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The Demands of Geometry on Color Vision

While studies of human color vision have made enormous strides, an overarching rationale for the circular sense of color relationships generated by two classes of color opponent neurons and three cone types is still lacking. Here we suggest that color circularity, color opponency and trichromacy may have arisen, at least in part, because of the geometrical requirements needed to unambiguously distinguish all possible spectrally different regions on a plane.

Introduction
Using sensory information to distinguish image regions that promote apt behavior in the physical world is generally assumed to be the broad purpose of animal vision. Whereas achromatic vision distinguishes regions on the basis of light intensity (luminance), color vision further distinguishes equiluminant regions on the basis of differences in the distribution of spectral energy, giving animals with this ability a behavioral advantage in dealing with objects and conditions in the world [1][2][3].
Despite a wealth of anatomical, electrophysiological and psychophysical evidence about color vision, several general questions remain. A puzzle since Newton's pioneering studies is why when asked to arrange objects with a full range of spectral qualities (e.g., Munsell chips) such that their apparent colors are minimally different, the result is a closed continuum ( Figure 1) [4,5]. Equally perplexing is why we perceive a color gamut based on four color classes-reds, greens, blues and yellows-each defined by a unique hue that has no apparent admixture of the other three color classes [6][7][8][9]. And while it has long been known that color vision is mediated by the spectral sensitivities of short, medium, and long-wavelength cones whose output is processed by red-green and blue yellow opponent neurons [7,8,[10][11][12], why these particular properties have evolved in humans is also incompletely understood [7,11,13]. . When asked to arrange a large number of equiluminant surfaces that vary in hue such that the color differences among them are minimal, subjects arrange them in a closed loop that comprises four basic color categories (reds, greens, blues and yellows), each defined by a particular hue (black dots) that has no admixture of the neighboring color classes (e.g., a red surface seen as having no appreciable yellowness or blueness). Although there are many other named color groups (oranges, aquamarines, etc.), these are always seen as mixtures of the two of the four primaries. As indicated, the location of the unique hues (black dots) are not orthogonal in perceptual color space, nor is the closed loop determined psychophysically a literal circle as shown in the diagram.
Although the retina is a curved surface, the information it captures (the retinal image near the fovea) is generally thought of as a two-dimensional (2D) plane. Effectively distinguishing spectral differences on a plane presents at least two geometrical challenges. First, to achieve high resolution, different perceived colors must be ascribed to all spectrally different points on the retinal image plane. Second, perception must entail a number of color classes sufficient to ensure that adjoining regions on the plane will not be conflated if they are spectrally different. This latter challenge is called the "four-color map problem", referring to the empirical minimum of four colors needed to ensure that countries on a map are always distinguishable (the "problem" in this phrase refers to the logic . When asked to arrange a large number of equiluminant surfaces that vary in hue such that the color differences among them are minimal, subjects arrange them in a closed loop that comprises four basic color categories (reds, greens, blues and yellows), each defined by a particular hue (black dots) that has no admixture of the neighboring color classes (e.g., a red surface seen as having no appreciable yellowness or blueness). Although there are many other named color groups (oranges, aquamarines, etc.), these are always seen as mixtures of the two of the four primaries. As indicated, the location of the unique hues (black dots) are not orthogonal in perceptual color space, nor is the closed loop determined psychophysically a literal circle as shown in the diagram.
Although the retina is a curved surface, the information it captures (the retinal image near the fovea) is generally thought of as a two-dimensional (2D) plane. Effectively distinguishing spectral differences on a plane presents at least two geometrical challenges. First, to achieve high resolution, different perceived colors must be ascribed to all spectrally different points on the retinal image plane. Second, perception must entail a number of color classes sufficient to ensure that adjoining regions on the plane will not be conflated if they are spectrally different. This latter challenge is called the "four-color map problem", referring to the empirical minimum of four colors needed to ensure that countries on a map are always distinguishable (the "problem" in this phrase refers to the logic underlying this requirement, which took more than a century to verify) [14][15][16]. The relevance of this geometrical requirement to color vision is that at least four perceived color classes would be needed to resolve the same cartographic concern in the retinal images [17].
The purpose of the present article is to examine whether perceptual color circularity, color opponency and physiological trichromacy could be related consequences of a need to meet these geometrical demands.

Geometrical Demands for Making Regional Distinctions in One Dimension
To appreciate the geometrical requirements that must be met in order to distinguish all possible regions of planar images by color percepts, consider the simpler challenge of distinguishing all possible regions in a hypothetical one-dimensional image.
From a geometrical perspective, two different qualities are all that is needed to distinguish any number of regions from their neighbors in a linear image ( Figure 2A). Thus, in this hypothetical one-dimensional (1D) scenario, color vision could distinguish equiluminant regions by assigning two different color percepts to different spectra. Ultimately, however, a continuum would be needed, as shown in Figure 2B. Since the number of different spectra at any given level of luminance is limited only by the ability of the visual system to distinguish spectral variations, color vision would presumably evolve as many equiluminant perceptions as this constraint allowed (see Figure 1B). If points (i.e., the smallest regions resolved by human visual acuity) were arranged according to minimal differences among spectra, the result would require a continuum of two equiluminant color qualities, as indicated. The perceived difference between the extremes of such a 1D color space would be maximal, with a colorless intermediate sensation (gray) that was equally different from the sensations elicited by the two extremes. The continuum in the figure thus represents gradual spectral deviation in two opposite directions from a colorless balance point, with the maximum deviation eliciting the perceptions of a unique hue, e.g., a blue with no yellow or vice versa in this example. In sum, given the rules of geometry, two color classes defined by two unique hues are sufficient to distinguish all the points in a 1D image.
Vision 2017, 1, 9 3 of 11 underlying this requirement, which took more than a century to verify) [14][15][16]. The relevance of this geometrical requirement to color vision is that at least four perceived color classes would be needed to resolve the same cartographic concern in the retinal images [17]. The purpose of the present article is to examine whether perceptual color circularity, color opponency and physiological trichromacy could be related consequences of a need to meet these geometrical demands.

Geometrical Demands for Making Regional Distinctions in One Dimension
To appreciate the geometrical requirements that must be met in order to distinguish all possible regions of planar images by color percepts, consider the simpler challenge of distinguishing all possible regions in a hypothetical one-dimensional image.
From a geometrical perspective, two different qualities are all that is needed to distinguish any number of regions from their neighbors in a linear image ( Figure 2A). Thus, in this hypothetical onedimensional (1D) scenario, color vision could distinguish equiluminant regions by assigning two different color percepts to different spectra. Ultimately, however, a continuum would be needed, as shown in Figure 2B. Since the number of different spectra at any given level of luminance is limited only by the ability of the visual system to distinguish spectral variations, color vision would presumably evolve as many equiluminant perceptions as this constraint allowed (see Figure 1B). If points (i.e., the smallest regions resolved by human visual acuity) were arranged according to minimal differences among spectra, the result would require a continuum of two equiluminant color qualities, as indicated. The perceived difference between the extremes of such a 1D color space would be maximal, with a colorless intermediate sensation (gray) that was equally different from the sensations elicited by the two extremes. The continuum in the figure thus represents gradual spectral deviation in two opposite directions from a colorless balance point, with the maximum deviation eliciting the perceptions of a unique hue, e.g., a blue with no yellow or vice versa in this example. In sum, given the rules of geometry, two color classes defined by two unique hues are sufficient to distinguish all the points in a 1D image. However, a continuum is needed when points must be distinguished according to relative spectral differences at equiluminance. Notice that the balance point in a color continuum would be perceived is neither one color nor the other (i.e., neither blue nor yellow but a shade of gray).

Quantification
Quantification of these spectral differences as vectors in 1D space is straightforward. Just as a line that extends from a null point in two directions can be specified by a pair of opposing direction vectors, such the x and −x vectors of a graphical axis, the spectral continuum in Figure 2B can be described by vectors (see Methods). The direction of each position vector from the null vector indicates the dominant color class at that location, and the distance from null vector indicates the relative contributions of the two unique hues. As the extremes of opposing direction vectors, the unique hues are necessarily opponent colors. The corresponding direction vectors indicate spectral Two different qualities (blue and yellow in this example) suffice to distinguish any number of neighboring regions from one another along a line; (B) However, a continuum is needed when points must be distinguished according to relative spectral differences at equiluminance. Notice that the balance point in a color continuum would be perceived is neither one color nor the other (i.e., neither blue nor yellow but a shade of gray).

Quantification
Quantification of these spectral differences as vectors in 1D space is straightforward. Just as a line that extends from a null point in two directions can be specified by a pair of opposing direction vectors, such the x and −x vectors of a graphical axis, the spectral continuum in Figure 2B can be described by vectors (see Methods). The direction of each position vector from the null vector indicates the dominant color class at that location, and the distance from null vector indicates the relative contributions of the two unique hues. As the extremes of opposing direction vectors, the unique hues are necessarily opponent colors. The corresponding direction vectors indicate spectral deviation from the uniform distribution of energy at the color neutral null vector, and the distance between any two position vectors indicates the perceived spectral difference between them.

