediate the translation from induction 1028 of non-synaptic plasticity to its expression are also similar (Shah et al., 2010) to those that 1029 mediate a similar transition in synaptic plasticity (Fig. 8). Several signaling cascades that are 1030 present on the pre-and post-synaptic sides mediate this translation, with retrograde messengers 1031 acting as mechanisms that signal the elevation of postsynaptic calcium to the presynaptic 1032 terminals. Specifically, the same set of enzymes and messengers that mediate synaptic plasticity 1033 also mediate non-synaptic plasticity (Fig. 8) 2014). It is therefore clear that there is no escape from the conclusion that activity-or 1065 experience-or pathology-dependent plasticity does not confine itself to a few constitutive 1066 components, but is rather expansive and even ubiquitous (Kim and Linden, 2007). There are 1067 considerable overlaps in the mechanisms that mediate the induction and expression of these 1068 forms of plasticity, and many-to-one and one-to-many mappings between the induction protocol 1069 (or behavioral experience) and achieving specific levels of plasticity in specific components (Fig.  1070   8).  Turrigiano, 2008;Turrigiano, 2007Turrigiano, , 2011Turrigiano, 1999Turrigiano, , 2008Turrigiano, , 2017Nelson, 1097 2000;van Rossum et al., 2000;Zenke et al., 2017). A prominent theme that spans several such 1098 stability theories is metaplasticity (Abraham, 2008;Abraham and Bear, 1996;Abraham and 1099 Tate, 1997; Hulme et al., 2013), where the profile of plasticity concomitantly changes with the 1100 induction of plasticity (Fig. 9A-B). An extremely useful mathematical treatise that has helped in 1101 the understanding metaplasticity and stability, especially for synaptic plasticity profiles in the 1102 hippocampus, is the Bienenstock-Cooper-Munro (BCM) rule (Bienenstock et al., 1982;Cooper 1103 andBear, 2012;Shouval et al., 2002;Yeung et al., 2004). This is despite the observation that the 1104 BCM framework and the synaptic plasticity framework in hippocampal synapses are not 1105 completely analogous to each other . It should also be noted that not all 1106 synapses follow a BCM-like synaptic plasticity profile, and therefore a stability theory dependent 1107 on this rule is not generalizable to all synapses (Abbott and Nelson, 2000;Jorntell andHansel, 1108 2006). encoding of space (Buzsaki, 1986(Buzsaki, , 1989(Buzsaki, , 2002(Buzsaki, , 2006 vitro data also suggest that an intact hippocampus could sustain theta oscillations on its own in a 1174 manner that is dependent on intra-hippocampal excitatory and inhibitory synaptic connections 1175 (Buzsaki, 2002(Buzsaki, , 2006Colgin, 2013Colgin, , 2016Goutagny et al., 2009;Kamondi et al., 1998;Traub et 1176Traub et al., 1989. A similar analysis, in terms of disparate underlying sources and mechanisms, holds 1177 for gamma frequency oscillations that are observed in the hippocampus as well ( (coincidence detector) as a consequence of the differential expression of different channels (Das 1237 and Narayanan, 2015). Therefore, it seems reasonable to postulate that the proximal and distal 1238 regions are respectively geared towards rate and temporal coding, with this location-dependent 1239 differential coding strategy extending to cortical and hippocampal neurons (Branco and Hausser, 1240Das and Narayanan, 2015). Finally, behaviorally-driven neuromodulatory inputs and 1241 activity-dependent plasticity could markedly alter the operating mode and the class of 1242 excitability of compartments of a single neuron, and the type of coding employed by a neuron is 1243 dependent not just on its operating mode but also the specific characteristics of the input. Thus, 1244 even from the perspective of encoding strategies within a single neuron, the arguments that pitch 1245 rate coding against temporal coding are oversimplifying the complexity of neural encoding and 1246 decoding. Instead, there are broad lines of evidence pointing to a hybrid rate/temporal coding 1247 system that encompasses degeneracy by achieving encoding goals through disparate 1248 combinations of several cellular and network components in a manner that is strongly dependent 1249 on several spatiotemporal aspects of neuronal and behavioral state (Das and Narayanan, 2014, Shadlen and Newsome, 1994Singer et al., 1997;Softky, 1994;Softky, 1995;1258Srivastava et al., 2017, hippocampal physiologists have concurred on the existence of 1259 dual/hybrid encoding schema for place-specific encoding. Specifically, place cells in the 1260 hippocampus elicit higher rates of firing when the animal enters a specific place field. In 1261 conjunction, the phase of action potential firing of place cells with reference to the extracellular 1262 theta rhythm also advances as a function of spatial location of the animal within the place field. 1993; Skaggs et al., 1996). In certain cases, it has been shown that the two coding schema act 1270 independent of each other and could act as the fail-safe mechanisms for each other (Aghajan et 1271(Aghajan et al., 2015Huxter et al., 2003). 