Contralateral dominance emerges from geometric transformation in bilateral control systems

Abstract

Introduction:

Contralateral organization is a defining feature of vertebrate nervous systems, yet its functional origin remains incompletely understood. We examined whether contralateral routing can arise as an advantageous solution in delayed bilateral control systems using a minimal computational framework.

Methods:

We constructed abstract bilateral sensorimotor networks composed of sensory, central, and motor units on the left and right sides, and systematically compared alternative architectures differing in sensory laterality, commissural coupling, and local connectivity. We evaluated one-dimensional and two-dimensional models, introducing in the latter a continuous twist parameter representing transformations between sensory and motor coordinate relationships. Dense parameter scanning and bootstrap analysis were used to estimate the transition point and its robustness.

Results:

In one-dimensional models, contralateral configurations were dynamically viable but sensitive to the choice of objective function. In two-dimensional models, the twist parameter reorganized the architecture landscape: without transformation, optimal solutions were predominantly ipsilateral, whereas under strong transformation they became predominantly contralateral. Intermediate conditions exhibited an abrupt transition rather than a gradual shift. Dense parameter scanning localized this transition to a threshold at θ_c ≈ 0.483. Bootstrap analysis showed that this threshold was stable (95% CI: 0.481766–0.483507) and only weakly dependent on longitudinal delay. Objective values were minimized near and just above the transition region.

Discussion:

These results indicate that, within an abstract dynamical framework, contralateral routing can become advantageous under conditions of transformed sensorimotor relationships and delayed interactions.

1 Introduction

Contralateral organization is a fundamental feature of vertebrate nervous systems, whereby sensory inputs and motor outputs are predominantly represented in the opposite hemisphere. This organization is evident across multiple levels of neural structure, including the decussation of retinal projections at the optic chiasm, contralateral motor control mediated by corticospinal pathways, and interhemispheric coordination via commissural systems such as the corpus callosum (Jeffery, 2001; Herrera and García-Frigola, 2008; Gazzaniga, 2000). Despite its ubiquity, the functional basis of contralateral organization remains incompletely understood.

Several explanatory frameworks have been proposed. Developmental and evolutionary accounts suggest that contralateral wiring arises from large-scale transformations of body plan geometry, including hypotheses such as axial twist or inversion during early embryogenesis (de Lussanet and Osse, 2012; Chédotal, 2019). Other approaches emphasize wiring economy and network efficiency, proposing that neural systems minimize connection length or metabolic cost while maintaining functional integration (Cherniak, 1994; Bullmore and Sporns, 2012). In addition, studies of spinal and cortical systems highlight the role of commissural pathways in coordinating bilateral activity and enabling integrated behavior (Kiehn, 2016; Maxwell et al., 2020; Roland et al., 2017). Classical neurobiological perspectives have also emphasized the importance of preserving orderly spatial relations in sensory representations, particularly in visual systems in which inversion of the sensory image must be reconciled with coherent mapping of external space (Cajal, 1995; Jeffery, 2001; Kaas, 1997). While these perspectives provide important insights, they primarily address how contralateral organization may arise, be maintained, or be developmentally constrained, rather than under what functional conditions contralateral routing becomes advantageous relative to ipsilateral alternatives.

This issue is especially important because contralateral organization is not uniform across all sensory and motor systems. Some modalities exhibit strongly structured cross-midline organization, whereas others do not. More generally, the functional consequences of laterality depend on how sensory coordinates, internal processing, and motor outputs are related to one another. Systems that preserve continuous spatial mappings may be subject to different architectural pressures from systems such as olfaction, which is less organized by a continuous topographic representation of external space and is correspondingly more ipsilateral in its primary projections (Shepherd, 2004). From a systems-level perspective, the problem can therefore be reframed not simply as one of anatomical laterality, but as one of architecture selection under dynamical and dynamical constraints and transformation structure.

Neural systems operate under delayed signal propagation, noise, and the need for stable bilateral coordination. In such systems, the relationship between sensory inputs and motor outputs depends not only on anatomical connectivity but also on the effective transformation between sensory and motor coordinate systems. When this relationship is direct, ipsilateral routing may be sufficient. When it is inverted or mismatched, however, different routing architectures may become functionally preferable. Thus, changes in the geometry of sensorimotor mapping may bias which bilateral architecture best supports accurate and robust behavior.