Biological Significance
In terms of photoreceptors, two cone types with overlapping spectral sensitivities could generate these distinctions ( Figure 3). The result would lead to the perceptual experience of human dichromats, and the majority of other mammals that posses only two types of cones (see Discussion) [18]. Thus individuals who lack L cones (protanopes) see spectral distributions that would have generated red or green for trichromats as shifts in brightness and/or saturation based on blue and yellow color classes, with a reduced color gamut. Similar findings have been reported for deuteranopes and tritanopes [19].
Vision 2017, 1, 9 4 of 11 deviation from the uniform distribution of energy at the color neutral null vector, and the distance between any two position vectors indicates the perceived spectral difference between them.

Biological Significance
In terms of photoreceptors, two cone types with overlapping spectral sensitivities could generate these distinctions ( Figure 3). The result would lead to the perceptual experience of human dichromats, and the majority of other mammals that posses only two types of cones (see Discussion) [18]. Thus individuals who lack L cones (protanopes) see spectral distributions that would have generated red or green for trichromats as shifts in brightness and/or saturation based on blue and yellow color classes, with a reduced color gamut. Similar findings have been reported for deuteranopes and tritanopes [19]. Hypothetical cone sensitivity curves. When stimulated equally, the perceptual result would be color neutrality. Middle panels. When the response of one of the photoreceptor types is maximal and the other minimal, the perception would be that of unique blue (left) or unique yellow (right). Bottom panel. Stimulation that would give rise to predominantly blue (left) or yellow (right) perceptions along the color continuum in Figure 2B.

Geometrical Demands for Making Regional Distinctions in Two Dimensions
As in a hypothetical 1D image, equiluminant color perceptions arising from a plane can be represented by direction and position vectors. However, whereas 1D space extends in only two directions, 2D space extends in all possible directions from a null point ( Figure 4A). Accordingly, position vectors in 2D must be expressed by two pairs of opposing direction vectors, as in the (−x, x) and (−y, y) axes that define any Cartesian co-ordinate system.
In vector addition (see Methods), two pairs of opposing direction vectors define the position vectors in all possible directions ( Figure 4B). Of the many possible combinations, any two pairs of opposing direction vectors can be used to define the position vectors in all directions. The vector space defined by all possible sets of opposing direction vector pairs thus forms a closed loop that bounds the portion of the plane held in common ( Figure 4C). Although not shown, the argument is the same whether or not the two pairs of opposing direction vectors are orthogonal. Hypothetical cone sensitivity curves. When stimulated equally, the perceptual result would be color neutrality. Middle panels. When the response of one of the photoreceptor types is maximal and the other minimal, the perception would be that of unique blue (left) or unique yellow (right). Bottom panel. Stimulation that would give rise to predominantly blue (left) or yellow (right) perceptions along the color continuum in Figure 2B.

Geometrical Demands for Making Regional Distinctions in Two Dimensions
As in a hypothetical 1D image, equiluminant color perceptions arising from a plane can be represented by direction and position vectors. However, whereas 1D space extends in only two directions, 2D space extends in all possible directions from a null point ( Figure 4A). Accordingly, position vectors in 2D must be expressed by two pairs of opposing direction vectors, as in the (−x, x) and (−y, y) axes that define any Cartesian co-ordinate system. In

Geometrical Rationale for Color Opponency
Given that the space held in common by all sets of opposing direction vector pairs in Figure 4C is bounded by a recursive perimeter, it follows that distinguishing points on a plane according to relative spectral differences would obey the same geometrical requirements.
In a two-dimensional (2D) space, however, the evolution of color vision would also have to contend with the geometrical demands apparent in map making ( Figure 5A). That is, a minimum of four color classes is needed to distinguish all possible regions on a plane-i.e., all spectrally different equiluminant points in a 2D image. This goal could be met by two pairs of direction vectors that gave rise to four color classes defined by four unique hues that were pair-wise opponents ( Figure 5B). Figure 5. The four-color demand for regional distinctions on a map and the color opponency that would be needed. (A) The demand in 2D geometry refers to the fact that abutting regions on a plane cannot be distinguished using fewer than four colors. The diagram shows a simple example which makes clear that these regions could not be distinguished from one another using fewer than four colors. If this pattern were an equiluminant retinal image, the four regions would need to elicit color sensations that could distinguish any possible hue within these four color classes (reds, greens, blues and yellows); (B) Two opposing color quality pairs (direction vectors) extending from a null point (white dot) would be sufficient to address this issue, at the same time as differentiating all points (position vectors) on a plane by a gamut of color sensations. Note that the opponent axes would not have to be orthogonal.

Geometrical Rationale for Color Opponency
Given that the space held in common by all sets of opposing direction vector pairs in Figure 4C is bounded by a recursive perimeter, it follows that distinguishing points on a plane according to relative spectral differences would obey the same geometrical requirements.
In a two-dimensional (2D) space, however, the evolution of color vision would also have to contend with the geometrical demands apparent in map making ( Figure 5A). That is, a minimum of four color classes is needed to distinguish all possible regions on a plane-i.e., all spectrally different equiluminant points in a 2D image. This goal could be met by two pairs of direction vectors that gave rise to four color classes defined by four unique hues that were pair-wise opponents ( Figure 5B).

Geometrical Rationale for Color Opponency
Given that the space held in common by all sets of opposing direction vector pairs in Figure 4C is bounded by a recursive perimeter, it follows that distinguishing points on a plane according to relative spectral differences would obey the same geometrical requirements.
In a two-dimensional (2D) space, however, the evolution of color vision would also have to contend with the geometrical demands apparent in map making ( Figure 5A). That is, a minimum of four color classes is needed to distinguish all possible regions on a plane-i.e., all spectrally different equiluminant points in a 2D image. This goal could be met by two pairs of direction vectors that gave rise to four color classes defined by four unique hues that were pair-wise opponents ( Figure 5B). Figure 5. The four-color demand for regional distinctions on a map and the color opponency that would be needed. (A) The demand in 2D geometry refers to the fact that abutting regions on a plane cannot be distinguished using fewer than four colors. The diagram shows a simple example which makes clear that these regions could not be distinguished from one another using fewer than four colors. If this pattern were an equiluminant retinal image, the four regions would need to elicit color sensations that could distinguish any possible hue within these four color classes (reds, greens, blues and yellows); (B) Two opposing color quality pairs (direction vectors) extending from a null point (white dot) would be sufficient to address this issue, at the same time as differentiating all points (position vectors) on a plane by a gamut of color sensations. Note that the opponent axes would not have to be orthogonal. Figure 5. The four-color demand for regional distinctions on a map and the color opponency that would be needed. (A) The demand in 2D geometry refers to the fact that abutting regions on a plane cannot be distinguished using fewer than four colors. The diagram shows a simple example which makes clear that these regions could not be distinguished from one another using fewer than four colors. If this pattern were an equiluminant retinal image, the four regions would need to elicit color sensations that could distinguish any possible hue within these four color classes (reds, greens, blues and yellows); (B) Two opposing color quality pairs (direction vectors) extending from a null point (white dot) would be sufficient to address this issue, at the same time as differentiating all points (position vectors) on a plane by a gamut of color sensations. Note that the opponent axes would not have to be orthogonal.

Geometrical Rationale for Color Perception as a Closed Loop
The demands of 2D geometry could also explain how the ability to order all equiluminant but spectrally different points on a plane according to minimal apparent differences leads to the closed continuum of hue sensations illustrated in Figure 1. Since the perimeter of a 2D space that extends equally in all directions is recursive (see Figure 4), the equiluminant sensations associated with the position vectors that lie between the opposing direction vectors in Figure 4B will also define a closed loop, with spectrally distinct points defined by vector addition based on the four representative spectral directions. Thus only four color classes are needed, although the number of perceived and named hues within each class can be large.

Geometrical Rationale for Retinal Trichromacy
This geometrical argument does not, however, indicate whether trichromacy could also be related to meeting the demands of plane geometry. On the contrary, from the constraints described so far one would expect that a least four cone types representing the two opponent axes would be needed to generate the four color classes illustrated in Figures 1 and 5B. How, then, could the three cone types in humans and Old World monkeys generate the four color classes needed to distinguish all the equiluminant but spectrally different points on a plane?
As shown in Figure 6A, the addition of any two non-opposing direction vectors can define all position vectors for all the directions that lie between them (see Methods). Accordingly, three direction vectors could, in principle, define all the position vectors on a plane. To do so, however, two of the three direction vectors would have to be non-orthogonal. As shown in Figure 6B, to satisfy these further geometrical demands, a third vector would have to lie within the area between the dashed blue lines.

Geometrical Rationale for Color Perception as a Closed Loop
The demands of 2D geometry could also explain how the ability to order all equiluminant but spectrally different points on a plane according to minimal apparent differences leads to the closed continuum of hue sensations illustrated in Figure 1. Since the perimeter of a 2D space that extends equally in all directions is recursive (see Figure 4), the equiluminant sensations associated with the position vectors that lie between the opposing direction vectors in Figure 4B will also define a closed loop, with spectrally distinct points defined by vector addition based on the four representative spectral directions. Thus only four color classes are needed, although the number of perceived and named hues within each class can be large.