1272 Whereas these lines of evidence make a case for employing disparate coding schemas in 1273 encoding the same input, the case for disparate mechanisms involved in encoding and 1274 maintaining the rate and temporal codes is also strong. Specifically, the role of afferent synaptic 1275 drive, local inhibition, several ion channels and receptors, dendritic spikes, spatiotemporal 1276 interactions between somatodendritic channels and receptors, and plasticity in each of these 1277 components have all been implicated in the emergence and maintenance of these codes (Bittner 1278 Skaggs et al., 1996;Tsien et al., 1996;Wills et al., 2005). In addition, there are lines of 1282 experimental evidence that suggest that subthreshold afferent synaptic inputs from several place 1283 fields arrive onto a single place cell, and that a silent cell could be converted to a place cell for 1284 any of these place fields by an appropriate plasticity-inducing stimulus Lee 1285, suggesting that disparate cells could achieve the same function of encoding a given 1286 spatial location. The expression profiles of several channels and receptors control the overall 1287 excitability of a neuron (Sec. 2.2), and there are several mechanisms that regulate the phase of 1288 intracellular voltage oscillations with reference to an external reference or to the overall afferent 1289 current (Geisler et al., 2010;Geisler et al., 2007;Harvey et al., 2009;Johnston, 1290 2008;Rathour et al., 2016;Narayanan, 2012a, 2014;Sinha and Narayanan, 2015;1291Skaggs et al., 1996. Together, these studies point to the possibility that similar rate and phase 1292 spatial codes in a neuron could be achieved through disparate combinations of constituent 1293 components, and several neurons could encode for the same place field with distinct 1294 combinations of these mechanisms. Future studies could further explore the manifestation of 1295 degeneracy in spatial coding in the hippocampus, focusing on the hybrid code involving rate as 1296 well as phase encoding of input features. 1297 The quest for the mechanistic basis for learning and memory in the hippocampus has 1309 spanned several decades, especially since the strong links between the hippocampal lesions and 1310 specific forms of memory were established (Scoville and Milner, 1957). This quest has spanned 1311 several scales of analysis, with efforts to link specific genes, receptors, channels and forms of 1312 cellular plasticity to learning and memory. Several studies have assessed the link between 1313 specific behavioral tasks and cellular/molecular substrates through targeted pharmacological 1314 blockades or genetic manipulations. The existence of divergent and numerous cellular/molecular 1315 components that impair specific learning tasks have been unveiled by these efforts, revealing 1316 considerable complexity in the plasticity networks and systems biology of learning and memory. 1317 As is evident from this complexity and associated animal-to-animal and cell-to-cell variability, 1318 which involves the ensemble of mechanisms and interactions discussed above not just from 1319 within the hippocampus but also from other brain regions, demonstrating causality with 1320 reference to learning and memory and any one specific form of plasticity or cellular/molecular 1321 substrate, has proven extremely challenging (Andersen et al., 2006;Bennett and Hacker, 2003;1322Bhalla, 2014Bhalla and Iyengar, 1999;Bliss and Collingridge, 1993 an AMPAR subunit that is important for expression of certain forms of synaptic plasticity, 1336 impaired only some forms of synaptic plasticity and not others at the cellular scale of analysis 1337 Phillips et al., 2008;Zamanillo et al., 1999). Similarly, at the behavioral 1338 level, although behavioral deficits were observed in certain learning tasks in GluA1 knockout 1339 mice, the knock out did not alter behavior in other learning tasks (Reisel et al., 2002;Zamanillo 1340Zamanillo et al., 1999. Several examples of such dissociations are reviewed in (Mayford et al., 2012), 1341 further emphasizing the difficulty in assigning a causal link between learning and memory and 1342 any one specific form of plasticity or cellular/molecular substrate. 1343 Although this parametric and interactional complexity might seem exasperating if the 1344 goal is to pinpoint the cellular/molecular component that is involved in hippocampal-dependent 1345 learning and memory, it is an extremely useful substrate for the effective expression of 1346 degeneracy in achieving the goal of robust learning and memory. The ability to achieve very 1347 similar learning indices through multiple routes involving disparate forms of plasticity in several 1348 constitutive components tremendously increases the ability of the system to achieve robust 1349 learning. As a consequence of the several forms of variability and state-dependence exhibited by 1350 the learning system, in terms of the underlying components, their plasticity and combinatorial 1351 interactions, it is possible that some of these disparate routes may not involve specific 1352 cellular/molecular components or forms of plasticity in the process of achieving certain learning 1353 goals. This also implies animal-to-animal and trial-to-trial variability in the mechanisms that 1354 mediate learning, thereby calling for utmost caution in assigning one-to-one relationships 1355 between behavioral learning and specific forms of plasticity in any single brain region (Bailey et  process. Therefore, we have shown that component X and its plasticity are necessary and 1394 sufficient for the specific learning behavior. This experimental plan is broadly similar to that 1395 proposed by (Stevens, 1998) to test the hypothesis that auditory synapses in the amygdala 1396 become strengthened by LTP during behavioral training that attaches "fear" to the tone, and that 1397 he memory of the tone as a fear-producing stimulus resides in the strength of the synapses from 1398 the auditory thalamus (Stevens, 1998): 1399 "How could this idea be tested? It should be that (1) blocking LTP prevents fear learning; 1400 (2) the sensory pathways from the thalamus and cortex to the amygdala are capable of 1401 LTP; (3) auditory fear conditioning increases the amygdala's postsynaptic response to the 1402 tone, and these increases are prevented by blocking LTP pharmacologically or in another 1403 way; and (4) inducing LTP in the thalamoamygdaloid pathway attaches "fear" to 1404 appropriate sensory stimuli." 