Recent work in computational neuroscience has emphasized how network architecture shapes dynamical function, including the effects of delays, recurrent interactions, and interhemispheric coupling on stability and coordination (Deco et al., 2011; Breakspear, 2017). However, most existing models assume a fixed relationship between sensory and motor coordinates and do not consider how transformations of this relationship influence the selection of bilateral architectures. As a result, it remains unclear whether contralateral routing can become favored as a consequence of general dynamical constraints, rather than being imposed a priori or attributed only to specific developmental histories.

Here, we address this question using a minimal computational framework that isolates the interaction between coordinate transformation, delay, and bilateral competition. We model a bilateral sensorimotor system composed of sensory, integrative, and motor components in each hemisphere, and systematically compare alternative architectures that differ in sensory laterality and interhemispheric coupling. To represent transformations of sensorimotor geometry, we introduce a continuous twist parameter that denotes the degree of inversion or mismatch between sensory and motor coordinate systems, that is, the extent to which spatial relations in sensory coordinates must be transformed to support appropriate motor mapping.

Our central hypothesis is that increasing sensorimotor transformation can shift the functional preference of the system toward cross-midline routing when delayed signal propagation and bilateral competition are present. Specifically, we test whether increasing transformation produces a sharp reorganization in the optimal architecture, such that ipsilateral mappings dominate under low transformation and contralateral mappings dominate under high transformation. Importantly, contralateral routing is not hard-wired as the outcome of the model, but is evaluated as one candidate solution within an abstract bilateral control system.

By combining exhaustive architecture comparison with dense parameter exploration, this study aims to identify the conditions under which contralateral routing becomes functionally advantageous in a minimal delayed dynamical system. In this sense, the present work does not attempt to reproduce the full anatomical or developmental complexity of vertebrate nervous systems. Rather, it seeks to identify a minimal dynamical principle by which transformations in sensorimotor geometry can bias the selection of bilateral routing architectures, thereby providing an abstract theoretical bridge between classical geometric accounts and systems-level dynamical considerations.

2 Materials and methods

2.1 Overview of the modeling framework

We constructed a minimal bilateral sensorimotor network to examine how contralateral organization can emerge from the interaction among delayed signal propagation, bilateral competition, and transformed sensorimotor mapping (Figure 1). The model consisted of two homologous pathways, left and right, each containing a sensory unit, a central integrative unit, and a motor unit. These pathways were treated as abstract bilateral processing channels rather than as anatomically explicit hemispheres with defined spatial embedding, cell types, or developmental identities. The purpose of the model was therefore not to reproduce vertebrate neuroanatomy directly, but to isolate the dynamical conditions under which alternative bilateral routing architectures become advantageous in a delayed control system.

FIGURE 1

At each point in parameter space, all candidate architectures were evaluated under identical task, noise, and delay conditions. Architecture selection was defined by the objective value of each candidate network, allowing the preferred routing pattern to be identified without hard-wiring contralateral organization as the outcome.

2.2 Network architecture

The model comprised six nodes:

sensory nodes

central integrative nodes

motor nodes

where the subscripts L and R denote the left and right pathways. Three architectural factors were varied. First, sensory input could be routed either ipsilaterally or contralaterally. In the ipsilateral configuration, S_L projected to C_L and S_R projected to C_R. In the contralateral configuration, S_L projected to C_R and S_R projected to C_L. Second, excitatory commissural coupling between the two central nodes could be either present or absent. Third, local sensory-central coupling within each side could be either present or absent. When present, this local coupling was bidirectional, linking S_L with C_L and S_R with C_R. These three binary factors generated 2 × 2 × 2 = 8 candidate architectures.

Motor output was fixed as ipsilateral in all simulations:

This restriction reduced the architectural degrees of freedom and allowed the analysis to focus specifically on sensory laterality and interhemispheric central interactions.

2.3 Connection weights, delays, and inhibitory competition

Connection strengths were fixed across simulations. Sensory-to-central projections had weight w_SC = 1.0. Local sensory-central feedback connections had weight w_CS = 0.4. Central-to-motor projections had weight w_CM = 1.0. Excitatory commissural connections had weight w_CC = 0.7. The gain of the nonlinear activation function was set to g = 1.0.

Two delay scales were used. A short delay of

time step was assigned to sensory-central projections, local within-side sensory-central feedback connections, central-to-motor projections, and inhibitory interhemispheric coupling. A longer delay,

was assigned only to excitatory commissural coupling between C_L and C_R when that coupling was present. Thus, d_long selectively controlled the delay of long-range excitatory interhemispheric communication.