Geometrical Rationale for Retinal Trichromacy
This geometrical argument does not, however, indicate whether trichromacy could also be related to meeting the demands of plane geometry. On the contrary, from the constraints described so far one would expect that a least four cone types representing the two opponent axes would be needed to generate the four color classes illustrated in Figures 1 and 5B. How, then, could the three cone types in humans and Old World monkeys generate the four color classes needed to distinguish all the equiluminant but spectrally different points on a plane?
As shown in Figure 6A, the addition of any two non-opposing direction vectors can define all position vectors for all the directions that lie between them (see Methods). Accordingly, three direction vectors could, in principle, define all the position vectors on a plane. To do so, however, two of the three direction vectors would have to be non-orthogonal. As shown in Figure 6B, to satisfy these further geometrical demands, a third vector would have to lie within the area between the dashed blue lines. To deal with the four-color map demand, however, the third direction vector would have to oppose the combined influence of other two direction vectors, i.e., vector P + Q indicated by the dashed black line.
Moreover, unless the third direction vector (vector R in Figure 6B) had a specific direction with respect to the two other vectors, only three color classes would arise, an arrangement that would be unable to contend with the four-color map concern illustrated in Figure 5A. Thus the third direction vector R would have to oppose the combined influence of the other two direction vectors (direction vector P + Q). An exception would be when vectors P and Q are equal. In this case, they would generate a null vector when vector R equals the combined influence of P and Q, as with the opposing direction vectors in Figure 5B. Thus P and Q are opponents only when direction vector R opposes the To deal with the four-color map demand, however, the third direction vector would have to oppose the combined influence of other two direction vectors, i.e., vector P + Q indicated by the dashed black line.
Moreover, unless the third direction vector (vector R in Figure 6B) had a specific direction with respect to the two other vectors, only three color classes would arise, an arrangement that would be unable to contend with the four-color map concern illustrated in Figure 5A. Thus the third direction vector R would have to oppose the combined influence of the other two direction vectors (direction vector P + Q). An exception would be when vectors P and Q are equal. In this case, they would generate a null vector when vector R equals the combined influence of P and Q, as with the opposing direction vectors in Figure 5B. Thus P and Q are opponents only when direction vector R opposes the vector sum P + Q. In this way the second opponent pair needed to resolve the four-color map issue would be provided.
Each of the four unique hues would correspond to the greatest deviation of spectral energy from the null vector of these directional extremes, i.e., the extremes of P, Q, R and P + Q in Figure 6. Intermediate color percepts would arise from the graded distribution of spectral energy between the extremes, as indicated by the gradients in Figure 5B. As shown in Figure 7, position vectors that lie between the three direction vectors in Figure 6B define a closed loop (cf. Figures 1 and 4C). The interaction of the two pairs of opposing direction vectors in Figure 6 (P vs. Q, and R vs. P + Q) would be analogous to interaction of L vs. M cones, and S vs. L + M cones.
Vision 2017, 1, 9 7 of 11 vector sum P + Q. In this way the second opponent pair needed to resolve the four-color map issue would be provided. Each of the four unique hues would correspond to the greatest deviation of spectral energy from the null vector of these directional extremes, i.e., the extremes of P, Q, R and P + Q in Figure 6. Intermediate color percepts would arise from the graded distribution of spectral energy between the extremes, as indicated by the gradients in Figure 5B. As shown in Figure 7, position vectors that lie between the three direction vectors in Figure 6B define a closed loop (cf. Figures 1 and 4C). The interaction of the two pairs of opposing direction vectors in Figure 6 (P vs. Q, and R vs. P + Q) would be analogous to interaction of L vs. M cones, and S vs. L + M cones. In short, the three cone types in humans and Old World monkeys may represent the minimum number of color receptors needed to generate the four color classes capable of distinguishing all resolvable equiluminant regions on a plane, at the same time resolving the need for four color classes to make unambiguous planar maps. The same argument would also explain why the four unique hues in human color space are not located at orthogonal extremes (see Figure 1B).

Discussion
The argument we have presented suggests that color circularity, color opponency, and trichromacy are related consequences of efficiently meeting the geometrical demands needed to distinguish all spectrally different points on the retinal image plane.
While this reasoning offers a unifying rationale for perceptual and physiological phenomena whose purposes are otherwise unclear, it also raises a number of questions. These issues and some speculative answers are as follows.

Why Are Red, Green, Blue and Yellow Perceptual Primaries?
The argument so far does not explain why the four primary color directions are red, green, yellow and blue, i.e., why visible spectra elicit these particular color classes.
Although a geometrical framework does not address this question, it nonetheless suggests an explanation. Just as the bias of magnetic north fixes the cardinal axes in geography, there are presumably biases in human spectral experience that would have determined the three direction vectors P, Q and R in Figure 6. The most obvious candidate for such biases is the distribution of light reflected from natural surfaces. Empirically, the reflectance efficiency functions of natural surfaces In short, the three cone types in humans and Old World monkeys may represent the minimum number of color receptors needed to generate the four color classes capable of distinguishing all resolvable equiluminant regions on a plane, at the same time resolving the need for four color classes to make unambiguous planar maps. The same argument would also explain why the four unique hues in human color space are not located at orthogonal extremes (see Figure 1B).

Discussion
The argument we have presented suggests that color circularity, color opponency, and trichromacy are related consequences of efficiently meeting the geometrical demands needed to distinguish all spectrally different points on the retinal image plane.
While this reasoning offers a unifying rationale for perceptual and physiological phenomena whose purposes are otherwise unclear, it also raises a number of questions. These issues and some speculative answers are as follows.

Why Are Red, Green, Blue and Yellow Perceptual Primaries?
The argument so far does not explain why the four primary color directions are red, green, yellow and blue, i.e., why visible spectra elicit these particular color classes.
Although a geometrical framework does not address this question, it nonetheless suggests an explanation. Just as the bias of magnetic north fixes the cardinal axes in geography, there are presumably biases in human spectral experience that would have determined the three direction vectors P, Q and R in Figure 6. The most obvious candidate for such biases is the distribution of light reflected from natural surfaces. Empirically, the reflectance efficiency functions of natural surfaces give rise to three spectral groups: foliage in the yellow-green region (~557-574 nm); "earths" in the yellow-orange region (~576-589 nm); and water, sky and distant objects in the blue region (~459-486 nm) [20]. These biases accord with the peak sensitivities of the three cone types, which in turn accord with the argument in Figure 6.
This agreement, however, does not explain why the combined influence of P and Q opposes R rather than the other options (i.e., Q and R opposing P, or P and R opposing Q). One possibility is a bias arising from the greater overlap of the spectral ranges of foliage and earth than from the overlap of either of these ranges with the blue range.
Finally, whereas that some primitive cultures lack names for these four color categories [21], the argument we outline implies that this deficiency in vocabulary is unlikely to arise from any differences in human visual physiology.

Why Can the Black-White Axis Not Serve as an Opponent Color Axis?
Since the perception of grays ranging from unique black to unique white forms an opponent axis, another question that arises is why this gray scale axis could not interact with a single color axis to distinguish all possible spectral points on a plane, at the same time resolving the four-color map problem.
The reason is that the color and gray scale axes concern different categories of information-light intensity versus the distribution of spectral energy-which are independent and lead to different sensory qualities (lightness versus hue). Although these domains can influence each other [7,22], like sensory qualities in other systems (e.g., pitch and loudness in audition) they are not combined in perception.

What about Other Rationales for these Phenomena?
Several plausible rationales for color opponency and trichromacy have been proposed. Opponency, which has been validated both psychophysically [12] and electrophysiologically [23,24] at several levels of the primary visual pathway in experimental animals, has been suggested to enhance the encoding of natural scene spectra [25], and/or to optimize the transfer of trichromatic color information [26,27]. By analogy with spatial sinusoids, trichromacy has also been interpreted in terms of comb-filtered spectra [28].
The difference in the present argument is that a geometrical explanation of color phenomenology is predicated on the advantages of distinguishing equiluminant image points. From this perspective, whatever else they may accomplish, opponency, color circularity and trichromacy are manifestations of resolving fundamental geometrical problems that would have to be addressed one way or another for the evolution of effective color vision.

What about Reports from Human Dichromats?
Another concern is the partial conflation of the trichromatic gamut in human dichromats, who retain some ability to perceive and identify colors that would be expected only in trichromats. For example, protanopes and deuteranopes show adaption to long wavelength light [29] and use the terms "red" and "green" as well as "blue" and "yellow" to describe what they see [30]. Montag and Boynton [31] have shown further that rods may contribute to these abilities. These further facts about color perception are not explained by the arguments here.