1405 1406 Although this experimental plan has shown that component X and its plasticity are 1407 necessary and sufficient for the specific learning behavior, given the complexity that we have 1408 elucidated thus far, this experimental design does not provide a causal link between component 1409 X or its plasticity with behavior. First, we were so focused on component X that we implicitly 1410 precluded the change of any other component either in the hippocampus or in other brain region. 1411 Given the rich complexity in the distinct components, their plasticity and interactions among 1412 them, it is infeasible that only component X in the hippocampus was changing in response to the 1413 behavioral stimulus. It is now well established that several cellular components change in 1414 response the same calcium signal or the activation of the same signaling cascade, and there are 1415 several parallel homeostasis mechanisms that also exhibit degeneracy. This implies that altering 1416 component X in the hippocampus without altering anything else across the brain is highly 1417 unlikely. Therefore, if we had performed the same set of experiments on another component Y, 1418 we might have arrived at similar conclusions (including correlated time courses). In other words, 1419 it is important not to interpret measurement correlations as evidence for causation, and to 1420 understand that absence of measurements in other forms of plasticity or plasticity in other brain 1421 regions does not mean they don't coexist with the form of plasticity that we are focused on. 1422 Second, when we blocked plasticity in component X, given the complexities elucidated 1423 above, it is highly unlikely that we specifically blocked plasticity in component X without Third, when we performed the experiment of artificially altering component X, it is 1437 obvious that it is highly unlikely that we achieved this without disturbing any other component in 1438 some brain region or without introducing metaplasticity in some form of plasticity. Therefore, 1439 the alternate interpretations of our observations (other than the "linear narrative" that concludes 1440 "plasticity in hippocampal component X mediates learning behavior") are innumerable given the 1441 staggering complexity of the underlying system and the degeneracy involved in accomplishing 1442 the learning task. Ruling out all these alternate interpretations is essential for convergence to the 1443 linear narrative, but is rather impossible because measurements of all constitutive components in 1444 all brain regions is currently infeasible. From a nonlinear dynamical system perspective 1445 (Guckenheimer and Holmes, 1983;Nayfeh and Balachandran, 1995;Strogatz, 2014), our "linear 1446 narrative" and the associated inference are equivalent to declaring a component to be critically 1447 important for system performance because perturbation to that one component, -which is part 1448 of a high-dimensional, adaptive, non-linear dynamical system with strong coupling across 1449 dimensions, -collapses the system. Additionally, especially given the expression of 1450 degeneracy, in our artificial perturbation experiment, we showed that the system could perform a 1451 specific behavior when we introduced a perturbation to component X. However, this observation 1452 does not necessarily imply that the system does employ a similar perturbation to component X to 1453 elicit the same behavior under normal ethological conditions (Adamantidis et al., 2015). Given 1454 the degeneracy framework, it is important to appreciate that the existence of a solution neither 1455 implies its uniqueness nor does it ensure that the solution is employed by the physiological 1456 system under standard ethological conditions. an experimental plan to establish causality that leaps multiple scales in a nonlinear dynamical 1481 system that expresses degeneracy are obvious from the analysis presented above. Here, it is 1482 critical to ask the impossible question on whether we are sure that nothing else has changed in 1483 neurons (and other cells) of the same brain region or the other, which could be 1484 mediating/contributing to the observed behavioral changes before declaring a causal one-to-one 1485 relationship between a molecular/cellular component and behavior. 