Interhemispheric competition was implemented as reciprocal inhibition between the two central nodes. The inhibitory weight was defined as

where

and

Accordingly, when inhibitory coupling was present, the model included

2.4 Node dynamics

At each time step, the state of node i was updated according to a nonlinear rate-based rule:

where x_i(t) is the state of node i, g is the gain parameter, and net_i(t) is the total input to that node at time t. The total input was defined as the sum of delayed synaptic inputs, externally applied task input, and additive Gaussian noise:

where w_ij denotes the connection weight from node j to node i, d_ij is the corresponding transmission delay, I_i(t) denotes externally applied task input to the sensory nodes, and epsilon_i(t) is zero-mean Gaussian noise. At each time step, external task input was applied only to the sensory nodes. Specifically, u_L(t) and u_R(t) were added to S_L and S_R, respectively, whereas no direct external input was applied to the central or motor nodes.

This formulation provided a bounded nonlinear integration rule while preserving a minimal dynamical structure.

2.5 Sensorimotor task

The network performed a continuous tracking task. In the one-dimensional simulations, the system tracked a target position along the lateral axis. In the two-dimensional simulations, the system tracked target positions along both the lateral (x) and orthogonal (y) axes. Target amplitudes were fixed at

At each time step, the sign of the target could switch stochastically. Along the lateral axis, sign reversal occurred with probability

and, in the two-dimensional case, independent sign reversal along the orthogonal axis occurred with probability

Tracking errors were defined as

and, in the two-dimensional case,

where x_body(t) and y_body(t) denote the current body position along the two task dimensions. Body position was updated using the motor output of the network. Along the lateral axis, the left and right motor nodes acted in opposition:

where m_L(t) and m_R(t) are the activities of M_L and M_R, respectively,

and eta_x(t) is Gaussian process noise with standard deviation

In the two-dimensional simulations, the orthogonal axis was controlled by a fixed proportional feedback rule rather than by the bilateral network itself:

where

and eta_y(t) is Gaussian process noise with standard deviation

This arrangement allowed lateralized architecture selection to be evaluated primarily through the x dimension, while the y dimension served as a stabilizing task component in the two-dimensional setting.

2.6 Transformation parameter

To represent transformations in sensorimotor mapping, we introduced a continuous parameter theta, constrained to the interval

In the present model, theta did not represent a literal anatomical twist. Rather, it denoted the degree of inversion or mismatch between the sensory error structure and the motor routing required to correct that error. The limiting cases were defined as follows:

purely ipsilateral mapping

fully inverted mapping

Intermediate values of theta were implemented as the simplest continuous interpolation between these two limiting mappings.

For the lateral tracking error e_x(t), ipsilateral and contralateral sensory drive components were defined using half-wave rectification:

The actual sensory inputs to the left and right sensory nodes were then given by

These task-dependent inputs were added to S_L and S_R at each time step. Thus, small values of theta favored near-direct ipsilateral correspondence between sensory error and motor correction, whereas large values progressively favored inverted correspondence.

2.7 Objective function

Architecture performance was quantified using a multi-component objective function:

where J_track is tracking cost, J_effort is motor effort cost, J_asym is asymmetry cost, J_delay is delay-related cost, and J_noise is noise-sensitivity cost. Baseline weighting coefficients were set to

Tracking cost was defined as the time-averaged squared tracking error. In the one-dimensional simulations,

whereas in the two-dimensional simulations,

Motor effort cost was defined as the time-averaged summed squared motor activity:

Asymmetry cost was defined as the time-averaged squared difference between left and right motor activity:

J_asym=mean_t[(m_L(t)−m_R(t))∧2]Delay-related cost was computed from the mean absolute activity of each source node, weighted by the absolute connection strength and transmission delay:

This term penalized architectures that relied more strongly on delayed communication. Noise-sensitivity cost was defined as the additional tracking cost observed when external noise amplitude was increased by a multiplicative factor kappa:

with

To compute this term, each architecture was evaluated both under the baseline noise level sigma and under an elevated noise level kappa × sigma. The objective function was therefore used as a common operational criterion for comparing candidate architectures rather than as a unique definition of biological optimality.

To assess the dependence of the results on the weighting scheme, we additionally performed a one-factor-at-a-time sensitivity analysis. In that analysis, each weighting coefficient was independently scaled to 0.5×, 1.0×, and 1.5× of its baseline value while the remaining coefficients were held fixed. The resulting effects on the estimated transition point and on contralateral dominance in the high-transformation regime were then quantified.