How Does the Argument Account of Color Metamers?
A final question concerns metameric stimuli-i.e., different distributions of spectral energy that elicit the same perceived colors in psychophysical matching tests. Such stimuli arise because the overlapping sensitivities the three human cone types allow similar relative activation by spectrally different stimuli. Since metameric image regions would elicit the same color percepts, metamers belie the idea that all spectrally different regions in arbitrarily complex images can be distinguished.
Although the question remains, the metameric stimuli used in colorimetry experiments are rare in natural images [32]. Thus the evolution of color vision may simply have ignored the legitimate conceptual problem posed by metamers.

Methods
As illustrated on Figure 8, we used vectors to describe the geometry of spectral images (to avoid any confusion, note that these diagrams are not a perceived color space). By the same token, the arguments here depend on the logic of plane geometry and not on any partiulcar metric of color space.
Vision 2017, 1, 9 9 of 11 Although the question remains, the metameric stimuli used in colorimetry experiments are rare in natural images [32]. Thus the evolution of color vision may simply have ignored the legitimate conceptual problem posed by metamers.

Methods
As illustrated on Figure 8, we used vectors to describe the geometry of spectral images (to avoid any confusion, note that these diagrams are not a perceived color space). By the same token, the arguments here depend on the logic of plane geometry and not on any partiulcar metric of color space. A plane is a 2D vector space in which any point can be specified as the position vector of that point with respect to an origin ( Figure 8A). Thus the position vector of the origin is a null vector whose initial and terminal points are coincident, with zero magnitude and no direction. The arguments in the Results depend on vector addition. If PQ and RS are any two non-zero vectors, their addition leads to a third vector PS that is different from both PQ and RS ( Figure 8B). The magnitude and direction of PS depends on the magnitude and direction of vectors PQ and RS. The addition of vectors with PQ and/or RS as null vectors is still valid, but the resultant vector PS may be equal to both or one of the addends.
When adding vectors, the initial point of the second vector is placed at the terminal point of the first, resulting in a vector co-initial with the first vector and co-terminus with the second vector. Since vector addition is commutative, either of the addends can be treated as the first vector. For addition involving more than two vectors, stepwise addition was performed by taking two vectors at a time, with the resultant vector of a pair being one of the addends for the subsequent addition.
Finally, when two vectors are adjacent sides of a parallelogram, their vector sum is given by the diagonal of the parallelogram ( Figure 8C). This parallelogram rule gives the same result as the tip-totail method, except that it operates on co-initial addends, and was used to define position vectors based on other position vectors ( Figure 8D). When two direction vectors are represented by adjacent A plane is a 2D vector space in which any point can be specified as the position vector of that point with respect to an origin ( Figure 8A). Thus the position vector of the origin is a null vector whose initial and terminal points are coincident, with zero magnitude and no direction. The arguments in the Results depend on vector addition. If PQ and RS are any two non-zero vectors, their addition leads to a third vector PS that is different from both PQ and RS ( Figure 8B). The magnitude and direction of PS depends on the magnitude and direction of vectors PQ and RS. The addition of vectors with PQ and/or RS as null vectors is still valid, but the resultant vector PS may be equal to both or one of the addends.
When adding vectors, the initial point of the second vector is placed at the terminal point of the first, resulting in a vector co-initial with the first vector and co-terminus with the second vector. Since vector addition is commutative, either of the addends can be treated as the first vector. For addition involving more than two vectors, stepwise addition was performed by taking two vectors at a time, with the resultant vector of a pair being one of the addends for the subsequent addition.
Finally, when two vectors are adjacent sides of a parallelogram, their vector sum is given by the diagonal of the parallelogram ( Figure 8C). This parallelogram rule gives the same result as the tip-to-tail method, except that it operates on co-initial addends, and was used to define position vectors based on other position vectors ( Figure 8D). When two direction vectors are represented by adjacent sides of a parallelogram, the included position vectors defined all the position vectors within that parallelogram (i.e., the black dotted lines connecting all the direction vectors in Figure 8D).

Conclusions
To be optimally successful, color vision must assign distinct percepts to all possible arrangements of spectrally different regions on a plane, while at the same time contending with the need of four color classes to make any planar map unambiguous. Here we suggest that the circularity of color perception, color opponency, and trichromacy have evolved at least in part as related ways of meeting these geometrical demands. This perspective provides a unified rationale for perceptual and physiological phenomena that are otherwise difficult to explain.


Dexmedetomidine attenuates neuropathic pain in chronic constriction injury by suppressing NR2B, NF-κB, and iNOS activation

The effective treatment of patients suffering from neuropathic pain remains challenging. Dexmedetomidine (DEX) possesses anti-inflammatory activity. However, the role of DEX in neuropathic pain is still unclear. The aim of the present study was to examine DEX an α2-adrenoceptor agonist could improve pain hypersensitivity and reduce inflammatory in a chronic constriction injury (CCI) model of the sciatic nerve in Sprague-Dawley rats. Dex was intrathecally administrated 1-h after operation. The paw mechanical withdrawal threshold (MWT) and paw withdrawal thermal latency (PWTL) were measured on day 1 before operation and on days 1, 7, 14 and 21 after operation, respectively. On day 21, all the rats were decapitated to collect the L4-6 segments of the spinal cord to examine IL-1, TNF-α, IL-6, NR2B, NF-κB, and iNOS mRNA levels using RT-PCR. The postoperative MWT and PWTL were significantly decreased in CCI, and DEX groups as compared to those before surgery and Sham group (P < 0.05). And DEX reversed this trend (P < 0.05). Interleukin 1 (IL-1), tumor necrosis factor α (TNF-α), IL-6 mRNA expression significantly increased postsurgery in CCI group as compared to that of Sham group (P < 0.05); DEX blocked increased IL-1, TNF-α, IL-6, N-methyl-D-aspartate (NMDA) receptor 2B (NR2B), nuclear factor κB (NF-κB), and inducible isoform of nitric oxide synthase (iNOS) mRNA levels (P < 0.05). DEX may alleviate neuropathic hypersensitivity and inflammation partially by inhibiting NR2B, NF-κB, and iNOS expression in the spinal cord of rats with neuropathic pain resulting from CCI of the sciatic nerve.

Introduction
Neuropathic pain is a common syndrome, which may result from many disorders including diabetic polyneuropathy, radicular back pain, postherpetic neuralgia, stroke, and spinal cord injury (Farghaly et al., 2014). It is characterized by hyperalgesia, allodynia and spontaneous pain (Zhou et al., 2014;Sun et al., 2006). The CCI of the sciatic nerve is a widely used model of neuropathic pain which evokes a series of molecular, biochemical and cytoarchitectural changes in primary sensory neurons and produces neuro-pathic pain sensations similar to those observed in humans (Farghaly et al., 2014). Ligation of the sciatic nerve also leads to the cardinal symptoms of neuropathic pain, namely apparent spontaneous pain, allodynia, and hyperalgesia (Farghaly et al., 2014;Xie, 1988a, 1988b).
Treatment of neuropathic pain remains difficult, due to an inadequate understanding of the mechanisms involved in the development and maintenance of neuropathic pain, and a relative absence of clinically effective treatments (Liu et al., 2012). Several animal studies have implicated the a2-adrenoceptors (a2-AR) in experimental neuropathic models of pain (Kalso et al., 1991;Brummett et al., 2009). In the 1990s, DEX, a newly developed a2-AR agonist was first introduced into clinical practice as a short-term intravenous sedative in the intensive care unit (Zhang et al., 2013). And also a study has confirmed Dex has the potential effect for pain treatment (Grosu and Lavand'homme, 2010), but the involved mechanism still remains to be elucidated.
Recently initiate and maintain inflammatory and neuropathic pain (He et al., 2014). Specifically, proinflammatory cytokines such as TNF-a, IL-1, IL-6 and iNOS have been strongly implicated in the initiation and development of inflammatory and neuropathic pain and can activate, or be activated by NF-jB (He et al., 2014).
In this study, we provide the evidence that DEX affords significant relief of inflammatory and neuropathic pain, and that this effect is likely related to inhibition of cytokines in the spinal cord.

Animals
Forty-five adult male Sprague-Dawley rats, weighting 180-220 g, were housed in a 12-h light-dark cycle with free access to food and water. Before experiments, animals were allowed to habituate to the housing facilities for a week. The present study was conducted with approval from the Animal Ethics Committee of the University.

Surgical procedure
The CCI model was performed as previously described by Xie (1988a, 1988b). Briefly, rats were anesthetized with 10% chlorate hydrate (350 mg/kg, i.p.), the left sciatic nerve was exposed at the mid-thigh level through a small incision, and four loose ligatures of chromic gut (4.0) tied around the nerve, with a 1 mm spacing between them.
The wound was then closed and secured using suture clips. The surgical procedure was identical for the sham operated animals except that the sciatic nerve was not ligated. The wound was treated with antibiotics.