1486 This is especially important because there are several properties that emerge at each jump 1487 along the multiscale axis of neuroscience (Fig. 1A), and leaps across multiple scales (like genes 1488 to behavior) traverses several emergent properties owing to innumerable nonlinear processes that 1489 exhibit degeneracy. This yields a system that is intractable even at the scale where the 1490 perturbations were introduced because of the complex feedback loops spanning several scales 1491 that mediate homeostasis and adaptation. Consequently, the outcomes of any perturbation at any 1492 scale are critically dependent on several components across scales, the nature of interactions of 1493 these components with the perturbation and importantly on the adaptation that is triggered by the 1494 perturbation in all these components across scales. Therefore, extreme caution should be 1495 exercised in assigning causal one-to-one relationship between components (or manifolds) that Together, while degeneracy is an invaluable asset to evolution, physiology and behavior 1499 in achieving robust functions through several degrees of freedom, it makes the resultant complex 1500 system rather intractable. This intractability makes it nearly impossible to achieve the goals of 1501 reductionism, where the pursuit has largely been for causal one-to-one relationships that leap 1502 across several scales. Several thorny debates in the field about apparent contradictions involving 1503 different components mediating the same function could be put to rest if this requirement of one-1504 to-one relationships is relaxed. Specifically, the ubiquitous expression of degeneracy spanning 1505 multiple scales offers an ideal reconciliation to these controversies, through the recognition that 1506 the distinct routes to achieve a functional goal are not necessarily contradictory to each other, but 1507 are alternate routes that the system might recruit towards accomplishment of the goal. The 1508 intense drive to make leaps across multiple scales to establish unique one-to-one relationships 1509 should instead be replaced by a steadfast recognition for degeneracy as an essential component in 1510 physiology, behavior and evolution. This recognition, apart from precluding one-to-one 1511 relationships, would provide clear warnings in assigning causal relationships that leap across 1512 multiple scales and multiple emergent properties. Importantly, this recognition would pave the 1513 way for a strong focus on integrative and holistic treatises to neuroscience and behavior, 1514 arguments for which have only been growing over the years (Bennett and Hacker, 2003

1527
In this review, we systematically presented lines of evidence for the ubiquitous expression of 1528 degeneracy spanning several scales of the mammalian hippocampus. We argued that the 1529 framework of degeneracy in an encoding system shouldn't be viewed from the limited 1530 perspective of maintaining homeostasis, but should be assessed from the perspective of 1531 achieving the twin goals of encoding information and maintaining homeostasis. Within the broad 1532 framework of degeneracy, it is extremely important that future studies focus on the fundamental 1533 questions on (i) how does the brain change its constituent components towards encoding new 1534 information without jeopardizing homeostasis?; and (ii) how do homeostatic mechanisms 1535 maintain robust function without affecting learning-induced changes in the brain? Without an 1536 effective answer to this overall question on concomitant learning and homeostasis in the face of 1537 staggeringly combinatorial complexity, our understanding of the nervous system in terms of its 1538 ability to systematically adapt to the environment will remain incomplete. Although the core 1539 conclusions on degeneracy reviewed and analyzed here would extend to other mammalian brain 1540 regions and functions that they have been implicated in encoding processes, this extrapolation 1541 should be preceded by careful assessment of the specifics associated with the constitutive 1542 components and specific interactions there. Additionally, although our focus here was on 1543 encoding, homeostasis and physiology, it is important that future studies also assess the 1544 implications for degeneracy in the emergence of pathological conditions (Edelman and Gally, 1545 2001; O'Leary et al., 2014). 1546 Finally, returning to the distinction between the "structure defines function" and the 1547 "form follows function" perspectives, it seems like the distinction also seemingly extends to the 1548 methodology that is deemed appropriate for assessing neuronal systems. At one end, a strong 1549 emphasis is placed on the requirement for an experimental approach (Buzsaki, 2006): 1550 "The complexity and precision of brain wiring make an experimental approach 1551 absolutely necessary. No amount of introspection or algorithmic modeling can help 1552 without parallel empirical exploration." 1553 1554 At the other end, the emphasis, reflecting Richard Feymann's quote "What I cannot create, I do 1555 not understand", is on in silico approaches (Sakmann, 2017): 1556 "At present however, it seems that "What we cannot reconstruct in silico and model 1557 we have not understood"." 1558 1559 Within the degeneracy framework, however, it is starkly evident from existing literature 1560  1565Tononi et al., 1994. 1566 Emphasizing the strong links between biology and evolution, Theodosius Dobzhansky 1567 had written "nothing in biology makes sense except in the light of evolution" (Dobzhansky, 1568(Dobzhansky, 1973. Given the ubiquitous prevalence of degeneracy and its strong links to evolution (Edelman 1569 and Gally, 2001), it is perhaps apt to add a corollary to this quote and state "nothing in 1570 physiology makes sense except in the light of degeneracy".