2.8 Simulation protocol

All simulations were run for

time steps. The first

time steps were excluded from analysis, and all summary measures were computed over the remaining post-warmup period. At each point in parameter space, all candidate architectures were evaluated under identical conditions, and the optimal architecture was defined as the one with the lowest objective value J.

To reduce stochastic dependence on a single realization, repeated simulations were performed for each architecture and parameter combination. In the exhaustive one-dimensional scan, each condition was evaluated with 12 repetitions. In the inhibitory one-dimensional scan, the tracking-cost one-dimensional scan, the one-dimensional endpoint comparison, the two-dimensional baseline scan, the discrete two-dimensional twist scan, and the dense two-dimensional twist scan, each condition was evaluated with 10 repetitions. In the pairwise comparison and architecture-class comparison analyses, repeated single-run evaluations were performed across five initial random realizations for each condition. Independent random number generators were initialized with distinct seeds for each repetition.

The primary outcome was the proportion of optimal solutions exhibiting contralateral sensory routing, denoted

At each point in parameter space, this quantity took the value 1 when the best-performing architecture used contralateral sensory routing and 0 otherwise. Averaging across cells or conditions therefore yielded the frequency with which contralateral architectures were selected as optimal.

2.9 Parameter exploration

The model was evaluated across multiple parameter grids. The long excitatory commissural delay was varied over

Noise amplitude was varied over the set

for the main inhibitory and two-dimensional analyses, and over a closely related set including 0.045 but excluding 0.09 and 0.11 in selected one-dimensional scans. Interhemispheric inhibitory strength was varied over

For the two-dimensional transformation analyses, discrete twist conditions of

were first evaluated, followed by a dense scan over

This dense sampling was used to localize the transition between ipsilateral-dominated and contralateral-dominated regimes.

2.10 Definition of the transition point

The transition point, denoted theta_c, was defined as the value of theta at which

For a given cross-frequency curve sampled at discrete twist values, theta_c was estimated by linear interpolation between the two neighboring values of theta that bracketed the 0.5 crossing. When the crossing occurred between consecutive points theta_k and theta_(k+1) with corresponding values f_k and f_(k+1), the estimate was computed as

provided that f_k and f_(k+1) lay on opposite sides of 0.5. This interpolation procedure was applied both to the global dense twist scan and to delay-specific cross-frequency curves.

2.11 Bootstrap analysis

The robustness of the transition was evaluated by bootstrap resampling of parameter-space points from the dense two-dimensional twist scan. In each bootstrap replicate, the full set of simulated cells was resampled with replacement, preserving the original sample size. A new mean cross_freq versus theta curve was then computed from the resampled data, and the corresponding theta_c value was re-estimated using the same interpolation rule described above. This yielded a bootstrap distribution of global transition points.

To assess the dependence of the transition on excitatory commissural delay, the same procedure was repeated separately for each value of d_long. For each replicate, a delay-specific estimate theta_c(d_long) was obtained, and a linear slope relating theta_c to d_long was computed across the full delay range. The bootstrap analysis used

resamples, from which median values and 95% confidence intervals were obtained for the global transition point and for the slope of its delay dependence.

2.12 Mechanistic analysis

To examine the mechanism underlying architecture selection, we quantified temporal mismatch and sign alignment between the required lateral motor correction and the motor command produced by the network. The required lateral correction was given by the instantaneous tracking error e_x(t), whereas the produced lateral motor command was given by the difference between right and left motor activity:

Temporal mismatch was defined as the absolute difference between these two quantities:

Sign alignment was defined as an indicator of whether the motor command had the correct sign relative to the required correction:

alignment(t) = 0, otherwise

For each architecture and twist condition, these measures were averaged across post-warmup time steps and then summarized across repetitions. This analysis was used to determine whether the twist-dependent shift in optimal architecture was associated with systematic changes in the temporal consistency between task demands and motor output.

3 Results

3.1 Contralateral architectures are not globally optimal in one-dimensional systems

We first examined whether contralateral organization is favored in a minimal one-dimensional setting. In pairwise comparisons across 260 parameter-space points, the proportion of conditions in which contralateral architectures outperformed ipsilateral ones was 0.503, with a mean objective difference of 0.00021. Mean objective values were 2.172 for contralateral architectures and 2.171 for ipsilateral architectures.