Intrathecal injection
The intrathecal injection procedure followed the method of Hylden and Wilcoxon in 1980 (Zhang et al., 2013;Hylden and Wilcox, 1980). Briefly, a stainless needle attached to a 25 ml micro-syringe was inserted between the L5 and L6 vertebrae of conscious rat. A sudden slight flick of the tail indicated the needle entered into the subarachnoid space. Ten microliters of Dex (1 lg/kg) solution or saline was injected over a period of more than 20 s. After complete injection of drug, the needle was removed after a 10 s wait, to ensure retention.

Assessment of mechanical allodynia
Mechanical allodynia, as a behavioral measure of neuropathic pain, was assessed by the paw withdrawal threshold. The mechanical withdrawal threshold (MWT) was evaluated by von Frey filaments as previously described Xie, 1988a, 1988b). The animals were habituated in a wire mesh cage 30 min before the experiment. An automated dynamic plantar aesthesiometer (Ugo Basile, Varese, Italy) was used to measure the MWT, which was recorded as the lowest force (g) causing a rapid withdrawal of the right hind paw. Each measurement was repeated three times at intervals of 5 min, and the average force evoking reliable withdrawals was taken as threshold. Quick withdraw or licking of the paw in response to the stimulus was considered a positive response.

Assessment of thermal hyperalgesia
Thermal hyperalgesia of hind paws was evaluated using a plantar test (7370, UgoBasile, Comeria, Italy) according to the method described by Hargreaves et al. (1988), Qu et al. (2009). After acclimation of 30 min, the heat source was positioned under the glass floor directly beneath the hind paw. The intensity of the thermal stimulus was adjusted to achieve an average baseline paw withdrawal latency of approximately 9-11 s. A digital timer automatically recorded the duration between the start of stimuli and the paw withdrawal thermal latency (PWTL). A maximal cutoff time of 20 s was used to prevent unnecessary tissue damage. Each paw was measured alternatively after more than 5 min.

RT-PCR
The expression levels of IL-1, TNF-a, IL-6, NR2B, NF-jB, and iNOS mRNA were determined by RT-PCR. Animals were decapitated and total RNA from L4-L5 spinal cord tissues was extracted on day 21 after the CCI surgery using the RNAiso plus kit (Takara Biotechnology, Dalian, China) according to the manufacturer's instructions. Then, the isolated RNA was reverse-transcribed to synthesize the first strand cDNA with the oligo (dT) 18 primer using the cDNA synthesis kit (Takara Biotechnology, Dalian, China), and the obtained cDNA was used as a template to perform PCR amplification using SYBR_ Premix Ex TaqTM II kit (Takara Biotechnology, Dalian, China).
Each 20 ll reaction system comprised 2 ll of cDNA, 10 ll SYBR Premix Ex Taq II, 10 lmol/l of both sense and antisense primers.
For normalization, b-actin was used to normalize mRNA.

Statistical analysis
Statistical analyses were performed using SPSS 19.0. Data were expressed as mean ± standard deviation (SD). Comparison between groups was performed with analysis of variance (ANOVA) and Student-Newman-Keuls test (q test). Statistical significance was assumed at a value of P < 0.05.

General behavioral observations
All experimental animals maintained good health throughout the experimental period, with no animals demonstrating significant weight loss, wounds or scars, or failure to groom. Furthermore, no infection, autonomy, or motor weakness was observed in any of the animals. The general health of rats with nerve injuries did not differ from sham-operated controls. No abnormal behavior or foot deformity was seen in the sham group. However, all CCI rats in the experimental groups developed varying degrees of abnormality of foot, gait and posture after surgery, including refrained from weight bearing on the affected paw and modified their stance accordingly, with eversion of the foot. Dex treatment alleviated those abnormal behaviors.

The effect of Dexmedetomidine (Dex) on mechanical allodynia
After CCI, rats were administered Dex (1 lg/kg intraperitoneal, once daily) for a period of 21 days. Mechanical withdrawal thresholds were assessed before operation and on days 1, 7, 14, and 21 after CCI. After surgery, animals (CCI group and Dex-treated group) developed a significant hypersensitivity to pain when compared with the sham group as previously described Xie, 1988a, 1988b). As shown in Fig. 1, the decrease in the paw withdraw threshold was significant from day 1 to 21. Dex reversed CCI-induced mechanical allodynia from day 1, which was significant as compared with CCI group from day 7 to 21 (p < 0.05).

The effect of Dexmedetomidine (Dex) on thermal hyperalgesia
Similar to these results of mechanical withdrawal threshold, as shown in Fig. 2, CCI operation elicited a rapid-onset and longlasting thermal hyperalgesia. The decreases were significant in CCI group and Dex group at day 1 after surgery, compared with sham group (p < 0.05). In contrast, treatment with Dex, significantly attenuated thermal hyperalgesia as compared with the CCI group from day 7 to 21 (p < 0.05). These results suggested Dex attenuated CCI induced nociceptive response.

Effects of Dex on pro-inflammatory cytokines in spinal cord
Some studies demonstrated the pro-inflammatory cytokines are involved in the neuropathic pain process. Therefore, we investigated the effects of Dex on pro-inflammatory cytokines in spinal cord. As shown in Fig. 3, there were significant increases in the mRNA levels of TNF-a (Fig. 3a), IL-1b (Fig. 3b) and IL-6 ( Fig. 3c) in spinal cord of CCI rats, as compared with the sham group. However, Dex reversed CCI-increased the levels of TNF-a, IL-1b and IL-6 (p < 0.05). Taken together, these results suggest that Dex attenuated the expression of TNF-a, IL-1b and IL-6 in spinal cord of CCI rats.

Effects of Dex on CCI-induced NR2B expression in spinal cord
CCI induced the higher-expression of NR2B at days 7, 14 and 21 in CCI group and Dex group compared with the sham group (p < 0.05), whereas the Dex-treated group significantly attenuated the NR2B mRNA expression (p < 0.05, Fig. 4a).

Effects of Dex on CCI-induced NF-jB expression in spinal cord
NF-jB is a key transcription factor complex that controls the expressions of pro-inflammatory and pain mediators (Zhou et al., 2014;Ahn et al., 2007). As shown in Fig. 4b, compared with the sham group, CCI significantly increased the expression of NF-jB at days 7, 14 and 21 (p < 0.05). But Dex significantly attenuated CCI-induced NF-jB expression level from at days 7, 14 and 21 (p < 0.05).

Effects of Dex on CCI-induced iNOS expression in spinal cord
In the CCI model, iNOS expression was also local in the sciatic nerve. Previous studies in the CCI models have shown that iNOS expression is concentrated mainly away from the ligatures and that Schwann cells are the main type of cell expressing iNOS in the early stages, with macrophages being more important later on (Lv et al., 2015). In the current study though, as shown in Fig. 4c, in comparison with the sham group, CCI significantly increased the expression of iNOS at days 7, 14 and 21 (p < 0.05). However, the levels of iNOS was significantly decreased compared to the CCI treated group from day 7 to day 21 after DEX treated groups (p < 0.05).

Discussion
The main findings of this study are that dexmedetomidine (Dex) reversed CCI-decreased mechanical withdrawal threshold and thermal withdrawal latency; Dex inhibited CCI-induced the levels of pro-inflammatory cytokines TNF-a, IL-1 and IL-6 in spinal cord. Furthermore, Dex reduced the elevated expression of NR2B, NF-jB and iNOS in spinal cord induced by CCI.
Several animal models have been developed to study neuropathic pain mechanisms. The chronic constriction injury model Fig. 1. Effects of Dex on the mechanical allodynia in neuropathic pain rats induced by spinal nerve ligation (mean ± SD). *P < 0.05, compared with Sham group; #P < 0.05, compared with CCI group at the corresponding time points. Fig. 2. Effects of Dex on thermal hyperalgesia in neuropathic pain rats induced by spinal nerve ligation (mean ± SD). *P < 0.05, compared with Sham group; #P < 0.05, compared with CCI group at the corresponding time points.
has provided a better understanding of nociception and the pathogenesis of chronic pain, which is probably the most frequently used model Xie, 1988a, 1988b). In this study, we used CCI model to evaluate the effects of Dex on neuropathic pain, and we found that CCI produced obvious mechanical allodynia and thermal hyperalgesia, which suggest that the model was successful Xie, 1988a, 1988b). In addition, we found that Dex attenuated mechanical allodynia and thermal hyperalgesia for 21 days, suggesting the possible of therapeutic efficacy of Dex.
In addition, proinflammatory cytokines have been involved in demyelination and degeneration of peripheral nerves, increase in sensory afferent excitability, and induction of neuropathic pain (Jancalek et al., 2010). Following activation, proinflammatory cytokines, such as TNF-a, IL-1, IL-6 and iNOS are expressed and facilitate activation of immune responses. TNF-a interacts with a diverse family of TNF receptors and serves as an important intermediate in the innate immune response. TNF-a mRNA expression was correlated with neuropathic pain development in CCI rat model. Proinflammatory cytokine IL-1 is known to modulate pain sensitivity and is commonly involved in the inflammatory response following CNS injury. In animal models, administration of cytokine inhibitors before nerve injury reduces neuropathology and pain-related behaviors. For example, intrathecal injection of IL-1b induces mechanical allodynia, and IL-1 receptor antagonist can inhibit hyperalgesic responses to IL-1b (Marchand and Perretti, 2005). Another cytokine IL-6 has been correlated with mechanical allodynia after nerve constriction injury (Marchand and Perretti, 2005). iNOS is the primary form active during the chronic inflammatory process. Two of the primary cytokines responsible for iNOS upregulation are TNF-a and IL-1, both of which act through the NF-jB pathway within several hours following injury.
In this study, we found that Dex significantly decreased the over-expression of spinal IL-1, TNF-a, and IL-6 in CCI model. We conclude that the analgesic effect of Dex might be mediated, at least partly, through the prevention of IL-1, TNF-a, and IL-6 products.
NR2B has a relatively restricted distribution in nociceptive transmission and pain regulatory pathways such as in the forebrain and in the superficial dorsal horn of the spinal cord Fig. 3. Dexmedetomidine reduces the expression of IL-1, TNF-a and IL-6 following CCI. The total RNA was extracted from spinal cord tissues using RNAiso kit. RT-PCR quantitation of IL-1, TNF-a and IL-6 expression mRNA in spinal cord. CCI significantly increased the expression of IL-1 (A) TNF-a (B) and IL-6 (C) mRNA in the spinal cord, whereas DEX injection inhibited the upregulation of these mRNAs. Data shown as mean ± SD. *P < 0.05 versus sham group; #P < 0.05 versus CCI group. (Moalem and Tracey, 2006;Baamonde et al., 2007). This kind of distribution suggests that NR2B subunit may play a role in pain transmission and in the development of chronic pain. Consistent with previous studies, the expression of NR2B was dramatically increased in spinal cord in CCI models, and DEX treatment significantly inhibited this upregulation.
This study demonstrates the possibility of using Dex for therapeutic intervention of neuropathic pain in CCI rat model, which resembles closely the clinical peripheral mononeuropathy. We suggest that the anti-neuroinflammatory actions of Dex could be attributed to the inhibition of IL-1, TNF-a, IL-6 release, which would result in the reduction of NR2B, NF-jB, and iNOS signaling pathways in spinal cord.