Exhaustive architecture selection across all candidate configurations yielded a mean contralateral frequency (cross_freq) of 0.490, with values ranging from 0.083 to 0.833.

These results indicate that contralateral architectures are dynamically viable but do not dominate the tested one-dimensional solution space.

3.2 Objective structure strongly modulates architecture selection

We next examined how the definition of the objective function influences architecture selection. Under an inhibitory scan across 1,680 parameter-space points, the mean contralateral frequency was 0.504, with values ranging from 0 to 0.900.

When the objective function emphasized tracking performance, contralateral architectures were strongly suppressed. Under this formulation, the mean contralateral frequency decreased to 1.19 × 10⁴, with a maximum of 0.100. The mean objective value increased to 11.181. Mean cost components were 7.363 (tracking), 6.615 (high-noise tracking), 0.535 (effort), 0.853 (asymmetry), 4.481 (delay), and −0.748 (noise sensitivity).

These results show that architecture selection in the present framework depends strongly on the balance between competing cost components.

3.3 Geometric transformation reorganizes the architecture landscape

We next introduced a geometric transformation of sensorimotor coordinates using the twist parameter θ. In the two-dimensional baseline condition without inversion (θ = 0), the system remained overwhelmingly ipsilateral, with a mean contralateral frequency of 0.000179 across 1,680 parameter-space points.

Under full inversion (θ = 1), contralateral architectures dominated completely, with a mean contralateral frequency of 1.000. Mean objective values decreased from 11.181 at θ = 0 to 7.144 at θ = 1, and mean tracking cost decreased from 7.363 to 3.306.

These results indicate that geometric transformation reorganizes the solution landscape such that ipsilateral-dominated regimes at low twist are replaced by contralateral-dominated regimes at high twist within the present abstract control framework.

3.4 A sharp transition in optimal architecture occurs with increasing twist

To characterize this reorganization in detail, we evaluated both discrete and densely sampled values of the twist parameter.

In discrete conditions, the mean contralateral frequency was 0.000238 at theta = 0, 0.0863 at theta = 1/3, 0.999881 at theta = 2/3, and 1.000 at theta = 1.

A dense scan of the twist parameter further localized this transition (Figure 2). Mean contralateral frequencies were 0.0519 at theta = 0.25, 0.0789 at theta = 0.30, 0.0927 at theta = 0.35, 0.113 at theta = 0.40, 0.168 at theta = 0.45, 0.677 at theta = 0.50, 0.991 at theta = 0.55, 0.998 at theta = 0.60, 0.9997 at theta = 0.65, and 0.9999 at theta = 0.70. At higher values (theta = 0.75, 0.80, 0.85), contralateral dominance remained saturated near 1.

FIGURE 2

The transition point, defined as the value of theta at which cross_freq reached 0.5 by linear interpolation between neighboring sampled values, was estimated as theta_c = 0.482623.

3.5 The transition is weakly dependent on interhemispheric delay

We next examined the dependence of the transition on interhemispheric delay. The two-dimensional phase diagram (Figure 3) shows that the boundary separating ipsilateral and contralateral regimes is nearly horizontal across the full range of d_long.

FIGURE 3

The estimated slope of the transition point as a function of delay was −0.000603931. Bootstrap analysis confirmed the robustness of this result (Figures 4, 5). The median transition point was 0.482618, with a 95% confidence interval of 0.481766–0.483507. The slope of the delay dependence had a median of −0.000612461, with a 95% confidence interval of −0.000777127 to −0.000447557.

FIGURE 4

FIGURE 5

These findings indicate that the location of the transition is governed primarily by the transformation parameter, whereas the effect of interhemispheric delay is comparatively small within the tested range.

3.6 Performance improves near and after the transition

We next examined how performance varies across the twist parameter (Figure 2). Mean objective values decreased from 10.634 at θ = 0.25 to 7.374 at θ = 0.45, reached their lowest values near the transition region (7.193 at θ = 0.50, 6.276 at θ = 0.55, and 6.246 at θ = 0.60), and then increased gradually at larger twist values.

These results show that the shift toward contralateral dominance in the model is associated with improved objective values, with the lowest values observed in the transition and immediate post-transition regime.

3.7 Summary of results

Taken together, the results show a consistent pattern across analyses. In one-dimensional systems, contralateral architectures are dynamically viable but do not dominate and are sensitive to the structure of the objective function. In two-dimensional systems without geometric transformation, the optimal architecture is overwhelmingly ipsilateral, whereas under full inversion contralateral architectures dominate completely. Between these regimes, the system exhibits a sharp reorganization of the optimal architecture over a narrow range of the twist parameter (Figure 2), with a transition point located near θ_c ≈ 0.483. This transition is robust under bootstrap resampling (Figures 4, 5), weakly dependent on interhemispheric delay (Figure 3), and associated with lower objective values near and just above the transition region (Figure 6).

FIGURE 6

3.8 Mechanistic basis of the twist-dependent transition

To directly test the mechanism underlying the reorganization of architecture, we quantified temporal mismatch and alignment between required motor correction and produced motor output across the twist parameter (Figures 7, 8).

FIGURE 7

FIGURE 8

Temporal mismatch showed a clear divergence between ipsilateral and contralateral architectures (Figure 7). At θ = 0.25, temporal mismatch was 2.1190 for the ipsilateral architecture and 77.9474 for the contralateral architecture. Near the transition region (θ = 0.50), the difference between architectures was minimal, with an ipsilateral-minus-contralateral difference of 0.0049. At higher twist values, temporal mismatch increased sharply for the ipsilateral architecture, while remaining low for the contralateral architecture.

A complementary pattern was observed in alignment (Figure 8). At θ = 0.85, sign alignment was 0.0005 in the ipsilateral architecture and 0.5487 in the contralateral architecture. Consistent with this, total tracking error strongly favored the contralateral architecture at high twist, with an ipsilateral-minus-contralateral difference of 8669.0757.

These results show that the shift in optimal architecture is associated with a reversal in temporal alignment. Under low twist, ipsilateral routing minimizes mismatch, whereas under high twist, contralateral routing provides superior alignment. Because the system includes interhemispheric competition, these differences are amplified into a rapid shift in the optimal architecture.

3.9 Sensitivity to objective weighting

To assess the dependence of the results on the specific weighting of the objective function, we performed a one-factor-at-a-time sensitivity analysis in which each objective weight was scaled to 0.5×, 1.0×, and 1.5× while the remaining weights were held fixed.

Across these perturbations, the qualitative structure of the results was preserved. In particular, the system consistently exhibited a transition from ipsilateral-dominated solutions at low twist to contralateral-dominated solutions at high twist.

The estimated transition point varied only modestly, ranging from theta_c = 0.4839 to 0.5023 across all tested weighting conditions. Contralateral dominance in the high-twist regime was also maintained, with the mean contralateral frequency for theta ≥ 0.70 ranging from 0.944 to 1.000 and the value at theta = 0.85 ranging from 0.963 to 1.000.

Sensitivity was greatest for the tracking term, particularly when its weight was reduced to 0.5×, but even in this condition the high-twist regime remained predominantly contralateral.

These results indicate that the existence of the ipsilateral-to-contralateral reorganization does not depend on a single specific choice of objective weights.

4 Discussion

The present study shows that contralateral routing can become functionally favored through the interaction between coordinate transformation, delayed signal propagation, and bilateral competition in a minimal sensorimotor system. The central result is not simply that contralateral architectures can outperform ipsilateral ones, but that the optimal architecture reorganizes sharply as a function of the transformation parameter. Within the present abstract control framework, this reorganization was robust across the tested parameter variations and was associated with lower objective values near and just above the transition region.

A central contribution of this work is the identification of a mechanistic basis for this reorganization. The additional analyses of temporal mismatch and sign alignment showed that the transition was associated with a reversal in temporal alignment between required motor corrections and produced motor outputs. Under low transformation, ipsilateral architectures minimized temporal mismatch and produced better-aligned control signals. As the degree of transformation increased, delayed processing in the ipsilateral pathway led to increasing misalignment. In contrast, contralateral routing maintained better alignment under these conditions, resulting in lower temporal mismatch and improved control performance. These findings indicate that the shift toward contralateral routing in the model is associated with improved temporal coordination in a delayed control system.

Importantly, this mechanism differs from explanations based solely on wiring economy or delay minimization. While wiring optimization has been proposed as an important organizing principle in neural systems (Cherniak, 1994; Bullmore and Sporns, 2012), the present results show that the transition was only weakly dependent on interhemispheric delay within the tested range. Instead, the dominant factor in the present framework was the interaction between coordinate transformation and temporal alignment. This suggests that routing preference cannot be understood fully in terms of connection length or transmission delay alone, but must also consider how signals are aligned with task-relevant coordinate frames.