Conclusion
Although precise mechanism of neuropathic pain was not exactly characterized in our study DEX may alleviate neuropathic hypersensitivity and inflammation partially by inhibiting NR2B, NF-RB, and iNOS expression in the spinal cord of rats with neuropathic pain resulting from CCI of the sciatic nerve. The present study suggests the potential use of Dex in the treatment of neuropathic pain.

Grant support & financial disclosures
None.

Declaration of interest
All authors declared there was no conflict of interests involved.


The Intricate Nature of SERS: Real‐Life Applications and Challenges

Testing for the presence of microorganisms in biological samples in order to diagnose infections is very common at all levels of health care. There is a growing need to ensure appropriate diagnosis by also minimizing the analysis time, both being very important concerns related to the risk of developing an antimicrobial resistance. Moreover, there are important medical and financial implications associated with infections. In this chapter, we will discuss the latest ultrasensitive and selective, but simple, rapid and inexpensive bacteria detection and identification methods by using receptor-free and innovative immobilization principles of the biomass. Raman spectroscopy, which combines the selectivity of the method with the sensitivity of the surface-enhanced Raman scattering (SERS) effect, is used in correlation with chemometric techniques in order to develop biosensors for pathogenic microorganisms.

Introduction
Lately, the pathogens can be individually identified by using surface-enhanced Raman scattering (SERS), without the need of labeling or specific receptor usage like antibodies, for instance. Colloidal metallic suspensions offer the advantage of ambient conditions, fast completion, and minimal number of reactants, being economical, and resulting in a ready-to-use product. However, despite the progress achieved, concerns and problems with the preparation of metal nanoparticles (NPs) remain, such as the byproducts from the reducing agent, the multiple steps often required, and the high concentration of protective agents. Furthermore, it has been a major bottleneck to elucidate the key factors (other than surface roughness enhanced electromagnetic fields) that play important roles in the SERS process of adsorbed biomolecules. The understanding of the mechanisms involved in the interaction of biological systems with inorganic materials is of interest in both fundamental and applied disciplines. Herein, the decisive know-how in investigating biological samples by using several SERS-active platforms will be described.

SERS effect
Raman spectroscopy requires the illumination of a sample with monochromatic light. The inelastic scattering of a small fraction (approximately one in a million) of the incident photons toward lower (Stokes scattering) or higher frequencies (anti-Stokes scattering) than the incident light is known as Raman scattering. A typical Raman spectrum plots the intensity of the scattered light versus the number of probed molecules. There are several noteworthy advantages of this technique, such as speed, versatility, and the functionality under ambient conditions in nonspecific environments (by using portable, miniaturized spectrometers); the simplicity of sample preparation; the possibility of remote detection of Raman signals by using optical fiber probes; the chance to examine transparent samples; and the obliviousness to water, ubiquitous element for biological samples. Probably the biggest disadvantage lies in the extremely small cross section, typically (10 −30 -10 −25 ) cm 2 /molecule, which can be translated into long acquisition times and considerable high sample concentrations.
Raman spectra can be used for the identification and classification of microorganisms once a procedure with good reproducibility and reliability is established [1][2][3][4]. However, the spontaneous Raman effect is so weak that fluorescence, when it occurs, obscures the Raman spectrum. SERS represents the enhancement of Raman-active vibrations associated with the intimate contact (within few nanometers) to a surface covered with plasmonic NPs. Moreover, additional modes not found in the traditional Raman spectrum can be present in the SERS spectrum, while other modes can disappear.
The surface-selection rules that apply to infrared and Raman spectroscopies are extended for surface-enhanced vibrational spectroscopy (SEVS) by taking into account the local field and/or the roughness of the surface. SEVS spectra are the expression of the analyte-radiation interaction when the molecule is in the close proximity or adsorbed on the metallic nanostructure, which supports the surface plasmons [5]. So the presence of the plasmon resonance, for instance, will define the observed spectral intensities. When electromagnetic radiation with the same frequency is incident upon the nanostructure, the electric field of the radiation drives the conduction electrons into collective oscillation. Electromagnetic enhancement, the major contribution in the SERS effect, relies on the Raman-active molecules being confined within large electromagnetic fields (EFs), generated by the excitation of the local surface plasmon resonance (LSPR). So the extreme sensitivity of SERS to small increases in the local field is easily seen since it scales roughly as ω 4 (where ω = frequency). Therefore, the fall-off in intensity of high frequency vibrations is also explained; the driving field and scattered field cannot simultaneously excite the particle resonance if they are of very different frequencies. This explains also the different excitation profiles for different bands; maxima for higher frequency vibrations occur at shorter wavelengths, as the scattered field is brought closer to resonance [6].
SERS represents a relatively inexpensive alternative, compared to the conventional detection methods that also meet the clinical tools' requirements: simplicity, reliability, uniformity (for testing various pathogens), and high specificity. It completely overcomes the shortcoming of Raman small cross sections. SERS is capable to characterize [7][8][9][10], identify [11,12], and differentiate [13,14] pathogenic microorganisms in synergy with chemometrics, based on the biochemical, chemical, and their structural properties.
Even though SERS is a highly specific and sensitive detection method, well suited for biological issues, SERS measurements still suffer from low reproducibility of spectra. Fluctuations of spectral characteristics are induced by variation between different colloid batches, colloid concentration dependence, and inconsistent enhancement even within one colloid batch mainly due to an inhomogeneous and a rather uncontrollable aggregation of NPs [15]. The main issues consist in the difficulty to generate uniform distributed EFs, large EFs occurring only at localized positions (hot-spots) and the polydispersity of colloidal clusters. As Nie and coworkers [16,17] have already quite convincingly demonstrated, the enhancement factor depends on the wavelength of exciting radiation, or rather on the relation between the wavelength and the size of the Ag NPs.
Still, for real-world applications, reproducibility is considered in particular cases more important than enhancement factors. Background signal from the food and environmental matrices represents a real challenge. In addition, proper and simplified sample pretreatment is needed before conducting a SERS measurement. For instance, sample preparation for SERS detection of bacteria is quite inconsistent referring to colloids as SERS-active substrates. The NPs can be either coated on the outside of the bacterial cell wall or directed to the interior of the bacterial cells. Whereas the first preparation results in spectral information mainly derived from cell wall components, the second one contains additional cytoplasmic information [18,19]. Figure 1 shows the SERS signal acquisition process from a microbiologic sample, when the silver coverage of the bacteria (in blue) is successful.
Conclusively, the SERS effect depends on a wide range of parameters, such as the particular features of the laser excitation (wavelength, polarization, and angle of incidence), the experimental setup (scattering configuration), substrate-related parameters (geometry, adsorption, orientation with respect to the incident beam direction, and polarization), and is distancedependent. However, readiness remains an important parameter in choosing the suitable, fast, and reliable tool for detection at trace level, for large-scale applications.