This point allows the present results to be related more directly to classical neurobiological accounts of contralaterality. In visual systems, contralateral projections have long been discussed in relation to the preservation of orderly spatial relations under inversion of the sensory image, that is, in terms of maintaining coherent mappings of external space across sensory processing stages (Cajal, 1995; Jeffery, 2001; Kaas, 1997). The present model does not reproduce retinotopic anatomy or optical inversion directly. However, it is consistent with the more general idea that when sensory and motor coordinate systems are sufficiently inverted or mismatched, routing architecture becomes functionally consequential. Under this interpretation, the transformation parameter should be understood not as a literal anatomical or embryological twist, but as an abstract measure of the degree of transformation between sensory and motor coordinate systems. This interpretation is more consistent with the scope of the present model and avoids treating the parameter as a direct representation of a specific developmental event.

This interpretation also helps resolve the apparent tension between contralateral organization in some modalities and more ipsilateral organization in others. Contralateral organization is not uniform across sensory systems, and the present framework does not imply that all modalities should converge on contralateral routing. Rather, it predicts that contralateral routing becomes favored when the effective mapping between sensory and motor coordinates contains a strong topological inversion or mismatch. Systems such as vision, in which orderly spatial relations must be preserved across transformed coordinate frames (Cajal, 1995; Kaas, 1997), may therefore correspond to higher values of the transformation parameter. By contrast, systems such as olfaction, which are less strongly organized by a continuous topographic mapping of external space and are more ipsilateral in their primary projections, may correspond to lower-transformation regimes in which ipsilateral routing remains sufficient (Shepherd, 2004). In this sense, the present results do not propose a modality-independent rule that all neural systems should become contralateral, but rather a conditional dynamical principle whose relevance depends on the structure of the underlying coordinate transformation.

Another important aspect of the present findings is that the reorganization of architecture was not gradual. The system did not smoothly interpolate between ipsilateral and contralateral strategies. Instead, the optimal architecture shifted over a relatively narrow range of the transformation parameter. This behavior reflects the nonlinear interaction between delayed feedback and competitive selection. Near the transition region, relatively small differences in temporal alignment produced large differences in objective value, which were then amplified by interhemispheric competition. As a result, the system selected one dominant routing architecture rather than maintaining an even mixture of the two.

From a computational perspective, this work contributes to the broader question of how network architecture can be shaped by dynamical constraints. Previous studies have shown that delays, noise, and recurrent interactions can shape neural dynamics and functional organization (Deco et al., 2011; Breakspear, 2017). The present results extend this perspective by showing that transformations in effective sensorimotor mapping can reorganize the landscape of preferred bilateral architectures. In this sense, the study does not provide a direct anatomical account of vertebrate wiring. Rather, it identifies a minimal dynamical principle by which routing preference can shift when transformation, delay, and bilateral competition are jointly present.

An additional issue concerns the dependence of the results on the specific weighting of the objective function. Because the objective combines multiple cost components, one possible concern is that the observed transition might reflect a particular weighting choice rather than a more general property of the system. To address this, we performed a one-factor-at-a-time sensitivity analysis in which each objective weight was scaled to 0.5×, 1.0×, and 1.5× while the remaining weights were held fixed. Across these perturbations, the qualitative structure of the results was preserved. The estimated transition point varied only modestly, and contralateral dominance in the high-transformation regime was maintained across tested weighting conditions. Sensitivity was greatest for the tracking term, but even in this case the high-transformation regime remained predominantly contralateral. These results indicate that the existence of the ipsilateral-to-contralateral reorganization does not depend on a single specific choice of objective weights.

Several limitations should be noted. First, the model is intentionally minimal, and the left and right pathways are abstract processing channels rather than anatomically embedded hemispheres with explicit spatial positions, cell types, or developmental identities. Second, the architecture space is discrete and simplified, and does not capture the full diversity of biological neural networks or the partial decussation often observed in real systems (Jeffery, 2001). Third, motor output was fixed in the present framework in order to isolate the effect of sensory laterality and interhemispheric coupling, and the model therefore does not capture the full range of biological sensorimotor crossing patterns. Fourth, although the qualitative results were preserved under moderate perturbations of objective weighting, the precise location of the transition point still depends to some extent on how performance is operationalized. Fifth, the study is theoretical and does not incorporate empirical neural or developmental data directly. These limitations constrain the strength of biological claims that can be made from the present framework.