Gold or silver NPs in biomedical applications?
Gold NPs (Au NPs) are promising SERS candidates in biomedicine and have already been successfully tested for various biomedical applications. They are easy to prepare, significantly more stable than other metallic NPs (not easily oxidized), and are highly biocompatible. They can act as artificial antibodies due to their simple surface chemistry, precise binding affinity, and possibility of tuning by varying the density of ligands on their surfaces. Lately, a continuous effort was made to develop new low-cost and easier synthesis strategies for increasing their cellular biocompatibility, by varying their geometries, their physical dimensions, and functionality. The mixing rate of the reactants could greatly influence the physical properties of the Au NPs, their stability over long periods of time, and their SERS sensitivity. It is reported that when the gold salt solution is rapidly added to the reaction mixture, preponderant spherical short-and long-chain polyethylene glycol (PEG) Au NPs with a mean diameter of 15 nm are obtained, whereas a drop-wise addition of the gold salt leads to a seeding effect and to Au NPs with a mean diameter of 60 nm [20]. The most common surface ligand used in biomedical applications is thiolated PEG (PEG-SH), which ensures the desired hydrophilicity and increased circulatory half-life in vivo systems [21]. Proteins, such as bovine serum albumin or collagen, can also serve as capping and stabilizing agents in the one-step synthesis of gold colloidal nanoassemblies and spherical Au NPs with tunable shape and size [22,23]. Furthermore, the in vitro uptake and toxicity effect of Au NPs grown with a native collagen shell exhibit a lower toxic effect on cervical carcinoma and lung adenocarcinoma cells than synthetic polymer-coated Au NPs [24]. Additionally, due to their ability to efficiently convert light into heat, gold NPs can specifically allow thermal ablation of the targeted biological region and by absorbing high amounts of X-ray radiation become enhancers in cancer radiation therapy or computed tomography [21].
However, silver NPs (Ag NPs) show stronger plasmon fields than Au NPs due to the simple fact that their plasmon band does not overlap with the interband electronic transitions, as in the case of Au NPs [25]. Figure 2 presents our recent results obtained by using different SERS- active substrates for the detection of E. coli. We synthesized several types of Ag and Au sols by using PEG with two chain lengths as reducing agent [20] and compared the obtained SERS signals with the in situ synthesized Ag NPs SERS signal of bacteria. The SERS spectra were recorded using a Raman microscope (Lab RAM HR, HORIBA Jobin Yvon, Japan). The 633-nm line of a HeNe laser was used as the excitation source. The excitation wavelength dependency of the SERS enhancement can be explained by the optical absorption of the silver colloidal suspensions. We already characterized the herein used NPs in our previous work; the Ag Hya NPs particles feature a plasmon resonance band of around 402 nm. Hence, excitation with the 532 nm laser line is favorable as compared to longer wavelengths (633 nm), being closer to the plasmonic band. However, in the case of the Au PEG NPs the plasmon resonance band is specific to gold and was determined around 540-560 nm, depending on the particles' diameter. Generally, we waited 30 min as incubation time in order to obtain the higher and more stable SERS signal from the irradiated sample. As an effect of incubation time we observed an increasing agglomeration of the SERS-active colloids, leading to a coupling of the plasmon Figure 2. SERS spectra of E. coli by using five distinct platforms of detection: AgPEG200NPs/AgPEG8000NPs-silver NPs with PEG200/PEG8000 layer, AuPEG200NPs/AuPEG8000NPs-gold NPs with PEG200/PEG8000 layer, and Ag Hya NPsin situ silver synthesized NPs by reduction with hydroxylamine hydrochloride. resonances, which again leads to a red-shift of the main absorption. In consequence, we achieved in these earlier works the best SERS performance with the 633 nm excitation wavelength. As an indicator we selected the intensity of the marker band found at 732 cm −1 which was about fivefold higher for the in situ approach. Even when we preconcentrated the Au PEG NPs by centrifugation (38× more concentrated Au colloidal suspension), the enhancement factor was not comparable with the one obtained for the hydroxylamine reduced in situ Ag colloid [12]. Moreover, the single-cell detection of bacteria was successfully obtained by using the in situ method, while the other tested colloids enabled us to detect bacteria only in rather high concentrations (>10 3 CFU/ml). For single-cell detection assays, this aspect could make a difference in selecting the SERS detection platform.

Label-free SERS-based assays
The impact on the public health demands sensitive analytical tools for detecting pathogens. Rapid, culture-free, ultrasensitive pathogens' detection and identification are of paramount importance, since there are infections caused by a single microorganism (mycobacteria) and some pathogens need 20 days to proceed through one division cycle (while some E. coli strains take only 20 min), making laboratory culture a slow process.
Conventional methods currently used for microorganisms' identification are nucleic acidbased polymerase chain reaction (PCR, qPCR, and real-time PCR), on-chip nucleic acid amplification [26], enzyme-linked immunosorbent assay (ELISA) [27], chemiluminescence-based microarrays [28,29], and matrix-assisted laser desorption/ionization (MALDI, MALDI-TOF) [30,31]. Major drawbacks of these culture-based detection techniques are the time required, the high costs, the need of prelabeling, and/or use of antibodies or DNA sequencing, and also the concerning increased rate of false negatives and false positives. In addition, biosensors for bacteria detection still rely on the specific capture of the targeted pathogen by using antibodies [9,11,32], aptamers [33], and substrates that contain metallic nanosculptured thin films [34], or other different complex surface morphologies fabricated by using photolithography combined with deposition techniques [35]. This approach leads to costly microarrays, which can only be handled by trained personnel, in laboratory conditions. However, before any of these wholeorganism fingerprint techniques can be used to analyze the samples, the microorganisms must be cultured in order to isolate the microorganism of interest from other sample constituents and/or produce sufficient biomass for analysis.
Recently, spectroscopic techniques look more and more promising with the development of low-cost, label-free, and ultrasensitive detection protocols enabling for the first time to be fast, specific, and sensitive enough in vital issues as healthcare. Particularly, Raman spectroscopy is a nonintrusive in situ analysis method, requiring small efforts for sample preparation and can be easily used outdoors with portable, miniaturized, and even handheld Raman spectrometers. Moreover, when using SERS, the spectral fingerprint reflects the physiological state of a bacterial cell, e.g., when pathogenic bacteria were cultured under conditions known to affect virulence, their SERS fingerprints changed significantly. It is also known that bacteria respond to environmental triggers, such as temperature, pH, and nutrient concentrations, by switching to different physiological changes in their biochemical profile, including the number and composition of outer membrane proteins, lipopolysaccharides (LPS), and cellular fatty acids [36].
For SERS detection of bacteria, several innovative approaches are reported. Sengupta and coworkers [37][38][39] reported straightforward analysis of a colloidal-bacterial mixture in an optical glass cuvette. The preferred excitation laser line is 514.5 nm in their study of the pH influence and the time-dependent behavior of colloidal-bacterial suspensions, even if this wavelength is too long to resonate with excitations of the aromatic ring breathing mode.
By using the same excitation wavelength, Kahraman et al. [40] developed a uniform bacterial sample preparation method based on the convective assembly. Aggregation and clustering was frequently applied for obtaining higher SERS signal from "hot-spots" [41]. Knauer and others [9,11,42] optimized the microarray detection of single-bacterium by using different Ag sols and aggregation with sodium chloride or sodium azide in low concentrations. However, in these studies, the 633 nm laser line was selected for SERS-based detection on the antibodyactivated microarray and the substrate used for enhancement was an Ag colloid produced by using a modified Leopold and Lendl method [43].
Efrima and Zeiri also proposed a novel approach, to use colloid produced in the presence of the biomass [18,19]. The authors used the 633 nm laser line as an excitation wavelength, therefore they were able to report the ring breathing mode band observed at 1004 cm −1 and assigned to the phenylalanine residue [10]. Excepting Knauer's group work [9,11,42] and recent studies reported by Zhou et al. [12][13][14]44], when applying the in situ approach, the Leopold and Lendl SERS active substrate was not so exploited in the bacteria detection, as the usage of the 633 nm laser line is mere. The hydroxylamine-reduced silver colloid was shown as ideal for obtaining SERS structural information on biological molecules contained in the bacterial cell wall, since it provides a high enhancement factor and shows almost no anomalies in the spectral band position upon aggregation [45] in comparison to the citrate-reduced Ag sols.
Another bacteria detection assay reported used crystal violet (CV) as Gram stain [46]: the procedure involved staining bacterial samples with CV which binds to the peptidoglycan layer of the Gram-positive and Gram-negative bacteria. Despite the simple and robust methodology of staining, the detection relies on optical microscopy, which is often susceptible to userdependent sampling error. Therefore, by developing magneto-fluorescent NPs, the detection was improved and was successfully tested for both Gram-positive and Gram-negative bacteria (E. coli and S. aureus).
Label-free SERS-based detection is a very promising alternative for rapid monitoring real samples, offering single-cell sensitivity [1,47], providing spectra with no contribution from the aqueous environment (prominent in the biological samples), and a high precision classification of bacteria, at strain level [1][2][3]. Recently, innovative approaches for the rapid SERS label-free detection of bacteria were developed: (i). Simple, receptor-free immobilization of bacteria on the glass surface [14]. Mircescu et al., based on molecular-specific SERS spectra of uropathogens at single-cell level, discriminated between rough and smooth strains of E. coli and P. mirabilis. The innovative and effective principle of bacteria immobilization through electrostatic forces, by inducing a positive charge on the silanized microarray surface was demonstrated for Gram-negative bacteria. In addition, the monitoring of single-cell SERS spectra of bacteria in different growth phases was assessed.
(ii). In situ silver NPs preparation in the presence of bacteria (Bacteria@ Ag NPs) [12]. Zhou et al. developed the in situ Ag colloid synthesis in two steps, resulting in coating the bacterial cell wall with a silver SERS-active layer. The assay requires about 10 min and only one sample droplet of 3 µl. By using this novel strategy, SERS detection (about 30-fold higher enhanced SERS signal) and hierarchy cluster analysis (HCA) discrimination of three strains of E. coli and one strain of S. epidermidis was reported.