These limitations suggest several directions for future work. One important extension is to embed sensory, integrative, and motor elements within an explicit shared spatial framework, for example by assigning positions, distances, and connectivity constraints in two- or three-dimensional space. Such an extension would allow laterality to be evaluated under physically instantiated geometry rather than abstract channel assignment alone. It would also be valuable to test whether the same mechanism is preserved in more realistic recurrent or heterogeneous network architectures, and to examine how routing preference depends on modality-specific task structure. In addition, future work could relate the present framework more directly to empirical systems by asking whether modalities with stronger effective coordinate inversion exhibit stronger tendencies toward contralateral routing. Finally, analytical treatment may help clarify why the transition occurs near a specific value of the transformation parameter and how that threshold depends on the balance between alignment, delay, and competitive interactions.

In summary, the present study identifies a minimal dynamical mechanism by which contralateral routing can become functionally favored in delayed bilateral control systems when sensory and motor coordinate systems are sufficiently transformed. By showing that contralateral architectures can improve temporal alignment under high transformation and that this advantage is amplified through bilateral competition, the results provide an abstract theoretical link between classical geometric accounts of contralaterality and systems-level dynamical considerations.

References

• 1

  BreakspearM. (2017). Dynamic models of large-scale brain activity.Nat. Neurosci.20340–352. 10.1038/nn.4497

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 2

  BullmoreE.SpornsO. (2012). The economy of brain network organization.Nat. Rev. Neurosci.13336–349. 10.1038/nrn3214

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 3

  CajalS. R. (1995). Histology of the Nervous System of Man and Vertebrates.Oxford: Oxford University Press. (Original work published 1899: Textura del sistema nervioso del hombre y de los vertebrados).

  • Google Scholar

• 4

  ChédotalA. (2019). Roles of axon guidance molecules in neuronal wiring in the developing spinal cord.Nat. Rev. Neurosci.20380–396. 10.1038/s41583-019-0168-7

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 5

  CherniakC. (1994). Component placement optimization in the brain.J. Neurosci.142418–2427. 10.1523/JNEUROSCI.14-04-02418.1994

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 6

  de LussanetM. H. E.OsseJ. W. M. (2012). An ancestral axial twist explains the contralateral forebrain and the optic chiasm in vertebrates.Anim. Biol.62193–216. 10.1163/157075611X617102

  • CrossRef
  • Google Scholar

• 7

  DecoG.JirsaV. K.McIntoshA. R. (2011). Emerging concepts for the dynamical organization of resting-state activity in the brain.Nat. Rev. Neurosci.1243–56. 10.1038/nrn2961

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 8

  GazzanigaM. S. (2000). Cerebral specialization and interhemispheric communication: Does the corpus callosum enable the human condition?Brain123(Pt 7), 1293–1326. 10.1093/brain/123.7.1293

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 9

  HerreraE.García-FrigolaC. (2008). Genetics and development of the optic chiasm.Front. Biosci.131646–1653. 10.2741/2788

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 10

  JefferyG. (2001). Architecture of the optic chiasm and the mechanisms that sculpt its development.Physiol. Rev.811393–1414. 10.1152/physrev.2001.81.4.1393

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 11

  KaasJ. H. (1997). Topographic maps are fundamental to sensory processing.Brain Res. Bull.44107–112. 10.1016/S0361-9230(97)00094-4

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 12

  KiehnO. (2016). Decoding the organization of spinal circuits that control locomotion.Nat. Rev. Neurosci.17224–238. 10.1038/nrn.2016.9

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 13

  MaxwellD. J.SoteropoulosD. S.BakerS. N. (2020). The mammalian spinal commissural system: Properties and functions.J. Neurophysiol.12345–59. 10.1152/jn.00347.2019

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 14

  RolandJ. L.SnyderA. Z.HackerC. D.MitraA.ShimonyJ. S.LimbrickD. D.et al. (2017). On the role of the corpus callosum in interhemispheric functional connectivity in humans.Proc. Natl. Acad. Sci. U. S. A.11413278–13283. 10.1073/pnas.1707050114

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 15

  ShepherdG. M. (2004). The human sense of smell: Are we better than we think?PLoS Biol.2:E146. 10.1371/journal.pbio.0020146

  • Pubmed Abstract
  • CrossRef
  • Google Scholar