In situ Ag NPs synthesis: extended approach
Currently and also in the future, biosensors with integrated nanotechnology promise to address the analytical needs in practical pathogen diagnosis. Recently, comprehensive reviews concerning the bacteria detection by using Raman and SERS spectroscopies were reported [15,48,49]. The increased sensitivity and high information content of SERS is acknowledged, mostly when this powerful tool is used in conjunction with advanced analysis and classification techniques. The key advantages that SERS-based biosensors include are the easy-to-use detection platforms and reduced testing time resulting in immediate diagnostic (within 5-15 min) [50,51], superior sensitivity and multiplex capability [52], reduced sample volume, and high sensitivity and specificity. Thus, a great deal of research has been invested into the development of SERS-based biosensors for pathogenic microorganisms.
For instance, SERS mapping by using Ag dendrites [53] as SERS active substrate, both for Gram-negative and Gram-positive bacteria was reported. Not so promising results were obtained in case of the Gram-positive bacteria, probably due to their different membrane structure, containing less outside proteins. Usually, the marker bands used for detection of the pathogens are either the 1332 cm −1 band assigned to the CH deformations in proteins [53], either the 730 cm −1 band assigned to adenine [14,54].
In this section we will mainly focus on the latest studies involving in situ Ag NPs synthesis approach for SERS detection in biomedical applications. In a more recent study, Zhou et al. [13] applied the Bacteria@ Ag NPs approach for live and dead bacteria counting/discrimination. Moreover, by using antibiotics (ampicillin, polymyxin B, and chloramphenicol) with different action mechanisms on bacteria and by monitoring the SERS signal decay in time, they were able to determine which microorganism is or not developing a drug resistance in less than 4 h. Lately, the same group [44] completed the previous work by applying the Bacteria@ Ag NPs approach on a microarray (containing antibodies). Figure 3 exhibits the schematic protocol of generating the Bacteria@ Ag NPs for SERS detection of microorganisms at single-cell level.
Since Efrima's group reported on producing in situ NPs through external (bacterial cell-wall) or internal (interior components mode) synthesis on bacteria [18], the use of in situ synthesized Ag colloids for bacteria detection was demonstrated in several assays only by Haisch's group [12-14, 44, 54].
Recently, a label-free NIR-SERS detection and discrimination of bacteria after pretreatment of bacterial cell membrane with disrupting agents was presented, featuring a sensitivity down to 10 3 CFU/ml and a measuring time of less than 5 min [55]. Latest studies underline the applicability of the in situ synthesized Ag colloids also in environmental research, for instance, for the detection of bacteria in plant roots [56] and for pesticide monitoring in spinach leaves [57]. These results demonstrate the applicability of SERS-based noninvasive detection approaches for identification and characterization of pathogens and their secreted metabolites. The in situ synthesis of Ag colloid ensures the structural integrity of the coated bacterial cells and thus helps to rapidly generate spectral bacterial signatures with high sensitivity and specificity. Figure 4 contains a collection of microscopic images illustrating the reproducible coverage of E. coli cells with a silver layer by using the in situ synthesis approach. The influence at strain level of the O-antigen presence was already demonstrated by using unspecific surface chemistry as means of bacteria adsorption and the in situ synthesis approach [14]. O-antigen is the terminal structural part of the Gram-negative bacterial outer membrane that contains the significant variation between virulent strains and lab-designed strains. The differences in the composition of the monosaccharide units and sugar linkages translate into strain discrimination, by using molecular serotyping tests and chemometric analysis. Considering all this, O-antigen is the most variable cell constituent and of great importance when dealing with bacteria identification at strain level.
Raw SERS spectra collected from single cells of four different strains of E. coli are shown in Figure 5. For the accurate detection and discrimination between these strains, one has to make sure that all experimental conditions are standardized for each measurement. In this context, we established a constant timeline in the preparation steps of the samples and we used constant experimental parameters in acquiring the SERS spectra. The used E. coli strains are rough (K12)-MG1655, TOP 10 ( Figure 5A and C) and smooth strains (B2)-536, UTI89 ( Figure 5B and D). Specific SERS bands in each case (with or without the O-antigen) are discussed in our previous study [14], where a clear discrimination between K12 and B2 strains is demonstrated by using chemometrics (principal component analysis, PCA).
In the last decades, SERS was used to identify: DNA bases [58], a wide range of explosives and trace materials [59], food additives [60], therapeutic agents [61], different species of pathogenic and nonpathogenic bacteria [62][63][64], protozoa [65], fungi [66,67], and their spores [68], respectively. Furthermore, as previously described, vibrational spectroscopy can be used to study the uniqueness of microorganisms. Consequently, we envision that the in situ synthesis approach could be used to some extent in other microorganisms' detection as well, not only bacteria.
Particularly, Raman and SERS spectroscopies were already applied in the detection, characterization, and monitoring of growth cycle for fungi. For example, various pathogens such as Candida albicans, C. glabrata, and C. tropicalis isolated from blood cultures have been rapidly identified [66]. Rapid diagnosis of infections caused by fungi from Candida genus is extremely important, since intra-abdominal infections caused by these fungi lead to high mortality rates [67]. Yang and Irudayaraj [69] were able to easily identify A. niger and F. verticillioides pathogenic fungi from apple surface, using FT-Raman spectroscopy. Szeghalmi and coworkers [70] studied the growth of A. nidulans strain A28 hyphae over the Au-coated Klarite SERS substrate, and they detected a strong signal in the close proximity of the hyphal cell wall because of the excretion of some extracellular components during growth.
Another field of interest in fungi studies using Raman spectroscopy and SERS is the characterization of various bioactive compounds extracted from different fungi. De Oliveira and coworkers [71] successfully identified the chemical composition of the extracts obtained from P. sanguineus fungus. The major bioactive components of P. sanguineus extracts are ergosterol and cinnabarin, the last one being responsible for the antibiotic activity of the extract [72].
Zinc oxide nanoparticles (ZnO NPs) were tested for their antifungal activity against B. cinerea and P. expansum fungi. He and coworkers [73] used traditional microbiological plating, along with SEM and Raman spectroscopy and showed that a concentration higher than 3 mmol/l of ZnO NPs can significantly inhibit the growth of B. cinerea and P. expansum. The last one is more sensitive to the action of ZnO NPs because these inhibit the development of conidiophores and conidia, resulting in the death of fungal hyphae. The detection of fungal infection in mice lungs with P. brasiliensis and follow-up treatment with magnetic NPs functionalized with amphotericin B can be achieved using SERS analysis [74].
SERS imaging and analysis have been effectively used for the characterization of in vitro biosynthesis of NPs by different species of fungi. In this regard, Mukherjee and coworkers [75] established a controlled biosynthetic route to obtain the nanocrystalline Ag particles using T. asperellum. Using TEM and XRD, the obtained Ag NPs were found to be in a range of 13-18 nm. C. cladosporioides was also reported to be able of Ag NPs extracellular biosynthesis [76]. In fact, fungi are not only able to biosynthesize Ag NPs, but also Au NPs. Extract from the filamentous fungi A. nidulans was used in the formation of Au NPs within and adjacent to hyphae. Also, the Neurospora crassa extract was tested by Quester and his coworkers [77] for the formation of Au NPs under different experimental conditions. The authors were able to synthesize Au NPs with different shapes and sizes ranging from 3 to 200 nm by using methylene blue as target molecule.
Concluding this chapter, it is a challenge to entrench how to use most effectively the SERS effect in our favor. The simple reasoning is that SERS is still a not fully understood phenomenon. However, the ongoing studies in the biomedical area show the huge potential of this ultrasensitive technique to actually improve our life quality and the diagnosis procedures of infections and to significantly prevail essential real-life issues. Apart from infections diagnostics, cancer treatment or imaging, drug delivery, and personalized medicine or other health care branches can greatly benefit from Raman/SERS detection and mapping in synergy with functionalized NPs and high-performance support vector machines.